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▶$69.95 algebraic topology, both of which provide applications of the main results. More on www.springer.com/978-3-642-19579-2 S. Abbott, Middlebury College, Middlebury, VT, USA Usually dispatched within 3 to 5 business days 2011. VIII, 122 p. 15 illus., 9 in color. (École d'Été de Understanding Analysis Probabilités de Saint-Flour, Vol. 2019) Softcover This book outlines an elementary, one-semester 978-3-642-19579-2 course which exposes students to both the process of ▶$49.95 rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to M. Abate, Università di Pisa, Italia; F. Tovena, Università Tor challenge and improve mathematical intuition rather Vergata, Roma, Italia than to verify it. The philosophy of this book is to focus attention on questions which give analysis its Curves and Surfaces inherent fascination. The book provides an introduction to Differential More on www.springer.com/978-0-387-95060-0 Geometry of Curves and Surfaces. The theory of Usually dispatched within 3 to 5 business days curves starts with a discussion of possible definitions of the concept of curve, proving in particular the 2001. XII, 257 p. 32 illus. (Undergraduate Texts in classification of 1-dimensional manifolds. We then Mathematics) Hardcover present the classical local theory of parametrized 978-0-387-95060-0 plane and space curves (curves in n-dimensional ▶$54.95 space are discussed in the complementary material): R.P. Agarwal, Florida Institute of Technology, Melbourne, FL, curvature, torsion, Frenet’s formulas and the USA; K. Perera, Florida Institute of Technology, Melbourne, fundamental theorem of the local theory of FL, USA; S. Pinelas, Universidade dos Açores, Ponta Delgada, Portugal curves. Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane An Introduction to Complex curves, introducing winding and rotation numbers, Analysis and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation This textbook introduces the subject of complex number of closed simple curves. The local theory of analysis to advanced undergraduate and graduate surfaces begins with a comparison of the concept students in a clear and concise manner. Key features of parametrized (i.e., immersed) surface with the of this textbook:-Effectively organizes the subject concept of regular (i.e., embedded) surface. We then into easily manageable sections in the form of 50 develop the basic differential geometry of surfaces class-tested lectures- Uses detailed examples to drive in R3: definitions, examples, differentiable maps the presentation -Includes numerous exercise sets R.J. Adler, Technion - Israel Institute of Technology, Haifa, and functions, tangent vectors (presented both that encourage pursuing extensions of the material, Israel; J.E. Taylor, Stanford University, Stanford, USA as vectors tangent to curves in the surface and as each with an “Answers or Hints” section -covers an derivations on germs of differentiable functions; we Topological Complexity of array of advanced topics which allow for flexibility in shall consistently use both approaches in the whole developing the subject beyond the basics -Provides a book) and orientation. Next we study the several Smooth Random Functions concise history of complex numbers An Introduction to Complex Analysis will be valuable to students in notions of curvature on a surface, stressing both the École d'Été de Probabilités de Saint-Flour mathematics, engineering and other applied sciences. geometrical meaning of the objects introduced and XXXIX-2009 the algebraic/analytical methods needed to study Prerequisites include a course in calculus. them via the Gauss map, up to the proof of Gauss’ These notes, based on lectures delivered in Saint More on www.springer.com/978-1-4614-0194-0 Flour, provide an easy introduction to the authors’ Teorema Egregium. Then we introduce vector fields Usually dispatched within 3 to 5 business days on a surface (flow, first integrals, integral curves) 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full and geodesics (definition, basic properties, geodesic 2011. XIV, 331 p. 94 illus. Hardcover curvature, and, in the complementary material, a monograph, they are also less exhausting, while 978-1-4614-0194-0 still covering the basic material, typically at a more full proof of minimizing properties of geodesics ▶$74.95 and of the Hopf-Rinow theorem for surfaces). intuitive and less technical level. They also cover Then we shall present a proof of the celebrated some more recent material relating to random Gauss-Bonnet theorem, both in its local and in its algebraic topology and statistical applications. The global form, using basic properties (fully proved notes include an introduction to the general theory in the complementary material) of triangulations of Gaussian random fields, treating classical topics of surfaces. As an application, we shall prove the such as continuity and boundedness. This is followed Poincaré-Hopf theorem on zeroes of vector fields. by a quick review of geometry, both integral and Finally, the last chapter will be devoted to several Riemannian, with an emphasis on tube formulae, important results on the global theory of surfaces, to provide the reader with the material needed to like for instance the characterization of surfaces with understand and use the Gaussian kinematic formula, constant Gaussian curvature, and the orientability of the main result of the notes. This is followed by compact surfaces in R3. chapters on topological inference and random More on www.springer.com/978-88-470-1940-9 Due: November 25, 2011

2012. XIII, 393 p. 65 illus. (La Matematica per il 3+2) Softcover 978-88-470-1940-9 springer.com 3

Ziegler... write: "... all we offer is the examples that J. Akiyama, Tokai University, Shibuya-ku, Japan; M. Kano, we have selected, hoping that our readers will share Ibaraki University, Hitachi, Japan our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the Factors and Factorizations of AMS, August 1999 "... This book is a pleasure to hold Graphs and to look at: ample margins, nice photos, instructive pictures, and beautiful drawings ... It is a pleasure to Proof Techniques in Factor Theory read as well: the style is clear and entertaining, the This book chronicles the development of graph level is close to elementary, the necessary background factors and factorizations. It pursues a comprehensive is given separately, and the proofs are brilliant. approach, addressing most of the important results Moreover, the exposition makes them transparent. ..." from hundreds of findings over the last century. One LMS Newsletter, January 1999 of the main themes is the observation that many M. Aigner, Freie Universität Berlin, Germany More on www.springer.com/978-3-642-00855-9 theorems can be proved using only a few standard proof techniques. This stands in marked contrast to Title available online only, not as print version. A Course in Enumeration the seemingly countless, complex proof techniques offered by the extant body of papers and books. In Combinatorial enumeration is a readily accessible 2010. VIII, 274 p. 250 illus., 6 in color. Hardcover subject full of easily stated, but sometimes 978-3-642-00855-9 addition to covering the history and development of this area, the book offers conjectures and discusses tantalizingly difficult problems. This book leads ▶$49.95 the reader in a leisurely way from the basic notions open problems. It also includes numerous explanatory of combinatorial enumeration to a variety of figures that enable readers to progressively and topics, ranging from algebra to statistical physics. intuitively understand the most important notions The aim of the author is to introduce readers to a and proofs in the area of factors and factorization. fascinating field, and to offer a sophisticated source of More on www.springer.com/978-3-642-21918-4 information for the professional mathematician who Usually dispatched within 3 to 5 business days wants to learn more about the subject. The book is 2011. XII, 353 p. 153 illus. (Lecture Notes in Mathematics, organized in three parts: Basics, Methods, and Topics. Vol. 2031) Softcover There are 666 exercises, and as a special feature every 978-3-642-21918-4 chapter ends with a highlight section, discussing in $89.95 detail a particularly beautiful or famous result. ▶ More on www.springer.com/978-3-540-39032-9 Online orders shipping within 2-3 days

2007. X, 565 p. 55 illus. (Graduate Texts in M. Akhmet, Middle East Technical University, Ankara, Turkey Mathematics, Vol. 238) Hardcover 978-3-540-39032-9 Nonlinear Hybrid Continuous/ ▶$89.95 Discrete-Time Models The book is mainly about hybrid systems with continuous/discrete-time dynamics. The major part of the book consists of the theory of equations with piece-wise constant argument of generalized type. The systems as well as technique of investigation were introduced by the author very recently. They both A.G. Aksoy, Claremont McKenna College, Claremont, CA, generalized known theory about differential equations USA; M.A. Khamsi, University of Texas at El Paso, El Paso, TX, with piece-wise constant argument, introduced USA by K. Cook and J. Wiener in the 1980s. Moreover, differential equations with fixed and variable A Problem Book in Real Analysis moments of impulses are used to model real world problems. We consider models of neural networks, Today, nearly every undergraduate mathematics M. Aigner, Freie Universität Berlin, Germany; G.M. Ziegler, blood pressure distribution and a generalized model program requires at least one semester of real Technische Universität Berlin, Germany of the cardiac pacemaker. All the results of the analysis. Often, students consider this course to be manuscript have not been published in any book, yet. the most challenging or even intimidating of all their Proofs from THE BOOK They are very recent and united with the presence mathematics major requirements. The primary goal of the continuous/discrete dynamics of time. It is of A Problem Book in Real Analysis is to alleviate This revised and enlarged fourth edition of "Proofs of big interest for specialists in biology, medicine, those concerns by systematically solving the problems from THE BOOK" features five new chapters, which engineering sciences, electronics. Theoretical related to the core concepts of most analysis courses. treat classical results such as the "Fundamental aspects of the book meet very strong expectations of In doing so, the authors hope that learning analysis Theorem of Algebra", problems about tilings, but mathematicians who investigate differential equations becomes less taxing and more satisfying. The wide also quite recent proofs, for example of the Kneser with discontinuities of any type. variety of exercises presented in this book range conjecture in graph theory. The new edition also from the computational to the more conceptual presents further improvements and surprises, among More on www.springer.com/978-94-91216-02-2 and varies in difficulty. They cover the following them a new proof for "Hilbert's Third Problem". Usually dispatched within 3 to 5 business days subjects: set theory; real numbers; sequences; From the Reviews "... Inside PFTB (Proofs from 2011. XIII, 216 p. 23 illus., 19 in color. (Atlantis Studies in limits of the functions; continuity; differentiability; The Book) is indeed a glimpse of mathematical Mathematics for Engineering and Science, Vol. 8) Hardcover integration; series; metric spaces; sequences; and heaven, where clever insights and beautiful ideas 978-94-91216-02-2 series of functions and fundamentals of topology. combine in astonishing and glorious ways. There is ▶$99.00 Furthermore, the authors define the concepts and vast wealth within its pages, one gem after another. cite the theorems used at the beginning of each Some of the proofs are classics, but many are new chapter. A Problem Book in Real Analysis is not and brilliant proofs of classical results. ...Aigner and simply a collection of problems; it will stimulate 4 springer.com its readers to independent thinking in discovering (ANTC) at the university.A common theme in It is structured into different chapters, written by analysis. Prerequisites for the reader are a robust the book is the study of q-series, an area which in outstanding experts in the field. Many fundamental understanding of calculus and linear algebra. recent years has witnessed dramatic advances having issues are considered, such as: the mathematical More on www.springer.com/978-1-4419-1295-4 significant impact on a variety of fields within and representation of vascular geometries extracted from outside of mathematics such as physics. Most major medical images, modelling blood rheology and the Usually dispatched within 3 to 5 business days aspects of the modern theory of q-series and how complex multilayer structure of the vascular tissue, they relate to number theory, combinatorics, and and its possible pathologies, the mechanical and 2010. X, 254 p. 17 illus., 8 in color. (Problem Books in special functions are represented in this volume. chemical interaction between blood and vascular Mathematics) Hardcover Topics include the theory of partitions via computer walls, and the different scales coupling local and 978-1-4419-1295-4 algebra, elementary asymptotic methods; expositions systemic dynamics. All of these topics introduce $59.95 ▶ on Ramanujan's mock theta-functions emphasizing challenging mathematical and numerical problems, the classical aspects as well as the recent exciting demanding for advanced analysis and efficient connections with the theory of harmonic Maass simulation techniques, and pay constant attention to S. Albeverio, University of Bonn, Germany; R. Fan, Texas forms; congruences for modular forms; a study of applications of relevant clinical interest. This book A&M University, College Station, TX, USA; F. Herzberg, theta-functions from elementary, function-theoretic is addressed to graduate students and researchers Bielefeld University, Germany and Riemann surface viewpoints; and a systematic in the field of bioengineering, applied mathematics analysis of multiple basic hypergeometric functions and medicine, wishing to engage themselves in the Hyperfinite Dirichlet Forms and associated with root systems of Lie algebras. The fascinating task of modeling the cardiovascular Stochastic Processes broad range of topics covered in this volume will be system or, more broadly, physiological flows. of interest to both researchers and graduate students More on www.springer.com/978-88-470-1934-8 This monograph treats the theory of Dirichlet who want to learn of recent developments in the forms from a comprehensive point of view, using theory of partitions, q-series and modular forms Due: September 29, 2011 "nonstandard analysis." Thus, it is close in spirit to and their far reaching impact on diverse areas of 2012. X, 240 p. 151 illus., 1 in color. (MS&A, Vol. 5) Hardcover the discrete classical formulation of Dirichlet space mathematics. 978-88-470-1934-8 theory by Beurling and Deny (1958). The discrete $109.00 More on www.springer.com/978-1-4614-0027-1 ▶ infinitesimal setup makes it possible to study the diffusion and the jump part using essentially the same Usually dispatched within 3 to 5 business days methods. This setting has the advantage of being 2012. XII, 224 p. (Developments in Mathematics, Vol. 23) independent of special topological properties of the Hardcover state space and in this sense is a natural one, valid 978-1-4614-0027-1 for both finite- and infinite-dimensional spaces. The ▶$124.00 present monograph provides a thorough treatment of the symmetric as well as the non-symmetric case, surveys the theory of hyperfinite Lévy processes, Forthcoming and summarizes in an epilogue the model-theoretic genericity of hyperfinite stochastic processes theory. L. Almasy, Southwest Foundation for Biomedical Research, San Antonio, TX, USA (Ed.) More on www.springer.com/978-3-642-19658-4 Usually dispatched within 3 to 5 business days Statistical Genetics 2011. XIV, 284 p. 1 illus. in color. (Lecture Notes of the Unione Matematica Italiana, Vol. 10) Softcover More on www.springer.com/978-1-58829-728-0 L. Ambrosio, Scuola Normale Superiore, Pisa, Italy; G. Da 978-3-642-19658-4 Due: January 31, 2012 Prato, Scuola Normale Superiore, Pisa, Italy; A. Mennucci, $59.95 Scuola Normale Superiore, Pisa, Italy ▶ 2012. (Methods in Molecular Biology, Tentative volume 2145) Hardcover 978-1-58829-728-0 Introduction to Measure Theory ▶approx. $99.50 and Integration This textbook collects the notes for an introductory course in measure theory and integration. The course was taught by the authors to undergraduate students of the Scuola Normale Superiore, in the years 2000-2011. The goal of the course was to present, in a quick but rigorous way, the modern point of view on measure theory and integration, putting Lebesgue's Euclidean space theory into a more general context and presenting the basic applications to Fourier series, calculus and real analysis. The text can also pave K. Alladi, University of Florida, Gainesville, FL, USA; F. Garvan, the way to more advanced courses in probability, University of Florida, Gainesville, FL, USA (Eds.) stochastic processes or geometric measure theory. Prerequisites for the book are a basic knowledge of Partitions, q-Series, and Modular calculus in one and several variables, metric spaces D. Ambrosi, Politecnico di Milano, Italy; A. Quarteroni, Ecole and linear algebra. All results presented here, as well Forms Polytechnique Federale De Lausanne, Switzerland; G. Rozza, as their proofs, are classical. The authors claim some This book contains a unique collection of Ecole Polytechnique Federale de Lausanne, Switzerland originality only in the presentation and in the choice both research and survey papers written by an (Eds.) international group of some of the world's experts on partitions, q-series, and modular forms, as outgrowths Modeling of Physiological Flows of a conference held at the University of Florida, This book offers a mathematical update of the state Gainesville in March 2008. The success of this of the art of the research in the field of mathematical conference has led to annual year-long programs and numerical models of the circulatory system. in Algebra, Number Theory, and Combinatorics springer.com 5 of the exercises. Detailed solutions to the exercises are provided in the final part of the book. More on www.springer.com/978-88-7642-385-7 Online orders shipping within 2-3 days

2011. 198 p. (Lecture Notes (Scuola Normale Superiore), Vol. 10) Softcover 978-88-7642-385-7 ▶$29.95

H. Ammari, École Normale Supérieure, Paris, France (Ed.) G.A. Anastassiou, The University of Memphis, TN, USA Mathematical Modeling in Inequalities Based on Sobolev Biomedical Imaging II Representations Optical, Ultrasound, and Opto-Acoustic Inequalities based on Sobolev Representations deals Tomographies exclusively with very general tight integral inequalities This volume reports on recent mathematical and of Chebyshev-Grüss, Ostrowski types and of integral computational advances in optical, ultrasound, means, all of which depend upon the Sobolev integral and opto-acoustic tomographies. It outlines the representations of functions. Applications illustrate state-of-the-art and future directions in these inequalities that engage in ordinary and weak partial fields and provides readers with the most recently derivatives of the involved functions. This book G. Amendola, University of Pisa, Italy; M. Fabrizio, developed mathematical and computational tools. It also derives important estimates for the averaged University of Bologna, Italy; J.M. Golden, Dublin Institute of Taylor polynomials and remainders of Sobolev Technology, Ireland is particularly suitable for researchers and graduate students in applied mathematics and biomedical integral representations. The results are examined engineering. in all directions and through both univariate Thermodynamics of Materials and multivariate cases. This book is suitable for More on www.springer.com/978-3-642-22989-3 with Memory researchers, graduate students, and seminars in Usually dispatched within 3 to 5 business days Theory and Applications subareas of mathematical analysis, inequalities, partial 2012. IX, 160 p. 43 illus., 38 in color. (Mathematical differential equations and information theory. This is a work in four parts, dealing with the Biosciences Subseries, Vol. 2035) Softcover More on www.springer.com/978-1-4614-0200-8 mechanics and thermodynamics of materials with 978-3-642-22989-3 memory, including properties of the dynamical ▶$49.95 Usually dispatched within 3 to 5 business days equations which describe their evolution in time 2011. IX, 65 p. (SpringerBriefs in Mathematics) Softcover under varying loads. The first part is an introduction 978-1-4614-0200-8 to Continuum Mechanics with sections dealing $49.95 V. Anandam, University of Madras, Chennai, India ▶ with classical Fluid Mechanics and Elasticity, linear and non-linear. The second part is devoted to Continuum Thermodynamics, which is used to derive Harmonic Functions and constitutive equations of materials with memory, Potentials on Finite or Infinite including viscoelastic solids, fluids, heat conductors and some examples of non-simple materials. In Networks part three, free energies for materials with linear Random walks, Markov chains and electrical memory constitutive relations are comprehensively networks serve as an introduction to the study of real- explored. The new concept of a minimal state is valued functions on finite or infinite graphs, with also introduced. Formulae derived over the last appropriate interpretations using probability theory decade for the minimum and related free energies are and current-voltage laws. The relation between this discussed in depth. Also, a new single integral free type of function theory and the (Newton) potential energy which is a functional of the minimal state is theory on the Euclidean spaces is well-established. analyzed in detail. Finally, free energies for examples The latter theory has been variously generalized, of non-simple materials are considered. In the final one example being the axiomatic potential theory G.A. Anastassiou, The University of Memphis, TN, USA part, existence, uniqueness and stability results on locally compact spaces developed by Brelot, with are presented for the integrodifferential equations later ramifications from Bauer, Constantinescu and Approximation by Multivariate describing the dynamical evolution of viscoelastic Cornea. A network is a graph with edge-weights materials. A new approach to these topics, based that need not be symmetric. This book presents Singular Integrals on the use of minimal states rather than histories, an autonomous theory of harmonic functions and Approximation by Multivariate Singular Integrals is is discussed in detail. There are also chapters on the potentials defined on a finite or infinite network, on the first monograph to illustrate the approximation controllability of thermoelastic systems with memory, the lines of axiomatic potential theory. Random walks of multivariate singular integrals to the identity-unit the Saint-Venant problem for viscoelastic materials and electrical networks are important sources for the operator. The basic approximation properties of the and on the theory of inverse problems. advancement of the theory. general multivariate singular integral operators is More on www.springer.com/978-1-4614-1691-3 More on www.springer.com/978-3-642-21398-4 presented quantitatively, particularly special cases Usually dispatched within 3 to 5 business days Usually dispatched within 3 to 5 business days such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral 2012. XV, 574 p. 4 illus. Hardcover 2011. X, 141 p. (Lecture Notes of the Unione Matematica operators are examined thoroughly. This book studies 978-1-4614-1691-3 Italiana, Vol. 12) Softcover the rate of convergence of these operators to the ▶$124.00 978-3-642-21398-4 unit operator as well as the related simultaneous $49.95 ▶ approximation. The last chapter, which includes many examples, presents a related Korovkin type 6 springer.com approximation theorem for functions of two variables. fields of research in science and engineering use and Statistics, Eastern Kentucky University, Richmond, KY, Relevant background information and motivation fractional calculus in order to describe results.This USA; G. Chen, Department of Mathematics, Southwest is included in this exposition, and as a result this book is a part of Fractional Calculus, therefore it University, Chongqing, P.R China; E. Cohen, Department book can be used as supplementary text for several is useful for researchers and graduate students for of Mathematics, Bar Ilan University, Ramat Gan, Israel; A. advanced courses. The results presented apply research, seminars and advanced graduate courses, Haj Ihia Hussam, Department of Mathematics, Alqasemi to many areas of pure and applied mathematics, in pure and applied mathematics, engineering and all Academic College of Education, Baqa El-Gharbieh, Israel; M. Muzychuk, Netanya Academic College, Kiryat Rabin, such a mathematical analysis, probability, statistics other applied sciences. Netanya, Israel and partial differential equations. This book is More on www.springer.com/978-1-4614-0702-7 appropriate for researchers and selected seminars at Usually dispatched within 3 to 5 business days On Normalized Integral Table the graduate level. 2011. X, 122 p. (SpringerBriefs in Mathematics) Softcover Algebras (Fusion Rings) More on www.springer.com/978-1-4614-0588-7 978-1-4614-0702-7 Usually dispatched within 3 to 5 business days Generated by a Faithful Non-real Element of ▶$49.95 Degree 3 2011. X, 79 p. (SpringerBriefs in Mathematics) Softcover 978-1-4614-0588-7 The theory of table algebras was introduced in ▶$49.95 1991 by Z. Arad and H.Blau in order to treat, in a uniform way, products of conjugacy classes and irreducible characters of finite groups. Today, table algebra theory is a well-established branch of modern algebra with various applications, including the representation theory of finite groups, algebraic combinatorics and fusion rules algebras. This book presents the latest developments in this area. Its main goal is to give a classification of the Normalized Integral Table Algebras (Fusion Rings) generated by a faithful non-real element of degree 3. Divided into 4 parts, the first gives an outline of the classification K. Aomoto, M. Kita approach, while remaining parts separately treat special cases that appear during classification. A Theory of Hypergeometric particularly unique contribution to the field, can G.A. Anastassiou, University of Memphis, TN, USA Functions be found in part four, whereby a number of the algebras are linked to the polynomial irreducible Advances on Fractional This book presents a geometric theory of complex representations of the group SL3(C).This book analytic integrals representing hypergeometric will be of interest to research mathematicians and Inequalities functions of several variables. Starting from PhD students working in table algebras, group an integrand which is a product of powers of representation theory, algebraic combinatorics and Advances on Fractional Inequalities use primarily the polynomials, integrals are explained, in an open affine integral fusion rule algebras. Caputo fractional derivative, as the most important space, as a pair of twisted de Rham cohomology and in applications, and presents the first fractional More on www.springer.com/978-0-85729-849-2 its dual over the coefficients of local system. It is differentiation inequalities of Opial type which shown that hypergeometric integrals generally satisfy Usually dispatched within 3 to 5 business days involves the balanced fractional derivatives. The a holonomic system of linear differential equations 2011. X, 274 p. 1 illus. (Algebra and Applications, Vol. 16) book continues with right and mixed fractional with respect to the coefficients of polynomials and Hardcover differentiation Ostrowski inequalities in the also satisfy a holonomic system of linear difference 978-0-85729-849-2 univariate and multivariate cases. Next the right and equations with respect to the exponents. These are ▶$99.00 left, as well as mixed, Landau fractional differentiation deduced from Grothendieck-Deligne’s rational inequalities in the univariate and multivariate de Rham cohomology on the one hand, and by cases are illustrated. Throughout the book many multidimensional extension of Birkhoff’s classical applications are given. Fractional differentiation Forthcoming theory on analytic difference equations on the other. inequalities are by themselves an important and D. Arapura, Purdue University, West Lafayette, IN, USA great mathematical topic for research. Furthermore More on www.springer.com/978-4-431-53912-4 they have many applications, the most important Usually dispatched within 3 to 5 business days Algebraic Geometry over the ones are in establishing uniqueness of solution in 2011. XVI, 317 p. 29 illus. (Springer Monographs in fractional differential equations and systems and Mathematics) Hardcover Complex Numbers in fractional partial differential equations. Also 978-4-431-53912-4 This textbook is a strong addition to existing they provide upper bounds to the solutions of the ▶$124.00 introductory literature on algebraic geometry. The above equations.Fractional Calculus has emerged as author’s treatment combines the study of algebraic very useful over the last forty years due to its many geometry with differential and complex geometry applications in almost all applied sciences. This and unifies these subjects using sheaf-theoretic is currently seen in applications in acoustic wave ideas. It is also an ideal text for showing students the propagation in inhomogeneous porous material, connections between algebraic geometry, complex diffusive transport, fluid flow, dynamical processes geometry, and topology, and brings the reader close to in self-similar structures, dynamics of earthquakes, the forefront of research in Hodge theory and related optics, geology, viscoelastic materials, bio-sciences, fields. Unique features of this textbook: - Contains a bioengineering, medicine, economics, probability rapid introduction to complex algebraic geometry - and statistics, astrophysics, chemical engineering, Includes background material on topology, manifold physics, splines, tomography, fluid mechanics, theory and sheaf theory - Analytic and algebraic electromagnetic waves, nonlinear control, signal approaches are developed somewhat in parallel The processing, control of power electronic, converters, presentation is easy going, elementary, and well chaotic dynamics, polymer science, proteins, polymer illustrated with examples. “Algebraic Geometry over physics, electrochemistry, statistical physics, rheology, Z. Arad, Department of Mathematics, Bar Ilan University, the Complex Numbers” is intended for graduate level thermodynamics, neural networks, etc. Almost all Ramat Gan, Israel; X. Bangteng, Department of Mathematics courses in algebraic geometry and related fields. It can springer.com 7 be used as a main text for a second semester graduate crystallography, physics and chemistry soap films course in algebraic geometry with emphasis on sheaf are used as separating surfaces between grids of theoretical methods or a more advanced graduate atoms. The video is completely computer generated. course on algebraic geometry and Hodge Theory. It explains the world of soap films and their properties More on www.springer.com/978-1-4614-1808-5 in an amusing story, in which a young boy named Kalle explores the palace of soap films. Under the Due: February 17, 2012 guidance of an old professor, Kalle gets fascinating insights and becomes a witness to never-before-seen 2012. XII, 330 p. 17 illus., 2 in color. (Universitext) shapes and animations of soap films. The video is Softcover designed to be understandable on two levels. On 978-1-4614-1808-5 the first level, it is intended for the general public, $74.95 ▶ and is understandable not only by students but also M. Arkowitz, Dartmouth College, Hanover, NH, USA by anyone interested in science. However, most of the geometric animations come from recent Introduction to Homotopy Theory mathematical research on minimal surfaces, some of which are new even for experts. Thus there is This is a book in pure mathematics dealing with a second level of understanding, accessible with a homotopy theory, one of the main branches of deeper knowledge of differential geometry as it is algebraic topology. The principal topics are as follows: taught at universities, making the video an ideal • Basic homotopy; • H-spaces and co-H-spaces; • complimentary source of information for people with Fibrations and cofibrations; • Exact sequences of such knowledge. By presenting scientific research in homotopy sets, actions, and coactions; • Homotopy the context of a video program the production team pushouts and pullbacks; • Classical theorems, disseminates interesting scientific material to a broad including those of Serre, Hurewicz, Blakers-Massey, audience. and Whitehead; • Homotopy sets; • Homotopy and homology decompositions of spaces and maps; and• More on www.springer.com/978-3-540-24041-9 E. Arbarello, Università di Roma "La Sapienza", Italy; M. Obstruction theory. The underlying theme of the Due: June 28, 2012 Cornalba, Università di Pavia, Italy; P.A. Griffiths, Institute for entire book is the Eckmann-Hilton duality theory. Advanced Studies, Princeton, NJ, USA This approach provides a unifying motif, clarifies 1999. 16 p. DVD. (Springer VideoMATH) many concepts, and reduces the amount of repetitious 978-3-540-24041-9 material. The subject matter is treated carefully with Geometry of Algebraic Curves ▶$49.95 Volume II with a contribution by Joseph Daniel attention to detail, motivation is given for many results, there are several illustrations, and there are Harris a large number of exercises of varying degrees of The second volume of the Geometry of Algebraic difficulty. It is assumed that the reader has had some Forthcoming Curves is devoted to the foundations of the exposure to the rudiments of homology theory and A. Arnez, Schönaich, Germany; K. Polthier, Technische theory of moduli of algebraic curves. Its authors fundamental group theory; these topics are discussed Universität Berlin, Germany; M. Steffens, Unterföhring, are research mathematicians who have actively in the appendices. The book can be used as a text for Germany; C. Teitzel, Unterföhring, Germany participated in the development of the Geometry the second semester of an algebraic topology course. of Algebraic Curves. The subject is an extremely The intended audience of this book is advanced Touching Soap Films fertile and active one, both within the mathematical undergraduate or graduate students. The book could community and at the interface with the theoretical also be used by anyone with a little background in "Touching Soap Films" is a scientific video about physics community. The approach is unique in its topology who wishes to learn some homotopy theory. the world of soap films designed for the general blending of algebro-geometric, complex analytic More on www.springer.com/978-1-4419-7328-3 public. Few other physical problems have influenced and topological/combinatorial methods. It treats as many branches of mathematics in the past 200 Usually dispatched within 3 to 5 business days important topics such as Teichmüller theory, years as have the study of soap films. A soap film the cellular decomposition of moduli and its is physically similar to a piece of rubber surface 2011. XIII, 344 p. 333 illus. (Universitext, 0) Softcover consequences and the Witten conjecture. The careful which tries to contract itself under surface tension 978-1-4419-7328-3 and comprehensive presentation of the material will to a surface with least area. Surfaces with least area $74.95 be of value to students who wish to learn the subject ▶ appear as optimal solutions of many problems. For and to experts as a reference source. The first volume example, since the 1960s, they have been used in appeared 1985 as volume 267 of the same series. architecture as models for light roof constructions More on www.springer.com/978-3-540-42688-2 Forthcoming such as the Olympic stadium in Munich. Also, in crystallography, physics and chemistry soap films A. Arnez, Schönaich, Germany; K. Polthier, Technische Online orders shipping within 2-3 days are used as separating surfaces between grids of Universität Berlin, Germany; M. Steffens, Unterföhring, atoms. 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A soap film the first level, it is intended for the general public, is physically similar to a piece of rubber surface and is understandable not only by students but also which tries to contract itself under surface tension by anyone interested in science. However, most to a surface with least area. Surfaces with least area of the geometric animations come from recent appear as optimal solutions of many problems. For mathematical research on minimal surfaces, some example, since the 1960s, they have been used in of which are new even for experts. Thus there is architecture as models for light roof constructions a second level of understanding, accessible with a such as the Olympic stadium in Munich. 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(Springer VideoMATH) 978-3-540-24093-8 Usually dispatched within 3 to 5 business days ▶$49.95 J.-P. Aubin, VIMADES, Paris, France; A.M. Bayen, University 2011. VIII, 332 p. (History of Mathematics Subseries, Vol. of California at Berkeley, Berkeley, CA, USA; P. Saint-Pierre, 2014) Softcover University of Paris Dauphine, Clamart, France 978-3-642-17853-5 $89.95 Viability Theory ▶ New Directions Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from biological evolution to economics, from environmental sciences to financial markets, from control theory and robotics to cognitive sciences. It involves interdisciplinary investigations spanning V.I. Arnold, Steklov Mathematical Institute, Moscow, Russia fields that have traditionally developed in isolation. The purpose of this book is to present an initiation Yesterday and Long Ago to applications of viability theory, explaining and M. Audin, Université de Strasbourg, France This is a charming collection of essays on life and motivating the main concepts and illustrating them science, by one of the leading mathematicians of with numerous numerical examples taken from Remembering Sofya our day. Vladimir Igorevich Arnold is renowned various fields. Kovalevskaya for his achievements in mathematics, and nearly More on www.springer.com/978-3-642-16683-9 as famous for his informal teaching style, and for Usually dispatched within 3 to 5 business days Sofia Kovalevskaya was a brilliant and determined the clarity and accessibility of his writing. The young Russian woman of the 19th century who 2011. XXI, 830 p. 141 illus., 20 in color. Hardcover chapter headings convey Arnold’s humor and restless wanted to become a mathematician and who 978-3-642-16683-9 imagination. A few examples: My first recollections; succeeded, in often difficult circumstances, in $279.00 The combinatorics of Plutarch; The topology of ▶ becoming arguably the first woman to have a surfaces according to Alexander of Macedon; professional university career in the way we Catching a pike in Cambridge. Yesterday and Long understand it today. This memoir, written by Ago offers a rare opportunity to appreciate the life a mathematician who specialises in symplectic and work of one of the world’s outstanding living geometry and integrable systems, is a personal mathematicians. exploration of the life, the writings and the mathematical achievements of a remarkable woman. More on www.springer.com/978-3-540-28734-6 It emphasises the originality of Kovalevskaya’s Online orders shipping within 2-3 days work and assesses her legacy and reputation as a 2007. XIV, 229 p. 43 illus. Hardcover mathematician and scientist. 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elimination methods and an in-depth presentation of the recent method CERES developed by the authors. It includes a detailed complexity analysis and comparison of CERES and of reductive methods. It presents several applications of CERES—to interpolation, fast cut-elimination, generalization of proofs and to the analysis of mathematical proofs. Finally, it provides an extension of CERES to non- classical logics, in particular to finitely-valued logics and to Gödel logic. S. Axler, San Francisco State University, CA, USA More on www.springer.com/978-94-007-0319-3 Linear Algebra Done Right Usually dispatched within 3 to 5 business days H. Bahouri, Université de Tunis, Manar, Tunisia; J.-Y. Chemin, Université Pierre et Marie Curie, Paris, France; R. Danchin, This text for a second course in linear algebra is aimed 2011. VI, 287 p. 360 illus. (Trends in Logic, Vol. 34) Hardcover 978-94-007-0319-3 Université Paris-Est, France at math majors and graduate students. The novel approach taken here banishes determinants to the ▶$139.00 Fourier Analysis and Nonlinear end of the book and focuses on the central goal of linear algebra: understanding the structure of linear Partial Differential Equations operators on vector spaces. The author has taken In recent years, the Fourier analysis methods have unusual care to motivate concepts and to simplify expereinced a growing interest in the study of partial proofs. For example, the book presents--without differential equations. In particular, those techniques having defined determinants--a clean proof that every based on the Littlewood-Paley decomposition have linear operator on a finite-dimensional complex proved to be very efficient for the study of evolution vector space (or an odd-dimensional real vector equations. The present book aims at presenting space) has an eigenvalue. A variety of interesting self-contained, state- of- the- art models of those exercises in each chapter helps students understand techniques with applications to different classes and manipulate the objects of linear algebra. No of partial differential equations: transport, heat, prerequisites are assumed other than the usual wave and Schrödinger equations. It also offers demand for suitable mathematical maturity. Thus, more sophisticated models originating from fluid the text starts by discussing vector spaces, linear mechanics (in particular the incompressible and independence, span, basis, and dimension. Students A. Badrikian, J. Hoffmann-Jørgensen, University of Aarhus, compressible Navier-Stokes equations) or general are introduced to inner-product spaces in the first Denmark; J. Kuelbs, University of Minnesota, Madison, relativity. It is either directed to anyone with a good half of the book and shortly thereafter to the finite- WI; USA; X. Fernique, Université Louis Pasteur et C.N.R.S., undergraduate level of knowledge in analysis or useful dimensional spectral theorem. This second edition Strasbourg, France for experts who are eager to know the benefit that one includes a new section on orthogonal projections and might gain from Fourier analysis when dealing with minimization problems. The sections on self-adjoint Probability in Banach Spaces at nonlinear partial differential equations. operators, normal operators, and the spectral theorem Saint-Flour have been rewritten. New examples and new exercises More on www.springer.com/978-3-642-16829-1 have been added, several proofs have been simplified, Founded in 1971, the Saint-Flour Probability Usually dispatched within 3 to 5 business days and hundreds of minor improvements have been Summer School is organised every year by the 2011. XVI, 522 p. (Grundlehren der mathematischen mathematics department of the Université Blaise made throughout the text. Wissenschaften, Vol. 343) Hardcover Pascal at Clermont-Ferrand, France, and held in the More on www.springer.com/978-0-387-98258-8 978-3-642-16829-1 pleasant surroundings of an 18th century seminary $129.00 Usually dispatched within 3 to 5 business days building in the city of Saint-Flour, located in the ▶ French Massif Central, at an altitude of 900 m.It 1997. XV, 251 p. (Undergraduate Texts in attracts a mixed audience of up to 70 PhD students, Mathematics) Softcover instructors and researchers interested in probability 978-0-387-98258-8 theory, statistics, and their applications, and lasts ▶$44.95 2 weeks. Each summer it provides, in three high- level courses presented by international specialists, a comprehensive study of some subfields in probability theory or statistics. The participants thus have the opportunity to interact with these specialists and also to present their own research work in short lectures.The lecture courses are written up by their authors for publication in the LNM series. More on www.springer.com/978-3-642-25276-1 Due: janvier 3, 2012 J. Bak, City College of New York, NY, USA; D.J. Newman 2012. 538 p. Avec Reprint of lectures originally published in the Lecture Notes in Mathematics volumes 539 (1976), Complex Analysis 480 (1975), 589 (1977) and 976 (1983).. (Probability at Saint- Flour, Vol.) Softcover This unusual and lively textbook offers a clear and 978-3-642-25276-1 intuitive approach to the classical and beautiful theory M. Baaz, Vienna University of Technology, Vienna, Austria; A. ▶$69.95 of complex variables. With very little dependence on Leitsch, Technische Universitaet Wien, Austria advanced concepts from several-variable calculus and topology, the text focuses on the authentic complex- Methods of Cut-Elimination variable ideas and techniques. Notable additions to "Complex Analysis, Third Edition," include: • The This book on methods of cut-elimination contains solution of the cubic equation and Newton’s method a thorough and rigorous analysis of reductive cut- for approximating the zeroes of any polynomial; 10 springer.com

• Expanded treatments of the Schwarz reflection Hella. The book includes 19 case studies that were on some of his major contributions by noteworthy principle and of the mapping properties of analytic conducted in real plants. They include chemical statisticians and mathematicians working today. functions on closed domains; • An introduction to plants, fossil power plants, wind power plants, nuclear More on www.springer.com/978-1-4614-1965-5 Schwarz-Christoffel transformations and to Dirichlet power plants, oil refineries, oil production plants, series; • A streamlined proof of the prime number injection molding fascilities and retail industry Usually dispatched within 3 to 5 business days December 31, 2011 theorem, and more. Accessible to students at their shops. All case studies were conducted by the author early stages of mathematical study, this full first year in cooperation and co-authorship with some of 2012. XIV, 159 p. 41 illus., 23 in color. (Lecture Notes in course in complex analysis offers new and interesting the leading industrial enterprises including RWE, Statistics - Proceedings, Vol. 205) Softcover 978-1-4614-1965-5 motivations for classical results and introduces Vattenfall, EDF, PetroChina, Vestolit, Sasol, and related topics stressing motivation and technique. Hella. The book includes 19 case studies that were ▶$79.95 Numerous illustrations, examples, and now 300 conducted in real plants. They include chemical exercises, enrich the text. Students who master this plants, fossil power plants, wind power plants, nuclear textbook will emerge with an excellent grounding in power plants, oil refineries, oil production plants, V. Barbu, Alexandru Ioan Cuza University, Iasi, Romania; O. complex analysis, and a solid understanding of its injection molding fascilities and retail industry Cârjă, Alexandru Ioan Cuza University, Iasi, Romania (Eds.) wide applicability. shops. All case studies were conducted by the author More on www.springer.com/978-1-4419-7287-3 in cooperation and co-authorship with some of Alexandru Myller Mathematical the leading industrial enterprises including RWE, Usually dispatched within 3 to 5 business days Seminar Centennial Conference Vattenfall, EDF, PetroChina, Vestolit, Sasol, and Hella. This volume contains articles that cover a wide 2010. XI, 320 p. 80 illus., 3 in color. (Undergraduate Texts in Mathematics) Hardcover More on www.springer.com/978-3-642-24973-0 spectrum of mathematical topics. Some are surveys of hot research topics in contemporary mathematics. 978-1-4419-7287-3 Due: January 31, 2012 The articles develop various areas of mathematics ▶$74.95 2012. XXII, 246 p. 66 illus., 30 in color. Softcover including pure mathematics, applied mathematics, 978-3-642-24973-0 interdisciplinary sciences and mathematical physics. ▶$99.00 More on www.springer.com/978-0-7354-0884-5 Online orders shipping within 2-3 days Forthcoming 2011. 306 p. (Mathematical and Statistical Physics, Vol. 1329) Softcover A. Barbour, Andrew Barbour, University of Zurich, 978-0-7354-0884-5 Switzerland; H.P. Chan, National University of Singapore, ▶$139.00 Republic of Singapore; D. Siegmund, David Siegmund, Stanford University, Stanford, CA, USA (Eds.) Probability Approximations and Beyond P. Bangert, algorithmica technologies GmbH, Bremen, In June 2010, a conference, Probability Germany Approximations and Beyond, was held at the National University of Singapore (NUS), in honor Optimization for Industrial of pioneering mathematician Louis Chen. Louis is perhaps best known for his elegant Poisson Problems approximation method, developed from Stein’s Industrial optimization lies on the crossroads between original approach to normal approximation. Another mathematics, computer science, engineering and of his important contributions has been to turn management. This book presents these fields as a Stein’s concentration inequality idea into an effective V. Barbu, University Al.I. Cuza, Iasi, Romania; T. Precupanu, conversation between the theory of mathematics and tool for providing error bounds for the normal University Al.I.Cuza, Iasi, Romania computer science and case studies demonstrating approximation in many settings, and in particular engineering and management. Most of all, the case for sums of random variables exhibiting only local Convexity and Optimization in studies illustrate what may reasonably be expected dependence. The conference attracted a large from an optimization project in a commercial audience that came to pay homage to Louis, and to Banach Spaces hear presentations by colleagues who have worked enterprise. While many other books treat some of An updated and revised edition of the 1986 title with him in special ways over the past 40 years. The the aspects of this book, it is practical and may be Convexity and Optimization in Banach Spaces, papers in this volume attest to how Louis Chen’s used as a manual for conducting an optimization this book provides a self-contained presentation ideas have influenced and continue to influence such project. This book will not make its reader into a of basic results of the theory of convex sets and diverse areas as molecular biology and computer mathematician but it will help him to improve his functions in infinite-dimensional spaces. The main science. He himself has developed applications of his plant. The book requires no mathematical or technical emphasis is on applications to convex optimization work on Poisson approximation to problems of signal background beyond a good high school training; all and convex optimal control problems in Banach detection in computational biology. The original else is addressed within. It is aimed at managers or spaces. A distinctive feature is a strong emphasis papers contained in this book provide historical engineers of industrial facilities and is also suitable on the connection between theory and application. context for Louis’s work, alongside commentary for university students and their professors as an This edition has been updated to include new results on some of his major contributions by noteworthy illustration of how academic material may be used pertaining to advanced concepts of subdifferential for statisticians and mathematicians working today.The in real life. The book includes 19 case studies that convex functions and new duality results in convex papers in this volume attest to how Louis Chen’s were conducted in real plants. They include chemical programming. The last chapter, concerned with ideas have influenced and continue to influence such plants, fossil power plants, wind power plants, nuclear convex control problems, has been rewritten and diverse areas as molecular biology and computer power plants, oil refineries, oil production plants, completed with new research concerning boundary science. He himself has developed applications of his injection molding fascilities and retail industry control systems, the dynamic programming equations work on Poisson approximation to problems of signal shops. All case studies were conducted by the author in optimal control theory and periodic optimal detection in computational biology. The original in cooperation and co-authorship with some of control problems. Finally, the structure of the book papers contained in this book provide historical the leading industrial enterprises including RWE, has been modified to highlight the most recent Vattenfall, EDF, PetroChina, Vestolit, Sasol, and context for Louis’s work, alongside commentary springer.com 11 progression in the field including fundamental results ends with suggested experiments to illustrate some and graduate students with a modestknowledge of on the theory of infinite-dimensional convex analysis of the scientific principles exploited in the chapter." - Algebraic Topology. and includes helpful bibliographical notes at the end FOOD & DRINK NEWSLETTER More on www.springer.com/978-3-642-22002-9 of each chapter. More on www.springer.com/978-3-540-67466-5 Usually dispatched within 3 to 5 business days More on www.springer.com/978-94-007-2246-0 Usually dispatched within 3 to 5 business days 2011. XVII, 170 p. 35 illus. (Lecture Notes in Mathematics, Due: December 31, 2011 2001. VIII, 244 p. 27 illus. Hardcover Vol. 2032) Softcover 2012. XII, 368 p. (Springer Monographs in Mathematics) 978-3-540-67466-5 978-3-642-22002-9 Hardcover ▶$69.95 ▶$49.95 978-94-007-2246-0 ▶$124.00

J. Barnes, Caversham, Reading, UK A. Barlotti, Universitá di Perugia, Italy (Ed.) Gems of Geometry P. Barham, Bristol, UK Finite Geometric Structures and Based on a series of lectures the author prepared for The Science of Cooking their Applications adult students at Reading University in the UK, this Lectures given at a Summer School of the Centro lively and entertaining book proves that, far from A kitchen is no different from most science Internazionale Matematico Estivo (C.I.M.E.) held being a dusty, dull subject, geometry is in fact full laboratories and cookery may properly be regarded in Bressanone (Bolzano), Italy, June 18-27, 1972 of beauty and fascination. The author's infectious as an experimental science. Food preparation and enthusiasm is put to use in explaining many of the cookery involve many processes which are well R.C. Bose: Graphs and designs.- R.H. Bruck: key concepts in the field, starting with the Golden described by the physical sciences. Understanding Construction problems in finite projective spaces.- Number and taking the reader on a geometrical the chemistry and physics of cooking should lead to R.H.F. Denniston: Packings of PG(3,q).- J. Doyen: journey via Shapes and Solids, Circles and Spheres, improvements in performance in the kitchen. For Recent results on Steiner triple systems.- H. Projective Geometry and Topology, into and out those of us who wish to know why certain recipes Lüneburg: Gruppen und endliche projektive Ebenen.- of the Fourth Dimension, and finishing up with work and perhaps more importantly why others fail, J.A. Thas: 4-gonal configurations.- H.P. Young: Affine Einstein's Theories of Relativity. Aimed at a general appreciating the underlying physical processes will triple systems. readership, and requiring only a basic understanding inevitably help in unravelling the mysteries of the "art" More on www.springer.com/978-3-642-10972-0 of mathematics, the text uses examples such as of good cooking. Strong praise from the reviewers Usually dispatched within 3 to 5 business days soap bubbles to make accessible complex subjects - "Will be stimulating for amateur cooks with an such as Chaos and Fractals, Steiner's porism and interest in following recipes and understanding 2011. 282 p. (C.I.M.E. Summer Schools, Vol. 60) Softcover Soddy's Hexlet. It includes a wealth of the author's how they work. They will find anecdotes and, 978-3-642-10972-0 own diagrams and illustrations, of which several are sprinkled throughout the book, scientific points ▶$49.95 in stereo. As well as material based on the lectures of information... The book is a pleasant read and themselves, including sets of exercises, the book is an invitation to become better acquainted with features a number of appendices that cover related the science of cooking." - NATURE "This year, at J.A. Barmak, University of Buenos Aires, Argentina topics and provide further reading and information. last, we have a book which shows how a practical Equally ideal as an educational gift for a youngster understanding of physics and chemistry can improve Algebraic Topology of Finite or as a nostalgic journey back into the world of culinary performance… [Barham] first explains, in a mathematics for older readers, John Barnes' book lucid non-textbooky way, the principles behind taste, Topological Spaces and is the perfect antidote for anyone whose maths flavour and the main methods of food preparation, Applications lessons at school are a source of painful memories. and then gives fool-proof basic recipes for dishes from Where once geometry was a source of confusion roast leg of lab to chocolate soufflé." - FINANCIAL This volume deals with the theory of finite topological and frustration, Barnes brings enlightenment and TIMES WEEKEND "This book is full of interesting spaces and itsrelationship with the homotopy entertainment. and relevant facts that clarify the techniques of and simple homotopy theory of polyhedra.The cooking that lead to the texture, taste and aroma of interaction between their intrinsic combinatorial and More on www.springer.com/978-3-642-05091-6 good cuisine. As a physicist the author introduces the topologicalstructures makes finite spaces a useful Online orders shipping within 2-3 days importance of models in preparing food, and their tool for studying problems inTopology, Algebra and 2010. XIII, 311 p. 340 illus. Hardcover modification as a result of testing (tasting)."- THE Geometry from a new perspective. In particular,the 978-3-642-05091-6 PHYSICIST "Focuses quite specifically on the physics methods developed in this manuscript are used ▶$39.95 and food chemistry of practical domestic cooking to study Quillen’sconjecture on the poset of p- in terms of real recipes... Each chapter starts with subgroups of a finite group and theAndrews-Curtis an overview of the scientific issues relevant to that conjecture on the 3-deformability of contractibletwo- food group, e.g. toughness of meat, thickening of dimensional complexes.This self-contained work sauces, collapse of sponge cakes and soufflés. 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H.H. Bauschke, University of British Columbia, Kelowna, B.C., M. Beck, San Francisco State University, CA, USA; R. Canada; P.L. Combettes, Université Pierre et Marie Curie, Geoghegan, State University of New York, NY, USA Paris, France The Art of Proof Convex Analysis and Monotone H.H. Bauschke, University of British Colombia, Canada; R.S. Burachik, University of South Australia; P.L. Combettes, Basic Training for Deeper Mathematics Operator Theory in Hilbert Spaces University of Pierre & Marie Curie - Paris VI; V. Elser, Cornell University, USA; D.R. Luke, Institut für Numerische und The Art of Proof is designed for a one-semester This book presents a largely self-contained account Angewandte Mathematik, Universität Göttingen, Lotzestr. or two-quarter course. A typical student will have of the main results of convex analysis, monotone 16-18, 37073 Göttingen, Germany; H. Wolkowicz, University studied calculus (perhaps also linear algebra) with operator theory, and the theory of nonexpansive of Waterloo, Canada (Eds.) reasonable success. With an artful mixture of operators in the context of Hilbert spaces. Unlike chatty style and interesting examples, the student's existing literature, the novelty of this book, and Fixed-Point Algorithms for previous intuitive knowledge is placed on solid indeed its central theme, is the tight interplay among intellectual ground. The topics covered include: the key notions of convexity, monotonicity, and Inverse Problems in Science and integers, induction, algorithms, real numbers, nonexpansiveness. The presentation is accessible Engineering rational numbers, modular arithmetic, limits, to a broad audience and attempts to reach out in and uncountable sets. Methods, such as axiom, particular to the applied sciences and engineering Fixed-Point Algorithms for Inverse Problems theorem and proof, are taught while discussing communities, where these tools have become in Science and Engineering presents some of the the mathematics rather than in abstract isolation. indispensable. Graduate students and researchers most recent work from leading researchers in Some of the proofs are presented in detail, while in pure and applied mathematics will benefit variational and numerical analysis. The contributions others (some with hints) may be assigned to the from this book. It is also directed to researchers in this collection provide state-of-the-art theory student or presented by the instructor. The authors in engineering, decision sciences, economics, and and practice in first-order fixed-point algorithms, recommend that the two parts of the book -- Discrete inverse problems, and can serve as a reference identify emerging problems driven by applications, and Continuous -- be given equal attention. The book book.Author Information: Heinz H. Bauschke is and discuss new approaches for solving these ends with short essays on further topics suitable for a Professor of Mathematics at the University of problems. This book is a compendium of topics seminar-style presentation by small teams of students, British Columbia, Okanagan campus (UBCO) explored at the Banff International Research Station either in class or in a mathematics club setting. These and currently a Canada Research Chair in Convex “Interdisciplinary Workshop on Fixed-Point include: continuity, cryptography, groups, complex Analysis and Optimization. He was born in Frankfurt Algorithms for Inverse Problems in Science and numbers, ordinal number, and generating functions. Engineering” in November of 2009. The workshop where he received his "Diplom-Mathematiker (mit More on www.springer.com/978-1-4419-7022-0 Auszeichnung)" from Goethe Universität in 1990. included a broad range of research including Usually dispatched within 3 to 5 business days He defended his Ph.D. thesis in Mathematics at variational analysis, numerical linear algebra, Simon Fraser University in 1996 and was awarded biotechnology, materials science, computational 2010. XXI, 182 p. 23 illus. (Undergraduate Texts in the Governor General's Gold Medal for his graduate solid-state physics, and chemistry. Key topics and features of this book include:· Theory of Fixed- Mathematics) Hardcover work. After a NSERC Postdoctoral Fellowship spent 978-1-4419-7022-0 at the University of Waterloo, at the Pennsylvania point algorithms: variational analysis, convex analysis, ▶$39.95 State University, and at the University of California convex and nonconvex optimization, subdifferential at Santa Barbara, Dr. Bauschke became College calculus, nonsmooth analysis, proximal point Professor at Okanagan University College in 1998. methods, projection methods, resolvent and related He joined the University of Guelph in 2001, and fixed-point theoretic methods, and monotone he returned to Kelowna in 2005, when Okanagan operator theory· Numerical analysis of fixed- University College turned into UBCO. In 2009, he point algorithms: choice of step lengths, of weights, became UBCO's first "Researcher of the Year".Patrick of blocks for block-iterative and parallel methods, L. Combettes received the Brevet d'Études du Premier and of relaxation parameters; regularization of Cycle from Académie de Versailles in 1977 and the ill-posed problems; numerical comparison of Ph.D. degree from North Carolina State University various methods· Applications: Image and in 1989. In 1990, he joined the City College and the signal processing, antenna optimization, location Graduate Center of the City University of New York problems The wide scope of applications presented where he became a Full Professor in 1999. Since in this volume easily serve as a basis for new and 1999, he has been with the Faculty of Mathematics innovative research and collaboration. of Université Pierre et Marie Curie -- Paris 6, More on www.springer.com/978-1-4419-9568-1 laboratoire Jacques-Louis Lions, where he is presently Usually dispatched within 3 to 5 business days a Professeur de Classe Exceptionnelle.He was elected Fellow of the IEEE in 2005. 2011. XII, 404 p. 35 illus., 22 in color. (Springer Optimization and Its Applications, Vol. 49) Hardcover More on www.springer.com/978-1-4419-9466-0 978-1-4419-9568-1 Usually dispatched within 3 to 5 business days ▶$149.00 2011. XVI, 468 p. 30 illus. (CMS Books in Mathematics) Hardcover 978-1-4419-9466-0 springer.com 13

mathematical results to be stated, proved, and unceasingly renewed spirit of geometry and that understood in a much easier and elegant way.From even so-called "elementary" geometry is very much the reviews of the Russian edition:"The main accent alive and at the very heart of the work of numerous is shifted to the application . . . in geometrical contemporary mathematicians. It is also shown that optics, thermostatics and control theory, and not there are innumerable paths yet to be explored and to the Hamiltonian mechanics only. . . . To make concepts to be created. The book is visually rich and the book fairly self-contained, full details of basic inviting, so that readers may open it at random places definitions and all proofs are included. In this way, and find much pleasure throughout according their the majority of the text can be read without the own intuitions and inclinations. Marcel Berger is the prerequisite of a course in geometry. The excellent author of numerous successful books on geometry, collection of examples illustrates the relatively hard this book once again is addressed to all students and and highly abstract mathematical theory and its teachers of mathematics with an affinity for geometry. L. Beilina, University of Technology, Gothenburg, Sweden; hidden difficulties. . . . The book can rise real interest More on www.springer.com/978-3-540-70996-1 M.V. Klibanov, University of North Carolina, Charlotte, NC, for specialists . . . . The . . . book is a significant USA input in the modern symplectic geometry and its Online orders shipping within 2-3 days applications."(Andrey Tsiganov, St. Petersburg 2010. XII, 860 p. 666 illus. Hardcover Approximate Global Convergence State University)Sergio Benenti is a professor of 978-3-540-70996-1 and Adaptivity for Coefficient mathematical physics at Università di Torino, Italy. ▶$89.95 His current fields of research include symplectic Inverse Problems geometry with applications to physical theories, Approximate Global Convergence and Adaptivity Riemannian geometry with applications to the theory for Coefficient Inverse Problems is the first of the separation of variables in the Hamilton-Jacobi book in which two new concepts of numerical equation and in other relevant differential equations solutions of multidimensional Coefficient Inverse of physics, and mathematical models of the dynamics Problems (CIPs) for a hyperbolic Partial Differential of non-holonomic systems. Equation (PDE) are presented: Approximate More on www.springer.com/978-1-4614-1498-8 Global Convergence and the Adaptive Finite Usually dispatched within 3 to 5 business days Element Method (adaptivity for brevity). Two central questions for CIPs are addressed: How to 2012. XIV, 258 p. 50 illus. (Universitext) Softcover obtain a good approximation for the exact solution 978-1-4614-1498-8 without any knowledge of a small neighborhood ▶$59.95 of this solution, and how to refine it given the B. Bergmann, M. Epple, Goethe-Universität, Frankfurt am approximation. The book also combines analytical Main, Germany; R. Ungar, Wolfgang Goethe University, convergence results with recipes for various Frankfurt am Main, Germany (Eds.) numerical implementations of developed algorithms. The developed technique is applied to two types of Transcending Tradition: Jewish blind experimental data, which are collected both in Mathematicians in German a laboratory and in the field. The result for the blind backscattering experimental data collected in the field Speaking Academic Culture addresses a real-world problem of imaging of shallow A companion publication to the international explosives. exhibition "Transcending Tradition: Jewish More on www.springer.com/978-1-4419-7804-2 Mathematicians in German-Speaking Academic Due: March 31, 2012 Culture", the catalogue explores the working lives and activities of Jewish mathematicians in German- 2012. XIV, 388 p. 78 illus., 75 in color. Hardcover 978-1-4419-7804-2 speaking countries during the period between the legal and political emancipation of the Jews in $169.00 M. Berger, IHÉS, Bures-sur-Yvette, France ▶ the 19th century and their persecution in Nazi Geometry Revealed Germany. It highlights the important role Jewish A Jacob's Ladder to Modern Higher Geometry mathematicians played in all areas of mathematical culture during the Wilhelmine Empire and the Both classical geometry and modern differential Weimar Republic, and recalls their emigration, flight geometry have been active subjects of research or death after 1933. throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. More on www.springer.com/978-3-642-22463-8 The underlying motivating concept for the present Due: February 28, 2012 book is that it offers readers the elements of a modern 2012. XI, 270 p. 226 illus., 164 in color. Hardcover geometric culture by means of a whole series of 978-3-642-22463-8 visually appealing unsolved (or recently solved) ▶$49.95 problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, M. Bergounioux, Université d'Orléans, France (Ed.) S. Benenti, Università di Torino, Italy spheres, polygons, polyhedra, curves, surfaces, convex sets, etc., crucial ideas and above all abstract concepts Mathematical Image Processing Hamiltonian Structures and needed for attaining the results are elucidated. University of Orléans, France, March 29th - April Generating Families These are conceptual notions, each built "above" the preceding and permitting an increase in abstraction, 1st, 2010 This book is an enhanced version of an earlier represented metaphorically by Jacob's ladder with The contributions appearing in this volume Russian edition. Besides thorough revisions, more its rungs: the 'ladder' in the Old Testament, that are a snapshot of the different topics that were emphasis was put on reordering the topics according angels ascended and descended... In all this, the discussed during the conference. They mainly to a category-theoretical view. This allows the aim of the book is to demonstrate to readers the concern, image reconstruction, texture extraction 14 springer.com and image classification and involve a variety of ▶$89.95 different methods and applications. Therefore it was impossible to split the papers into generic groups which is why they are presented in alphabetic order. However they mainly concern : texture analysis (5 papers) with different techniques (variational analysis, wavelet and morphological component analysis, fractional Brownian fields), geometrical methods (2 papers ) for restoration and invariant feature detection, classification (with multifractal analysis), neurosciences imaging and analysis of Multi-Valued Images. S. Bianchini, SISSA, Trieste, Italy; E.A. Carlen, Rutgers More on www.springer.com/978-3-642-19603-4 University, Piscataway NJ, USA; A. Mielke, WIAS, Berlin, Usually dispatched within 3 to 5 business days Germany; C. Villani, Université de Lyon, France 2011. X, 197 p. 30 illus., 14 in color. (Springer Proceedings in P.H. Bezandry, Howard University, Washington D.C. 20059, Mathematics, Vol. 5) Hardcover Nonlinear PDE’s and Applications USA; T. Diagana, Howard University, Washington D.C., 978-3-642-19603-4 20059, USA C.I.M.E. Summer School, Cetraro, Italy 2008, ▶$124.00 Editors: Luigi Ambrosio, Giuseppe Savaré Almost Periodic Stochastic This volume collects the notes of the CIME course Processes "Nonlinear PDE’s and applications" held in Cetraro (Italy) on June 23–28, 2008. It consists of four Almost Periodic Stochastic Processes is among series of lectures, delivered by Stefano Bianchini the few published books that is entirely devoted (SISSA, Trieste), Eric A. Carlen (Rutgers University), to almost periodic stochastic processes and their Alexander Mielke (WIAS, Berlin), and Cédric Villani applications. The topics treated range from existence, (Ecole Normale Superieure de Lyon).They presented uniqueness, boundedness, and stability of solutions, a broad overview of far-reaching findings and exciting to stochastic difference and differential equations. new developments concerning, in particular, optimal Motivated by the studies of the natural fluctuations transport theory, nonlinear evolution equations, in nature, this work aims to lay the foundations for functional inequalities, and differential geometry. A a theory on almost periodic stochastic processes and sampling of the main topics considered here includes their applications.This book is divided in to eight optimal transport, Hamilton-Jacobi equations, chapters and offers useful bibliographical notes at the Riemannian geometry, and their links with sharp S. Bertoluzza, CNR, Pavia, Italy; R.H. Nochetto, University end of each chapter. Highlights of this monograph geometric/functional inequalities, variational methods of Maryland, College Park, MD, USA; A. Quarteroni, EPFL, include the introduction of the concept of p-th for studying nonlinear evolution equations and their Lausanne, Switzerland; K.G. Siebert, University of Stuttgart, mean almost periodicity for stochastic processes Germany; A. Veeser, Università degli Studi di Milano, Italy scaling properties, and the metric/energetic theory and applications to various equations. The book of gradient flows and of rate-independent evolution Multiscale and Adaptivity: offers some original results on the boundedness, problems.The book explores the fundamental stability, and existence of p-th mean almost periodic connections between all of these topics and points to Modeling, Numerics and solutions to (non)autonomous first and/or second new research directions in contributions by leading order stochastic differential equations, stochastic experts in these fields. Applications partial differential equations, stochastic functional C.I.M.E. Summer School, Cetraro, Italy differential equations with delay, and stochastic More on www.springer.com/978-3-642-21718-0 2009Editors: Giovanni Naldi, Giovanni Russo difference equations. Various illustrative examples Usually dispatched within 3 to 5 business days are also discussed throughout the book.The results This book is a collection of lecture notes for the CIME 2011. XIII, 224 p. 8 illus., 7 in color. (C.I.M.E. Foundation provided in the book will be of particular use to Subseries, Vol. 2028) Softcover course on "Multiscale and Adaptivity: Modeling, those conducting research in the field of stochastic 978-3-642-21718-0 Numerics and Applications," held in Cetraro (Italy), processing including engineers, economists, and $59.95 in July 2009.Complex systems arise in several ▶ statisticians with backgrounds in functional analysis physical, chemical, and biological processes, in which and stochastic analysis. Advanced graduate students length and time scales may span several orders of with backgrounds in real analysis, measure theory, magnitude. Traditionally, scientists have focused and basic probability, may also find the material in on methods that are particularly applicable in only this book quite useful and engaging. one regime, and knowledge of the system on one scale has been transferred to another scale only More on www.springer.com/978-1-4419-9475-2 indirectly. Even with modern computer power, the Usually dispatched within 3 to 5 business days complexity of such systems precludes their being 2011. XV, 235 p. Hardcover treated directly with traditional tools, and new 978-1-4419-9475-2 mathematical and computational instruments have ▶$99.00 had to be developed to tackle such problems. The outstanding and internationally renowned lecturers, coming from different areas of Applied Mathematics, have themselves contributed in an essential way to J.R. Birge, University of Chicago, Booth School of Business, the development of the theory and techniques that Chicago, IL, USA; F. Louveaux, University of Namur, Namur, constituted the subjects of the courses. Belgium More on www.springer.com/978-3-642-24078-2 Introduction to Stochastic Due: January 31, 2012 2012. IX, 314 p. 30 illus., 25 in color. (C.I.M.E. Foundation Programming Subseries, Vol. 2040) Softcover The aim of stochastic programming is to find optimal 978-3-642-24078-2 decisions in problems which involve uncertain springer.com 15 data. This field is currently developing rapidly with prior experience with mathematical proofs and who compromised. Reviews of the first edition: This is a contributions from many disciplines including have not previously studied real analysis. The text well-written book, based on very sound pedagogical operations research, mathematics, and probability. includes over 350 exercises. Key features of this ideas. It would be an excellent choice as a textbook At the same time, it is now being applied in a wide textbook: - provides an unusually thorough treatment for a 'transition' course.—Zentralblatt Math'Proofs variety of subjects ranging from agriculture to of the real numbers, emphasizing their importance and Fundamentals' has many strengths. One notable financial planning and from industrial engineering as the basis of real analysis - presents material strength is its excellent organization... There are large to computer networks. This textbook provides a in an order resembling that of standard calculus exercise sets throughout the book... the exercises are first course in stochastic programming suitable courses, for the sake of student familiarity, and for well integrated with the text and vary appropriately for students with a basic knowledge of linear helping future teachers use real analysis to better from easy to hard... Perhaps the book’s greatest programming, elementary analysis, and probability. understand calculus - emphasizes the direct role of strength is the author’s zeal and skill for helping The authors aim to present a broad overview of the the Least Upper Bound Property in the study of limits, students write mathematics better.—MAA Online main themes and methods of the subject. Its prime derivatives and integrals, rather than relying upon More on www.springer.com/978-1-4419-7126-5 goal is to help students develop an intuition on how to sequences for proofs; presents the equivalence of model uncertainty into mathematical problems, what various important theorems of real analysis with the Usually dispatched within 3 to 5 business days uncertainty changes bring to the decision process, Least Upper Bound Property - includes a thorough 2011. XXIV, 359 p. 31 illus. (Undergraduate Texts in and what techniques help to manage uncertainty discussion of some topics, such as decimal expansion Mathematics) Hardcover in solving the problems.In this extensively updated of real numbers, transcendental functions, area and 978-1-4419-7126-5 new edition there is more material on methods the number p, that relate to calculus but that are not $74.95 and examples including several new approaches always treated in detail in real analysis texts - offers ▶ for discrete variables, new results on risk measures substantial historical material in each chapter This in modeling and Monte Carlo sampling methods, book will serve as an excellent one-semester text a new chapter on relationships to other methods for undergraduates majoring in mathematics, and V. Blomer, University of Gottingen, Germany; P. Mihăilescu, including approximate dynamic programming, for students in mathematics education who want a University of Gottingen, Germany (Eds.) robust optimization and online methods.The book thorough understanding of the theory behind the real is highly illustrated with chapter summaries and number system and calculus. Contributions in Analytic and many examples and exercises. Students, researchers More on www.springer.com/978-0-387-72176-7 Algebraic Number Theory and practitioners in operations research and the optimization area will find it particularly of interest. Usually dispatched within 3 to 5 business days Festschrift for S. J. Patterson Review of First Edition:"The discussion on modeling Contributions in Analytic and Algebraic Number 2011. XXVIII, 553 p. 42 illus. Hardcover issues, the large number of examples used to illustrate 978-0-387-72176-7 Theory: Festschrift for S. J. Patterson is a collection of the material, and the breadth of the coverage surveys and original work from experts in the fields $84.95 make 'Introduction to Stochastic Programming' an ▶ of algebraic number theory, analytic number theory, ideal textbook for the area." (Interfaces, 1998) harmonic analysis, and hyperbolic geometry. A More on www.springer.com/978-1-4614-0236-7 portion of the collected contributions were developed from lectures presented at the “Patterson 60++ Usually dispatched within 3 to 5 business days International Conference on the Occasion of the 60th Birthday of Samuel J. Patterson,” held at the 2011. XXV, 485 p. 44 illus. (Springer Series in Operations Research and Financial Engineering) Hardcover University of Göttingen, July 27-29, 2009. Many of 978-1-4614-0236-7 the included chapters were contributed by invited participants. This volume presents and investigates ▶$74.95 the most recent developments in various key topics in analytic number theory and several related areas of mathematics. It is intended for graduate students and researchers of number theory as well as applied mathematicians interested in this broad field.

E.D. Bloch, Department of Mathematics, Bard College, More on www.springer.com/978-1-4614-1218-2 Annandale-on-Hudson, NY, USA Usually dispatched within 3 to 5 business days 2012. XVIII, 290 p. 3 illus. in color. (Springer Proceedings in Proofs and Fundamentals Mathematics, Vol. 9) Hardcover A First Course in Abstract Mathematics 978-1-4614-1218-2 ▶$149.00 This textbook is designed to introduce undergraduates to the writing of rigorous mathematical proofs, and to fundamental E.D. Bloch, Bard College, Annandale-on-Hudson, NY, USA mathematical ideas such as sets, functions, relations, and cardinality. The book serves as a bridge between The Real Numbers and Real computational courses such as calculus and more theoretical courses such as linear algebra, abstract Analysis algebra, and real analysis. This second edition has This text is a rigorous, detailed introduction to real been significantly enhanced, while maintaining analysis that presents the fundamentals with clear the balance of topics and careful writing of the exposition and carefully written definitions, theorems, previous edition. Part 1 presents logic and basic proof and proofs. The choice of material and the flexible techniques; Part 2 thoroughly covers fundamental organization, including three different entryways material such as sets, functions and relations; and into the study of the real numbers, making it equally Part 3 introduces a variety of extra topics such as appropriate to undergraduate mathematics majors groups, combinatorics and sequences, and suggests who want to continue in mathematics, and to future avenues for independent student explorations. A mathematics teachers who want to understand the gentle, friendly style is used, in which motivation theory behind calculus. The Real Numbers and and informal discussion play a key role, and yet Real Analysis is accessible to students who have high standards in rigor and in writing are never 16 springer.com

and mathematical physics applying the theory of and techniques involved in state-of-the-art sensor Riemann surfaces in their research. It is the first book research. on numerics of Riemann surfaces that reflects the More on www.springer.com/978-0-387-88618-3 progress made in this field during the last decade, and it contains original results. There are a growing Usually dispatched within 3 to 5 business days number of applications that involve the evaluation 2012. X, 242 p. 73 illus., 17 in color. (Springer Optimization of concrete characteristics of models analytically and Its Applications, Vol. 61) Hardcover described in terms of Riemann surfaces. Many 978-0-387-88618-3 problem settings and computations in this volume are ▶$124.00 motivated by such concrete applications in geometry and mathematical physics.

J. Blowey, Durham University, UK; M. Jensen, Durham More on www.springer.com/978-3-642-17412-4 University, UK (Eds.) Usually dispatched within 3 to 5 business days 2011. XII, 257 p. (Lecture Notes in Mathematics, Vol. 2013) Frontiers in Numerical Analysis - Softcover Durham 2010 978-3-642-17412-4 ▶$59.95 This book contains detailed lecture notes on four topics at the forefront of current research in computational mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the P. Boito, Université de Limoges, France key results. The notes start from a level suitable for first year graduate students in applied mathematics, Structured Matrix Based Methods mathematical analysis or numerical analysis, and proceed to current research topics. The reader should for Approximate Polynomial GCD therefore be able to gain quickly an insight into the Defining and computing a greatest common divisor important results and techniques in each area without of two polynomials with inexact coefficients is a recourse to the large research literature. Current classical problem in symbolic-numeric computation. (unsolved) problems are also described and directions The first part of this book reviews the main results for future research are given. This book is also suitable V.L. Boginski, University of Florida, Gainesville, FL, USA; C.W. that have been proposed so far in the literature. As for professional mathematicians who require a succint Commander, Eglin AFB, FL, USA; P.M. Pardalos, University of usual with polynomial computations, the polynomial and accurate account of recent research in areas Florida, Gainesville, FL, USA; Y. Ye, Stanford University, CA, GCD problem can be expressed in matrix form: the parallel to their own, and graduates in mathematical USA (Eds.) second part of the book focuses on this point of view sciences. and analyses the structure of the relevant matrices, More on www.springer.com/978-3-642-23913-7 Sensors: Theory, Algorithms, and such as Toeplitz, Toepliz-block and displacement Due: January 28, 2012 Applications structures. New algorithms for the computation of approximate polynomial GCD are presented, along 2012. XI, 282 p. 39 illus. (Lecture Notes in In recent years, technological advances have resulted with extensive numerical tests. The use of matrix Computational Science and Engineering, Vol. 85) Hardcover in the rapid development of a new and exciting structure allows, in particular, to lower the asymptotic 978-3-642-23913-7 research direction – the interdisciplinary use of computational cost from cubic to quadratic order ▶$59.95 sensors for data collection, systems analysis, and with respect to polynomial degree. monitoring. These highly calibrated sensors require precision engineering techniques that play an More on www.springer.com/978-88-7642-380-2 important role in analyzing and integrating large Online orders shipping within 2-3 days A.I. Bobenko, TU Berlin, Germany; C. Klein, Université de datasets. Sensor networks in particular represent 2011. 250 p. (Theses (Scuola Normale Superiore), Vol. 15) Bourgogne, Dijon, France (Eds.) a very active area of research, including work on Softcover problems such as sensor network localization 978-88-7642-380-2 Computational Approach to and network design. Application areas for sensors and ▶$24.95 Riemann Surfaces sensor networks include environmental monitoring, military surveillance, computational neuroscience, This volume offers a well-structured overview of seismic detection, and a great deal more. The existent computational approaches to Riemann A. Bonfiglioli, University of Bologna, Italy; R. Fulci, University fundamental problems of utilizing the collected data of Bologna, Italy surfaces and those currently in development. The for efficient system operation and decision making authors of the contributions represent the groups encompasses multiple research areas, including Topics in Noncommutative providing publically available numerical codes in this applied mathematics, optimization, signal/image field. Thus this volume illustrates which software tools processing, as well as emerging areas that require Algebra are available and how they can be used in practice. In interdisciplinary techniques from several fields The Theorem of Campbell, Baker, Hausdorff and addition examples for solutions to partial differential of research. Sensors: Theory, Algorithms, and Dynkin equations and in surface theory are presented. The Applications brings together recent developments intended audience of this book is twofold. It can be from researchers representing various fields from Motivated by the importance of the Campbell, Baker, used as a textbook for a graduate course in numerics engineering, mathematics, and computer science, Hausdorff, Dynkin Theorem in many different of Riemann surfaces, in which case the standard along with application areas of biomedicine, branches of Mathematics and Physics (Lie group-Lie undergraduate background, i.e., calculus and linear transportation, and military systems. This volume algebra theory, linear PDEs, Quantum and Statistical algebra, is required. In particular, no knowledge is ideal for scientists, practitioners, and graduate Mechanics, Numerical Analysis, Theoretical Physics, of the theory of Riemann surfaces is expected; the students who are interested in the knowledge, ideas, Control Theory, sub-Riemannian Geometry), this necessary background in this theory is contained monograph is intended to:1) fully enable readers in the Introduction chapter. At the same time, this (graduates or specialists, mathematicians, physicists book is also intended for specialists in geometry or applied scientists, acquainted with Algebra or springer.com 17 not) to understand and apply the statements and algebra, and visualization and interactive geometric numerous corollaries of the main result;2) provide a computation. It is intended for upper-undergraduate wide spectrum of proofs from the modern literature, students, and as a reference guide for anyone who comparing different techniques and furnishing wishes to learn to use the Maple program. a unifying point of view and notation;3) provide More on www.springer.com/978-1-4614-0121-6 a thorough historical background of the results, together with unknown facts about the effective Usually dispatched within 3 to 5 business days N. Bouleau, Ecole des Ponts ParisTech, Marne la Vallée, early contributions by Schur, Poincaré, Pascal, 2011. XVI, 216 p. 86 illus., 81 in color. (Springer France Campbell, Baker, Hausdorff and Dynkin;4) give an Undergraduate Texts in Mathematics and Technology, 0) outlook on the applications, especially in Differential Hardcover Risk and Meaning Geometry (Lie group theory) and Analysis (PDEs of 978-1-4614-0121-6 subelliptic type);5) quickly enable the reader, through Adversaries in Art, Science and Philosophy ▶$59.95 a description of the state-of-art and open problems, This richly illustrated book is an exploration of how to understand the modern literature concerning chance and risk, on the one hand, and meaning or a theorem which, though having its roots in the significance on the other, compete for the limelight in beginning of the 20th century, has not ceased to art, in philosophy, and in science. In modern society, provide new problems and applications.The book prudence and probability calculation permeate our assumes some undergraduate-level knowledge of daily lives. Yet it is clear for all to see that neither algebra and analysis, but apart from that is self- cautious bank regulations nor mathematics have contained. Part II of the monograph is devoted to the prevented economic crises from occurring time and proofs of the algebraic background. The monograph again. Nicolas Bouleau argues that it is the meaning may therefore provide a tool for beginners in Algebra. we assign to an event that determines the perceived More on www.springer.com/978-3-642-22596-3 risk, and that we generally turn a blind eye to this important fact, because the word "meaning" is itself Usually dispatched within 3 to 5 business days awkward to explain. He tackles this fundamental 2012. XXII, 539 p. 5 illus. (Lecture Notes in Mathematics, Vol. question through examples taken from cultural fields 2034) Softcover ranging from painting, architecture, and music, to 978-3-642-22596-3 O. Bottema poetry, biology, and astronomy. This enables the ▶$119.00 reader to view overwhelming risks in a different light. Topics in Elementary Geometry Bouleau clarifies that the most important thing in a This small book has for a long time been a unique time of uncertainty is to think of prudence on a higher place to find classical results from geometry, such level, one that truly addresses the various subjective as Pythagoras' theorem, the nine-point circle, interpretations of the world. Morley's triangle, Poncelet's polygons, and many More on www.springer.com/978-3-642-17646-3 other subjects. In addition, this book contains recent, Online orders shipping within 2-3 days geometric theorems which have been obtained in this classical field over the past years. There are 27 2011. VII, 302 p. 161 illus., 75 in color. Hardcover 978-3-642-17646-3 independent chapters on a wide range of topics in elementary plane Euclidean geometry, at a level just ▶$79.95 beyond what is usually taught in a good high school or college geometry course. The selection of topics is intelligent, varied, and stimulating. In a small space J.M. Borwein, University of Newcastle, NSW, Australia; M.P. the author provides many thought-provoking ideas. Skerritt, University of Newcastle, NSW, Australia This book will fit in well with the increasing interest for geometry in research and education. This book An Introduction to Modern was originally published in Dutch, and this will be the Mathematical Computing first English translation. This translation also includes a new foreword by Robin Hartshorne. "This highly With Maple™ entertaining book will broaden the reader's historical Thirty years ago, mathematical computation perspective in an enlightening manner and it provides was difficult to perform and thus used sparingly. attractive topics for classroom discussion." -Hendrik However, mathematical computation has become Lenstra, Universiteit Leiden far more accessible due to the emergence of More on www.springer.com/978-0-387-78130-3 M. Bounkhel, King Saud University, Riyadh, Saudi Arabia the personal computer, the discovery of fiber- Usually dispatched within 3 to 5 business days optics and the consequent development of the Regularity Concepts in modern internet, and the creation of Maple™, 2008. XII, 142 p. 76 illus. Softcover Mathematica®, and Matlab®. An Introduction to 978-0-387-78130-3 Nonsmooth Analysis Modern Mathematical Computing: With Maple™ ▶$44.95 Theory and Applications looks beyond teaching the syntax and semantics of Maple and similar programs, and focuses on Regularity concepts have played an increasingly why they are necessary tools for anyone who important role in the applications of nonsmooth engages in mathematics. It is an essential read for analysis, including differential inclusions, mathematicians, mathematics educators, computer optimization, and variational inequalities. This scientists, engineers, scientists, and anyone who heightened role has made it beneficial to introduce wishes to expand their knowledge of mathematics. graduate students and young researchers to the basic This volume will also explain how to become an concepts of regularity and their applications. This “experimental mathematician,” and will supply useful book is devoted to the study of various regularity information about how to create better proofs. The notions in nonsmooth analysis and their applications. text covers material in elementary number theory, It is the first thorough study of the regularity of calculus, multivariable calculus, introductory linear functions, sets, and multifunctions, as well as their 18 springer.com applications to differential inclusions and variational edition: "A strength of the book is the large number viscous systems, basic principles in the modeling of inequalities. Regularity Concepts in Nonsmooth of biologically-motivated problem sets. These and the turbulent mixing, transonic flows past an obstacle and Analysis is divided into three accessible parts. The references to the original biological papers would be a fluid dynamic approach for isometric embedding first section presents a thorough introduction valuable resources for an instructor." (UK Nonlinear in geometry, models of nonlinear elasticity, the to nonsmooth analysis theory, using examples News, 2001) Monge problem, and transport equations with rough and exercises to explain main concepts and show More on www.springer.com/978-1-4614-1685-2 coefficients. In addition, there are a number of papers useful results. The second part demonstrates the devoted to applications. These include: models of most recent results of various regularity concepts Usually dispatched within 3 to 5 business days blood flow, self-gravitating compressible fluids, of sets, functions, and set-valued mappings in granular flow, charge transport in fluids, and the 2012. XXIII, 508 p. (Texts in Applied Mathematics, Vol. nonsmooth analysis. The final section addresses modeling and control of traffic flow on networks. 40) Hardcover different applications, including first order and 978-1-4614-1685-2 More on www.springer.com/978-1-4419-9553-7 second order differential inclusions, quasi-variational, $84.95 and equilibrium theory. This book is designed ▶ Usually dispatched within 3 to 5 business days for graduate students, researchers, and general 2011. XI, 490 p. 20 illus. (The IMA Volumes in Mathematics practitioners interested in the applications of and its Applications, Vol. 153) Hardcover nonsmooth analysis. 4st Edition 978-1-4419-9553-7 ▶$149.00 More on www.springer.com/978-1-4614-1018-8 M. Braun, City University of New York, Flushing, NY, USA Usually dispatched within 3 to 5 business days December 31, 2011 Differential Equations and Their 2012. XV, 261 p. 15 illus., 14 in color. (Springer Optimization Applications and Its Applications, Vol. 59) Hardcover 978-1-4614-1018-8 An Introduction to Applied Mathematics ▶$99.00 Used in undergraduate classrooms across the USA, this is a clearly written, rigorous introduction to differential equations and their applications. Fully understandable to students who have had one year of calculus, this book distinguishes itself from other differential equations texts through its engaging application of the subject matter to interesting scenarios. This fourth edition incorporates earlier introductory material on bifurcation theory and adds H. Brezis, Rutgers University, Piscataway, NJ, USA a new chapter on Sturm-Liouville boundary value problems. Computer programs in C, Pascal, and Functional Analysis, Sobolev Fortran are presented throughout the text to show readers how to apply differential equations towards Spaces and Partial Differential quantitative problems. Equations More on www.springer.com/978-0-387-97894-9 F. Brauer, University of British Columbia, Vancouver, BC, Uniquely, this book presents a coherent, concise Usually dispatched within 3 to 5 business days Canada; C. Castillo-Chavez, Arizona State University, and unified way of combining elements from two Phoenix, AZ, USA distinct “worlds,” functional analysis (FA) and 1993. XVI, 578 p. 68 illus. (Texts in Applied partial differential equations (PDEs), and is intended Mathematics, Vol. 11) Hardcover Mathematical Models in 978-0-387-97894-9 for students who have a good background in real analysis. This text presents a smooth transition from Population Biology and $74.95 ▶ FA to PDEs by analyzing in great detail the simple Epidemiology case of one-dimensional PDEs (i.e., ODEs), a more manageable approach for the beginner. Although This textbook provides an introduction to the field A. Bressan, Penn State University, University Park, PA, there are many books on functional analysis and of mathematical biology through the integration USA; G.-Q.G. Chen, Oxford Centre for Nonlinear PDE, many on PDEs, this is the first to cover both of these of classical applications in ecology with more Oxford, United Kingdom; M. Lewicka, Rutgers University, closely connected topics. Moreover, the wealth of recent applications to epidemiology, particularly Piscataway, NJ , USA; D. Wang, University of Pittsburgh, exercises and additional material presented, leads in the context of spread of infectious diseases. It Pittsburgh, PA , USA (Eds.) the reader to the frontier of research. This book has integrates modeling, mathematics, and applications its roots in a celebrated course taught by the author in a semi-rigorous way, stating theoretical results Nonlinear Conservation Laws and for many years and is a completely revised, updated, and giving references but not necessarily giving Applications and expanded English edition of the important detailed proofs, providing a solid introduction to “Analyse Fonctionnelle” (1983). Since the French the field to undergraduates (junior and senior level), This volume contains the proceedings of the book was first published, it has been translated into graduate students in applied mathematics, ecology, Summer Program on Nonlinear Conservation Spanish, Italian, Japanese, Korean, Romanian, Greek epidemiology or evolutionary biology, sustainability Laws and Applications held at the IMA on July and Chinese. The English version is a welcome scientists, and to researchers who must routinely read 130-31, 2009. Hyperbolic conservation laws is a addition to this list. The first part of the text deals the practical and theoretical results that come from classical subject, which has experienced vigorous with abstract results in FA and operator theory. modeling in ecology and epidemiology. This new growth in recent years. The present collection The second part is concerned with the study of edition has been updated throughout. In particular provides a timely survey of the state of the art in spaces of functions (of one or more real variables) the chapters on epidemiology have been updated and this exciting field, and a comprehensive outlook on having specific differentiability properties, e.g., the extended considerably, and there is a new chapter open problems. Contributions of more theoretical celebrated Sobolev spaces, which lie at the heart of the on spatially structured populations that incorporates nature cover the following topics: global existence modern theory of PDEs. The Sobolev spaces occur in dispersal. The number of problems has been increased and uniqueness theory of one-dimensional systems, a wide range of questions, both in pure and applied and the number of projects has more than doubled, multidimensional conservation laws in several space mathematics, appearing in linear and nonlinear PDEs in particular those stressing connections to data. variables and approximations of their solutions, which arise, for example, in differential geometry, In addition some examples, exercises, and projects mathematical analysis of fluid motion, stability and harmonic analysis, engineering, mechanics, physics include use of Maple and Matlab. Review of first dynamics of viscous shock waves, singular limits for springer.com 19 etc. and belong in the toolbox of any graduate student studying analysis. More on www.springer.com/978-0-387-70913-0 Usually dispatched within 3 to 5 business days

2011. XIV, 600 p. 9 illus. (Universitext) Softcover 978-0-387-70913-0 ▶$84.95

H. Broer, University of Groningen, The Netherlands; F. A.E. Brouwer, Eindhoven University of Technology, Takens, University of Groningen, The Netherlands Netherlands; W.H. Haemers, Tilburg University, Netherlands Dynamical Systems and Chaos Spectra of Graphs Over the last four decades there has been extensive This book provides an elementary treatment of development in the theory of dynamical systems. the basic material about graph spectra, both for This book starts from the phenomenological point of ordinary, and Laplace and Seidel spectra. It covers view reviewing examples. Hence the authors discuss standard topics such as bounds on the sizes of cliques oscillators, like the pendulum in many variation and cocliques, chromatic number and Shannon including damping and periodic forcing , the Van capacity, the connection between randomness and der Pol System, the Henon and Logistic families, the the 'eigenvalue gap', and applications. It continues D. Brigo, Banca IMI, Milan, Italy; F. Mercurio, Banca IMI, Newton algorithm seen as a dynamical system and with a presentation of some new material on trees, Milan, Italy the Lorenz and Rossler system are also discussed. The strongly regular graphs, two-graphs, association Interest Rate Models - Theory and phenomena concern equilibrium, periodic, multi- schemes, p-ranks of configurations and similar topics. or quasi-periodic and chaotic dynamic dynamics Exercises at the end of each chapter provide practice Practice as these occur in all kinds of modeling and are met and vary from easy yet interesting applications of With Smile, Inflation and Credit both in computer simulations and in experiments. the treated theory, to little excursions into related The application areas vary from celestial mechanics topics. Tables, references at the end of the book, an The 2nd edition of this successful book has several and economical evolutions to population dynamics author and subject index enrich the text. Spectra new features. The calibration discussion of the basic and climate variability. The book is aimed at a broad of Graphs is written for researchers, teachers and LIBOR market model has been enriched considerably, audience of students and researchers. The first four students interested in graph spectra. The reader is with an analysis of the impact of the swaptions chapters have been used for an undergraduate course assumed to be familiar with basic linear algebra and interpolation technique and of the exogenous in Dynamical Systems and material from the last eigenvalues, although some more advanced topics in instantaneous correlation on the calibration two chapters and from the appendices has been linear algebra, like the Perron-Frobenius theorem and outputs. A discussion of historical estimation of used for master and PhD courses by the authors. All eigenvalue interlacing are included. the instantaneous correlation matrix and of rank chapters conclude with an exercise section. One of More on www.springer.com/978-1-4614-1938-9 reduction has been added, and a LIBOR-model the challenges is to help applied researchers acquire consistent swaption-volatility interpolation technique background for a better understanding of the data Due: January 31, 2012 has been introduced. The old sections devoted to the that computer simulation or experiment may provide 2012. XIV, 248 p. 24 illus. (Universitext) Hardcover smile issue in the LIBOR market model have been them with the development of the theory. Henk Broer 978-1-4614-1938-9 enlarged into several new chapters. New sections on and Floris Takens, professors at the Institute for ▶$59.95 local-volatility dynamics, and on stochastic volatility Mathematics and Computer Science of the University models have been added, with a thorough treatment of Groningen, are leaders in the field of dynamical of the recently developed uncertain-volatility systems. They have published a wealth of scientific Forthcoming approach. Examples of calibrations to real market papers and books in this area and both authors are data are now considered. The fast-growing interest members of the Royal Netherlands Academy of Arts M. Burgin, University of California, Department of for hybrid products has led to new chapters. A special and Sciences (KNAW). Mathematics, Los Angeles, CA 90095 USA focus here is devoted to the pricing of inflation- linked derivatives. The three final new chapters of More on www.springer.com/978-1-4419-6869-2 Hypernumbers and this second edition are devoted to credit. Since Credit Usually dispatched within 3 to 5 business days Derivatives are increasingly fundamental, and since Extrafunctions in the reduced-form modeling framework much of 2011. XVI, 313 p. (Applied Mathematical Sciences, Extending the Classical Calculus the technique involved is analogous to interest-rate Vol. 172) Hardcover 978-1-4419-6869-2 Encountering problems that they were not able modeling, Credit Derivatives -- mostly Credit Default to solve, mathematicians, as a rule, introduced ▶$74.95 Swaps (CDS), CDS Options and Constant Maturity new structures, extending the existing ones and CDS - are discussed, building on the basic short rate- making possible to solve previously ”unsolvable” models and market models introduced earlier for the problems. For instance, irrational, real and complex default-free market. Counterparty risk in interest rate numbers were introduced to make possible solving payoff valuation is also considered, motivated by the all algebraic equations. The stimulus to develop recent Basel II framework developments. the theory of hypernumbers and extrafunctions More on www.springer.com/978-3-540-22149-4 comes from physics. Exploring mysteries of the Usually dispatched within 3 to 5 business days microworld, physicists often encounter situations when their formulas acquire infinite values due 2006. LVI, 981 p. 124 illus. (Springer Finance) Hardcover the divergence of the used series and integrals. At 978-3-540-22149-4 the same time, all measured values are naturally $109.00 ▶ finite. A popular way to eliminate this discrepancy between theory and experiment was an artificial manipulation with formulas, which often allowed 20 springer.com to get rid of infinite values. Another natural way to acquainted with the current trends in these central deal with such situation is to learn how to rigorously fields of modern mathematics. work with infinities and come to finite values More on www.springer.com/978-3-642-22841-4 given by measurements. Mathematicians suggested several approaches to a rigorous operation with Due: February 28, 2012 infinite values by introducing infinite numbers. 2012. VIII, 523 p. 19 illus. (Springer Proceedings in The most popular of them are: transfinite numbers Mathematics, Vol. 17) Hardcover of Cantor, nonstandard analysis of Robinson, and 978-3-642-22841-4 surreal numbers. However, all these constructions, ▶$149.00 which contributed a lot to the development of mathematics, especially, Cantor’s set theory, brought very little to the realm of physics. However, there is a mathematical theory called the theory of A. Camina, School of Mathematics, University of East distributions, which allowed physicists to rigorously Anglia, Norwich NR4 7TJ, UK; B. Lewis, The Mathematical operate with functions that take infinite values. An Association, Leicester, UK example of such a function is the Heaviside-Dirac’s delta-function. Although at first physicists were An Introduction to Enumeration skeptical about this theory, now it has become one of Written for students taking a second or third year the most efficient tools of theoretical physics. In this undergraduate course in mathematics or computer book, we represent another rigorous mathematical science, this book is the ideal companion to a approach to operation with infinite values. At first, course in enumeration. Enumeration is a branch the concepts of real and complex numbers are of combinatorics where the fundamental subject extended in such a way that the new universe of matter is numerous methods of pattern formation and numbers called hypernumbers includes infinite N. Bäuerle, Karlsruhe Institute of Technology, Germany; U. counting. An Introduction to Enumeration provides quantities. It is necessary to remark that in contrast Rieder, University of Ulm, Germany a comprehensive and practical introduction to this to nonstandard analysis, there are no infinitely subject giving a clear account of fundamental results small hypernumbers. This is more relevant to the Markov Decision Processes with and a thorough grounding in the use of powerful situation in physics, where infinitely big values Applications to Finance techniques and tools.Two major themes run in emerge from theoretical structures but physicists parallel through the book, generating functions and have never encountered infinitely small values. The The theory of Markov decision processes focuses group theory. The former theme takes enumerative next step of extending the classical calculus based on controlled Markov chains in discrete time. sequences and then uses analytic tools to discover on real and complex functions is introduction of The authors establish the theory for general state how they are made up. Group theory provides a extrafunctions, which generalize not only the concept and action spaces and at the same time show its concise introduction to groups and illustrates how of a conventional function but also the concept of a application by means of numerous examples, mostly the theory can be used to count the number of distribution. This made possible to solve previously taken from the fields of finance and operations symmetries a particular object has. These enrich and “unsolvable” problems. For instance, there are research. By using a structural approach many extend basic group ideas and techniques.The authors linear partial differential equations for which it is technicalities (concerning measure theory) are present their material through examples that are proved that they do not have solutions not only in avoided. They cover problems with finite and infinite carefully chosen to establish key results in a natural conventional functions but even in distributions. horizons, as well as partially observable Markov setting. The aim is to progressively build fundamental At the same, it is proved that all these and many decision processes, piecewise deterministic Markov theorems and techniques. This development is other equations have solutions in extrafunctions. decision processes and stopping problems. The book interspersed with exercises that consolidate ideas Extrafucntions have been also efficiently used for a presents Markov decision processes in action and and build confidence. Some exercises are linked rigorous mathematical definition of the Feynman includes various state-of-the-art applications with to particular sections while others range across a path integral, as well as for solving some problems a particular view towards finance. It is useful for complete chapter. Throughout, there is an attempt in probability theory, which is also important for upper-level undergraduates, Master's students and to present key enumerative ideas in a graphic way, contemporary physics. researchers in both applied probability and finance, using diagrams to make them immediately accessible. More on www.springer.com/978-1-4419-9874-3 and provides exercises (without solutions). The development assumes some basic group theory, Due: April 21, 2012 More on www.springer.com/978-3-642-18323-2 a familiarity with analytic functions and their power series expansion along with some basic linear algebra. 2012. 120 p. (SpringerBriefs in Mathematics) Softcover Usually dispatched within 3 to 5 business days 978-1-4419-9874-3 More on www.springer.com/978-0-85729-599-6 ▶approx. $49.95 2011. XVI, 388 p. 24 illus. (Universitext) Softcover Usually dispatched within 3 to 5 business days 978-3-642-18323-2 ▶$74.95 2011. XII, 232 p. 62 illus. (Springer Undergraduate Forthcoming Mathematics Series, 0) Softcover 978-0-85729-599-6 C. Bär, University of Potsdam, Germany; J. Lohkamp, ▶$49.95 University of Münster, Germany; M. Schwarz, University of Leipzig, Germany (Eds.) H.E.A.E. Campbell, University of New Brunswick, Fredericton, Global Differential Geometry NB, Canada; D.L. Wehlau, Royal Military College of Canada, This volume contains a collection of well-written Kingston, ON, Canada surveys provided by experts in Global Differential Geometry to give an overview over recent Modular Invariant Theory developments in Riemannian Geometry, Geometric This book covers the modular invariant theory of Analysis and Symplectic Geometry.The papers are finite groups, the case when the characteristic of written for graduate students and researchers with the field divides the order of the group. It explains a general interest in geometry, who want to get a theory that is more complicated than the study of the classical non-modular case, and it describes many open questions.Largely self-contained, the book springer.com 21 develops the theory from its origins up to modern to the test. The solution to all exercises is provided, ▶$49.95 results. It explores many examples, illustrating the and very often the procedure for solving is outlined. theory and its contrast with the better understood More on www.springer.com/978-88-470-1783-2 non-modular setting. It details techniques for the computation of invariants for many modular Online orders shipping within 2-3 days representations of finite groups, especially the case of 2010. X, 543 p. (Universitext) Softcover the cyclic group of prime order. It includes detailed 978-88-470-1783-2 examples of many topics as well as a quick survey of the elements of algebraic geometry and commutative ▶$74.95 algebra as they apply to invariant theory. The book is aimed at both graduate students and researchers— an introduction to many important topics in modern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter. More on www.springer.com/978-3-642-17403-2 G. Capriz, Universitá di Pisa, Italy; G. Stampacchia, SNS Pisa, Usually dispatched within 3 to 5 business days Italy (Eds.) 2011. XIII, 233 p. (Encyclopaedia of Mathematical Sciences, Vol. 139) Hardcover New Variational Techniques in 978-3-642-17403-2 Mathematical Physics ▶$124.00 Lectures given at a Summer School of the Centro Internazionale Matematico Estivo (C.I.M.E.) held M. Capiński, AGH University of Science and Technology, in Bressanone (Bolzano), Italy, June 17-26, 1973 Kraków, Poland; T. Zastawniak, University of York, UK C. Baiocchi: Problèmes à frontière libre liés à des Mathematics for Finance questions d’hydraulique.- Ch. Castaing: Intégrales An Introduction to Financial Engineering convexes duales.- G. Duvaut: Etude de problèmes unilateraux en mécanique par des méthodes As with the first edition, Mathematics for Finance: variationnelles.- D. Kinderlehrer: Remarks about the An Introduction to Financial Engineering combines free boundaries occurring in variational inequalities.- financial motivation with mathematical style. H. Lanchon: Torsion élastoplastique d’arbres Assuming only basic knowledge of probability and cylindriques: problèmes ouverts.- J.M. Lasry: Dualité calculus, it presents three major areas of mathematical en calcul des variations.- J.J. Moreau: On unilateral finance, namely option pricing based on the no- constraints, friction and plasticity.- B. Nayroles: arbitrage principle in discrete and continuous time Point de vue algébrique. Convexité et intégrantes setting, Markowitz portfolio optimisation and the C.G. Canuto, Politecnico di Torino, Italia; A. Tabacco, convexes en mécanique des solides.- W. Noll: On Capital Asset Pricing Model, and basic stochastic Politecnico di Torino, Italia certain convex sets of measures and phases of reacting interest rate models in discrete setting.In this mixtures.- W. Velte: On complementary variational Mathematical Analysis II second edition, the material has been thoroughly inequalities. revised and rearranged. New features include:• More on www.springer.com/978-3-642-10958-4 The purpose of this textbook is to present an array A case study to begin each chapter – a real-life of topics in Calculus, and conceptually follow our situation motivating the development of theoretical Usually dispatched within 3 to 5 business days previous effort Mathematical Analysis I.The present tools;• A detailed discussion of the case study at 2011. 420 p. (C.I.M.E. Summer Schools, Vol. 63) Softcover material is partly found, in fact, in the syllabus of the the end of each chapter;• A new chapter on time- 978-3-642-10958-4 typical second lecture course in Calculus as offered continuous models with intuitive outlines of the ▶$69.95 in most Italian universities. While the subject matter mathematical arguments and constructions;• known as `Calculus 1' is more or less standard, and Complete proofs of the two fundamental theorems concerns real functions of real variables, the topics of mathematical finance in discrete setting.From the of a course on `Calculus 2'can vary a lot, resulting reviews of the first edition:”This text is an excellent in a bigger flexibility. For these reasons the Authors introduction to Mathematical Finance. Armed with tried to cover a wide range of subjects, not forgetting a knowledge of basic calculus and probability a that the number of credits the current programme student can use this book to learn about derivatives, specifications confers to a second Calculus course is interest rates and their term structure and portfolio not comparable to the amount of content gathered management.”(Zentralblatt MATH)”Given these here. The reminders disseminated in the text make basic tools, it is surprising how high a level of the chapters more independent from one another, sophistication the authors achieve, covering such allowing the reader to jump back and forth, and thus topics as arbitrage-free valuation, binomial trees, and enhancing the versatility of the book. On the website: risk-neutral valuation.” (www.riskbook.com)”The http://calvino.polito.it/canuto-tabacco/analisi 2, the reviewer can only congratulate the authors with interested reader may find the rigorous explanation of successful completion of a difficult task of writing C. Cattaneo, Università di Roma, Italy (Ed.) the results that are merely stated without proof in the a useful textbook on a traditionally hard topic.” (K. book, together with useful additional material. The Borovkov, The Australian Mathematical Society Authors have completely omitted the proofs whose Gazette, Vol. 31 (4), 2004) Relativistic Fluid Dynamics Lectures given at a Summer School of the Centro technical aspects prevail over the fundamental notions More on www.springer.com/978-0-85729-081-6 and ideas. The large number of exercises gathered Internazionale Matematico Estivo (C.I.M.E.) held Usually dispatched within 3 to 5 business days according to the main topics at the end of each in Bressanone (Bolzano), Italy, June 7-16, 1970 chapter should help the student put his improvements 2011. XIII, 336 p. 66 illus. (Springer Undergraduate Pham Mau Quam: Problèmes mathématiques en Mathematics Series) Softcover hydrodynamique relativiste.- A. Lichnerowicz: 978-0-85729-081-6 Ondes de choc, ondes infinitésimales et rayons 22 springer.com en hydrodynamique et magnétohydrodynamique Planck equations, as well as Markov chain Monte relativistes.- A.H. Taub: Variational principles in Carlo algorithms, renormalization and dimensional general relativity.- J. Ehlers: General relativistic reduction, and basic equilibrium and non-equilibrium kinetic theory of gases.- K. Marathe: Abstract statistical mechanics. The applications include data Minkowski spaces as fibre bundles.- G. 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The book will be useful for scientists and engineers working in a wide range of fields and Finsler Geometry applications."Chorin and Hald provide excellent An Approach via Randers Spaces explanations with considerable insight and deep mathematical understanding, especially toward the "Finsler Geometry: An Approach via Randers Spaces" end of the book in the context of simplified versions exclusively deals with a special class of Finsler metrics of the famous statistical mechanics models of Ising -- Randers metrics, which are defined as the sum and of Mori and Zwanzig."(SIAM Review) of a Riemannian metric and a 1-form. Randers metrics derive from the research on General Relativity More on www.springer.com/978-1-4419-1001-1 Theory and have been applied in many areas of Usually dispatched within 3 to 5 business days the natural sciences. They can also be naturally D. Cheng, Institute of Systems Science, AMSS, Chinese deduced as the solution of the Zermelo navigation 2009. X, 162 p. 7 illus. (Surveys and Tutorials in the Academy of Sciences, China; X. Hu, Royal Institute of problem. The book provides readers not only with Applied Mathematical Sciences, Vol. 1) Softcover Technology, Sweden; T. Shen, Sophia University, Japan essential findings on Randers metrics but also 978-1-4419-1001-1 the core ideas and methods which are useful in ▶$44.95 Analysis and Design of Nonlinear Finsler geometry. It will be of significant interest to researchers and practitioners working in Finsler Control Systems geometry, even in differential geometry or related C. Clavero, University of Zaragoza, Spain; J.L. Gracia, "Analysis and Design of Nonlinear Control Systems" natural fields.Xinyue Cheng is a Professor at the University of Zaragoza, Spain; F.J. Lisbona, University of provides a comprehensive and up to date introduction School of Mathematics and Statistics of Chongqing Zaragoza, Spain (Eds.) to nonlinear control systems, including system University of Technology, China. Zhongmin Shen is a analysis and major control design techniques. Professor at the Department of Mathematical Sciences BAIL 2010 - Boundary and Interior of Indiana University Purdue University, USA. The book is self-contained, providing sufficient Layers, Computational and mathematical foundations for understanding the More on www.springer.com/978-3-642-24887-0 contents of each chapter. Scientists and engineers Due: April 28, 2012 Asymptotic Methods engaged in the field of Nonlinear Control Systems will find it an extremely useful handy reference book. Dr. 2012. Approx. 200 p. 5 illus. Hardcover This volume will contain selected papers from the 978-3-642-24887-0 Daizhan Cheng, a professor at Institute of Systems lectures held at the BAIL 2010 Conference, which Science, Chinese Academy of Sciences, has been ▶$109.00 took place from July 5th to 9th, 2010 in Zaragoza working on the control of nonlinear systems for (Spain). The papers present significant advances in over 30 years and is currently a Fellow of IEEE and a the modeling, analysis and construction of efficient Fellow of IFAC, he is also the chairman of Technical numerical methods to solve boundary and interior Committee on Control Theory, Chinese Association layers appearing in singular perturbation problems. of Automation. Special emphasis is put on the mathematical foundations of such methods and their application More on www.springer.com/978-3-642-11549-3 to physical models. Topics in scientific fields such as Online orders shipping within 2-3 days fluid dynamics, quantum mechanics, semiconductor 2011. 690 p. 100 illus. Hardcover modeling, control theory, elasticity, chemical reactor 978-3-642-11549-3 theory, and porous media are examined in detail. ▶$139.00 More on www.springer.com/978-3-642-19664-5 Usually dispatched within 3 to 5 business days 2011. VII, 300 p. (Lecture Notes in Computational Science A. Chorin, University of California, Berkeley, CA, USA; O.H. and Engineering, Vol. 81) Hardcover Hald, University of California, Berkeley, CA, USA 978-3-642-19664-5 Stochastic Tools in Mathematics ▶$124.00 and Science Stochastic Tools in Mathematics and Science is an introductory book on probability-based modeling. It covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. 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solutions in finite fields, then proceeds to lift these geometry. This book collects the lecture notes solutions to local solutions using Hensel lifting. The which were written up by the speakers. The main second is the global aspect: the use of number fields, topics concern diophantine equations, local-global and in particular of class groups and unit groups. principles, diophantine approximation and its This classical subject is here illustrated through a relations to Nevanlinna theory, and rationally wide range of examples. The third aspect deals with connected varieties.The book is divided into three specific classes of equations, and in particular the parts, corresponding to the courses given by J-L general and Diophantine study of elliptic curves, Colliot-Thélène Peter Swinnerton Dyer and Paul including 2 and 3-descent and the Heegner point Vojta. method. These subjects form the first two parts, More on www.springer.com/978-3-642-15944-2 forming Volume I. The study of Bernoulli numbers, the gamma function, and zeta and L-functions, and Usually dispatched within 3 to 5 business days H. Cohen, California State University, Los Angeles, California, of p-adic analogues is treated at length in the third 2010. XI, 232 p. (C.I.M.E. Foundation Subseries, Vol. 2009) USA part of the book, including many interesting and Softcover original applications. Much more sophisticated 978-3-642-15944-2 Numerical Approximation techniques have been brought to bear on the subject ▶$59.95 Methods of Diophantine equations, and for this reason, the π ≈ 355/113 author has included five chapters on these techniques forming the fourth part, which together with the third O. Costin, Ohio State University, Columbus, OH, USA; This book presents numerical approximation part forms Volume II. These chapters were written by F. Fauvet, Université de Strasbourg, France; F. Menous, techniques for solving various types of mathematical Yann Bugeaud, Guillaume Hanrot, Maurice Mignotte, Université Paris-Sud, Orsay, France; D. Sauzin, CNRS Paris, problems that cannot be solved analytically. In Sylvain Duquesne, Samir Siksek, and the author, and France / SNS Pisa, Italy (Eds.) addition to well-known methods, it contains a contain material on the use of Galois representations, collection of non-standard approximation techniques points on higher-genus curves, the superfermat Asymptotics in Dynamics, that appear in the literature but are not otherwise equation, Mihailescu's proof of Catalan's Conjecture, well known. This text also contains original methods and applications of linear forms in logarithms. The Geometry and PDEs; Generalized developed by the author. It includes an extensive book contains 530 exercises of varying difficulty from Borel Summation treatment of approximate solutions to various types immediate consequences of the main text to research Proceedings of the conference held in CRM Pisa, of integral equations. Examples are used extensively problems, and contain many important additional 12-16 October 2009, Vol. I to illustrate the theory. Problems at the end of the results. chapters are provided for practice. The book is These are the proceedings of a one-week international More on www.springer.com/978-0-387-49922-2 suitable as a textbook or as a reference for students conference centered on asymptotic analysis and taking a course in numerical methods. Researchers Usually dispatched within 3 to 5 business days its applications. They contain major contributions in need of approximation methods in their work will dealing with - mathematical physics: PT symmetry, also find this book useful. 2007. XXIII, 650 p. (Graduate Texts in Mathematics, perturbative quantum field theory, WKB analysis, - Vol. 239) Hardcover local dynamics: parabolic systems, small denominator More on www.springer.com/978-1-4419-9836-1 978-0-387-49922-2 questions, - new aspects in mould calculus, with Usually dispatched within 3 to 5 business days ▶$64.95 related combinatorial Hopf algebras and application to multizeta values, - a new family of resurgent 2011. XIII, 485 p. 21 illus. Hardcover functions related to knot theory. 978-1-4419-9836-1 ▶$84.95 More on www.springer.com/978-88-7642-374-1 Online orders shipping within 2-3 days 2011. 450 p. (CRM Series, Vol. 12.1) Softcover 978-88-7642-374-1 ▶$34.95

J.-L. Colliot-Thélène, Université de Paris-Sud, France; P. Swinnerton-Dyer, University of Cambridge, UK; P. Vojta, Universitiy of California, Berkeley, CA, USA; P. Corvaja, Università di Udine, Italy; C. Gasbarri, Université de H. Cohen, Université Bordeaux I, Talence, France Strasbourg, France (Eds.) Number Theory Arithmetic Geometry Volume I: Tools and Diophantine Equations Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10-15, 2007 D.A. Cox, Amherst College, Amherst, MA, USA; J. Little, The central theme of this graduate-level number College of the Holy Cross, Worcester, MA, USA; D. O'Shea, theory textbook is the solution of Diophantine Arithmetic Geometry can be defined as the part of Mount Holyoke College, South Hadley, MA, USA equations, i.e., equations or systems of polynomial Algebraic Geometry connected with the study of equations which must be solved in integers, rational algebraic varieties over arbitrary rings, in particular Using Algebraic Geometry numbers or more generally in algebraic numbers. over non-algebraically closed fields. It lies at the This theme, in particular, is the central motivation for intersection between classical algebraic geometry In recent years, the discovery of new algorithms for the modern theory of arithmetic algebraic geometry. and number theory.A C.I.M.E. Summer School dealing with polynomial equations, coupled with their In this text, this is considered through three aspects. devoted to arithmetic geometry was held in Cetraro, implementation on fast inexpensive computers, has The first is the local aspect: one can do analysis in p- Italy in September 2007, and presented some of the sparked a minor revolution in the study and practice adic fields, and here the author starts by looking at most interesting new developments in arithmetic of algebraic geometry. These algorithmic methods 24 springer.com have also given rise to some exciting new applications disproportionate contributions made by Scottish and of algebraic geometry. This book illustrates the Irish alumni in establishing a research community. many uses of algebraic geometry, highlighting some Gradually, Cambridge was transformed from a near- of the more recent applications of Gröbner bases moribund institution into a world-renowned centre and resultants. In order to do this, the authors for the mathematical and physical sciences. Many provide an introduction to some algebraic objects famous scientists and mathematicians are profiled, and techniques which are more advanced than one among them G. Green, G.G. Stokes, J.C. Adams, W. typically encounters in a first course, but nonetheless Thomson (Lord Kelvin), A. Cayley and J.C. Maxwell, of great utility. The book is written for nonspecialists and many lesser-known figures too, including the and for readers with a diverse range of backgrounds. first professors in Australia and the tutor to an Indian It assumes knowledge of the material covered in a maharajah. In addition, and as a special highlight, standard undergraduate course in abstract algebra, Hopkins’ own collection of portraits of his top and it would help to have some previous exposure students, attributed to the artist T.C. Wageman, J. Cvitanic, California Institute of Technology, Pasadena,USA; to Gröbner bases. The book does not assume the are published here – in colour – for the first time. J. Zhang, University of Southern California; Los Angeles, USA reader is familiar with more advanced concepts such Scholarly yet non-technical, this is a fascinating as modules. For this new edition the authors added look at Cambridge during the Victorian era that is Contract Theory in Continuous- two new sections and a new chapter, updated the accessible to anyone with an interest in the history of Time Models references and made numerous minor improvements science and mathematics; the history of education; the throughout the text. interaction of science and religious belief; the history In recent years there has been a significant increase of interest in continuous-time Principal-Agent More on www.springer.com/978-0-387-20733-9 of Cambridge University; and Victorian Britain generally. Alex D.D. Craik is a graduate of St Andrews models, or contract theory, and their applications. Usually dispatched within 3 to 5 business days and Cambridge. For many years, he taught applied Continuous-time models provide a powerful and mathematics at St Andrews University, where he is elegant framework for solving stochastic optimization 2005. X, 558 p. 24 illus. (Graduate Texts in presently an emeritus professor. problems of finding the optimal contracts between Mathematics, Vol. 185) Softcover two parties, under various assumptions on the 978-0-387-20733-9 More on www.springer.com/978-1-84800-132-9 information they have access to, and the effect they ▶$54.95 Online orders shipping within 2-3 days have on the underlying "profit/loss" values. This 2007. XIV, 410 p. 78 illus., 48 in color. Softcover monograph surveys recent results of the theory 978-1-84800-132-9 in a systematic way, using the approach of the so- ▶$69.95 called Stochastic Maximum Principle, in models driven by Brownian Motion. Optimal contracts are characterized via a system of Forward-Backward Stochastic Differential Equations. In a number of interesting special cases these can be solved explicitly, enabling derivation of many qualitative economic conclusions. More on www.springer.com/978-3-642-14199-7 Due: June 7, 2012 2012. X, 280 p. (Springer Finance, 0) Hardcover 978-3-642-14199-7 A.D.D. Craik, University of St. Andrews, UK ▶approx. $99.00 Mr Hopkins' Men Cambridge Reform and British Mathematics in Z. Cvetkovski, European University - Skopje, R. Macedonia, the 19th Century Informatics Department, Macedonia The 19th century was a key period in the development of the mathematical sciences in Britain. Subjects such Inequalities as rigid-body dynamics, hydrodynamics, elasticity, Theorems, Techniques and Selected Problems optics, heat, electricity and magnetism were extended This work is about inequalities which play an and given firmer foundations; new areas of pure important role in mathematical Olympiads. It mathematics were explored; and major advances took contains 175 solved problems in the form of exercises place in statistics, astronomy, geology and glaciology. and, in addition, 310 solved problems. The book The mid-19th century also brought dramatic changes also covers the theoretical background of the most to Cambridge University. Before 1850, the only important theorems and techniques required for pathway to an honours degree was the Mathematical solving inequalities. It is written for all middle and G. Da Prato, Università di Pisa, Italy; G. Geymonat (Eds.) Tripos - taken by all aspiring students whatever high-school students, as well as for graduate and their destined careers - and the best teaching was undergraduate students. School teachers and trainers provided by private tutors, the most renowned being Hyperbolicity for mathematical competitions will also gain benefit Lectures given at a Summer School of the Centro the remarkable William Hopkins. This wide-ranging from this book. book tells the story of Hopkins and the education Internazionale Matematico Estivo (C.I.M.E.) held and subsequent careers of his top "wranglers", many More on www.springer.com/978-3-642-23791-1 in Cortona (Arezzo), Italy, June 24 - July 2, 1976 of whom went on to have illustrious careers as Due: December 31, 2011 Lectures: J. Chazarain, A. Piriou: Problèmes mixtes bishops, judges, politicians, scientists or educators. 2012. X, 444 p. Softcover hyperboliques: Première partie: Les problèmes It draws on first-hand accounts of life at Cambridge 978-3-642-23791-1 mixtes hyperboliques vérifiant 1a condition de to give the reader a glimpse inside its colleges, and ▶$49.95 Lopatinski uniforme; Deuxième partie: Propagation it charts the evolution of the curriculum and the et réflexion des singularités.- L. Gårding: Introduction slow, often reluctant, reforms that led to Cambridge’s to hyperbolicity.- T. Kato: Linear and quasi- dominance of British higher education. It surveys the linear equations of evolution of hyperbolic type.- scientific achievements of the time and considers the springer.com 25

K.W. Morton: Numerical methods for non-linear Summing Up: Highly recommended.”– J. R. Burke, Forthcoming hyperbolic equations of mathematical physics.- Gonzaga University for CHOICE Reviews D.A. Dawson, Carleton University, Ottawa ON, Canada; E. Seminars: H. Brezis: First-order quasilinear equation More on www.springer.com/978-1-4419-9478-3 Perkins, The University of British Columbia, Vancouver BC, on a torus. Usually dispatched within 3 to 5 business days Canada More on www.springer.com/978-3-642-11104-4 Due: February 28, 2012 2011. XIII, 376 p. 56 illus. (Undergraduate Texts in Superprocesses at Saint-Flour Mathematics) Hardcover 2012. 242 p. (C.I.M.E. Summer Schools, Vol. 72) Softcover Founded in 1971, the Saint-Flour Probability 978-1-4419-9478-3 978-3-642-11104-4 Summer School is organised every year by the $74.95 ▶$49.95 ▶ mathematics department of the Université Blaise Pascal at Clermont-Ferrand, France, and held in the pleasant surroundings of an 18th century seminary building in the city of Saint-Flour, located in the French Massif Central, at an altitude of 900 m.It attracts a mixed audience of up to 70 PhD students, instructors and researchers interested in probability theory, statistics, and their applications, and lasts 2 weeks. Each summer it provides, in three high- level courses presented by international specialists, a comprehensive study of some subfields in probability theory or statistics. The participants thus have the opportunity to interact with these specialists and also to present their own research work in short lectures.The lecture courses are written up by their U. Daepp, Bucknell University, Lewisburg, PA, USA; P. Gorkin, D. van Dalen, Dirk van Dalen, Utrecht University, Utrecht, authors for publication in the LNM series. The Netherlands Bucknell University, Lewisburg, PA, USA More on www.springer.com/978-3-642-25431-4 Reading, Writing, and Proving The Selected Correspondence of Due: January 3, 2012 A Closer Look at Mathematics L.E.J. Brouwer 2012. Approx. 310 p. With Reprint of lectures originally published in the Lecture Notes in Mathematics volumes Reading, Writing, and Proving is designed to L.E.J. Brouwer (1881-1966) is best known for his 1541 (1993) and 1781 (2002).. (Probability at Saint-Flour, guide mathematics students during their transition revolutionary ideas on topology and foundations of Vol.) Softcover from algorithm-based courses such as calculus, to mathematics (intuitionism). The present collection 978-3-642-25431-4 theorem and proof-based courses. This text not only contains a mixture of letters; university and faculty ▶$49.95 introduces the various proof techniques and other correspondence has been included, some of which foundational principles of higher mathematics in shed light on the student years, and in particular great detail, but also assists and inspires students to on the exchange of letters with his PhD adviser, develop the necessary abilities to read, write, and Korteweg. Acting as the natural sequel to the prove using mathematical definitions, examples, publication of Brouwer’s biography, this book and theorems that are required for success in provides instrumental reading for those wishing navigating advanced mathematics courses.In addition to gain a deeper understanding of Brouwer and to an introduction to mathematical logic, set theory, his role in the twentieth century. Striking a good and the various methods of proof, this textbook balance of biographical and scientific information, prepares students for future courses by providing a the latter deals with innovations in topology strong foundation in the fields of number theory, (Cantor-Schoenflies style and the new topology) and abstract algebra, and analysis. Also included are foundations. The topological period in his research a wide variety of examples and exercises as well is well represented in correspondence with Hilbert, as a rich selection of unique projects that provide Schoenflies, Poincaré, Blumenthal, Lebesgue, Baire, J.A. De Loera, University of California, Davis, CA, USA; students with an opportunity to investigate a topic Koebe, and foundational topics are discussed in J. Rambau, University of Bayreuth, Germany; F. Santos, independently or as part of a collaborative effort.New letters exchanged with Weyl, Fraenkel, Heyting, Universidad de Cantabria, Santander, Spain features of the Second Edition include the addition van Dantzig and others. There is also a large part of of formal statements of definitions at the end of correspondence on matters related to the interbellum Triangulations each chapter; a new chapter featuring the Cantor– scientific politics. This book will appeal to both Structures for Algorithms and Applications Schröder–Bernstein theorem with a spotlight on graduate students and researchers with an interest in the continuum hypothesis; over 200 new problems; topology, the history of mathematics, the foundations Triangulations appear everywhere, from volume two new student projects; and more. An electronic of mathematics, philosophy and general science. computations and meshing to algebra and topology. solutions manual to selected problems is available This book studies the subdivisions and triangulations More on www.springer.com/978-0-85729-527-9 online. From the reviews of the First Edition:“The of polyhedral regions and point sets and presents book…emphasizes Pòlya’s four-part framework for Usually dispatched within 3 to 5 business days the first comprehensive treatment of the theory problem solving (from his book How to Solve It)… 2011. VII, 529 p. 15 illus. With online files/update. (Sources of secondary polytopes and related topics. 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With Fung for MAA Reviews“… A book worthy of serious many examples and exercises, and with nearly five consideration for courses whose goal is to prepare hundred illustrations, the book gently guides readers students for upper-division mathematics courses. through the properties of the spaces of triangulations of "structured" (e.g., cubes, cyclic polytopes, lattice 26 springer.com polytopes) and "pathological" (e.g., disconnected ▶approx. $149.00 spaces of triangulations) situations using only elementary principles. More on www.springer.com/978-3-642-12970-4 Forthcoming Online orders shipping within 2-3 days R. Der, MPI-MIS, Leipzig, Germany; G. Martius, MPI-DS, Göttingen, Germany 2010. X, 539 p. 496 illus., 281 in color. (Algorithms and Computation in Mathematics, Vol. 25) Hardcover The Playful Machine 978-3-642-12970-4 Theoretical Foundation and Practical Realization ▶$84.95 of Self-Organizing Robots Autonomous robots may become our closest P. Deuflhard, Zuse-Institut Berlin (ZIB), Germany A. Defant, Carl von Ossietzky University of Oldenburg, companions in the near future. While the technology Oldenburg, Germany for physically building such machines is already Newton Methods for Nonlinear available today, a problem lies in the generation of Classical Summation the behavior for such complex machines. Nature Problems Affine Invariance and Adaptive Algorithms in Commutative and proposes a solution: young children and higher animals learn to master their complex brain-body This book deals with the efficient numerical solution Noncommutative Lp-Spaces systems by playing. Can this be an option for of challenging nonlinear problems in science and robots? How can a machine be playful? 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The in a playful and obviously embodiment- related term 'affine invariance' means that the presented over a noncommutative measure space (a von way: a dog-like robot starts playing with a barrier, Neumann algebra of operators acting on a Hilbert algorithms and their convergence analysis are eventually jumping or climbing over it; a snakebot invariant under one out of four subclasses of space together with a faithful normal state on this develops coiling and jumping modes; humanoids algebra). affine transformations of the problem to be solved. develop climbing behaviors when fallen into a Compared to traditional textbooks, the distinguishing More on www.springer.com/978-3-642-20437-1 pit, or engage in wrestling-like scenarios when affine invariance approach leads to shorter theorems Usually dispatched within 3 to 5 business days encountering an opponent. The book also develops and proofs and permits the construction of fully guided self-organization, a new method that helps adaptive algorithms. Lots of numerical illustrations, 2011. VIII, 171 p. (Lecture Notes in Mathematics, Vol. 2021) to make the playful machines fit for fulfilling tasks Softcover comparison tables, and exercises make the text useful in the real world.The book provides two levels of 978-3-642-20437-1 in computational mathematics classes. At the same presentation. Students and scientific researchers ▶$49.95 time, the book opens many directions for possible interested in the field of robotics, self-organization future research. and dynamical systems theory may be satisfied by the in-depth mathematical analysis of the principle, the More on www.springer.com/978-3-642-23898-7 Forthcoming bootstrapping scenarios, and the emerging behaviors. Usually dispatched within 3 to 5 business days But the book additionally comes with a robotics J. Demongeot, Université Joseph Fourier, La Tronche, simulator inviting also the non- scientific reader to 2011. XII, 424 p. 49 illus. (Springer Series in France; D. Hilhorst, CNRS and University of Paris-Sud 11, Computational Mathematics, Vol. 35) Softcover Orsay CX, France; H. Matano, University of Tokyo, Japan; M. simply enjoy the fabulous world of playful machines 978-3-642-23898-7 Mimura, Meiji University, Kawasaki, Japan (Eds.) by performing the numerous experiments. $74.95 More on www.springer.com/978-3-642-20252-0 ▶ Spatio-temporal Patterns: From Due: December 21, 2011 Mathematical to Biomedical 2012. XX, 336 p. 118 illus., 103 in color. (Cognitive Systems Forthcoming Monographs, Vol. 15) Hardcover Applications 978-3-642-20252-0 J.-D. Deuschel, Technische Universität Berlin, Germany; B. The aim of the book can be described as follows: ▶$109.00 Gentz, Bielefeld University, Germany; W. König, Weierstrass morphogenetic processes appearing during the Institute Berlin, Germany; M. von Renesse, Technische development of biological organisms as well as genetic Universität Berlin, Germany; M. Scheutzow, Technische Universität Berlin, Germany; U. Schmock, Vienna University and epigenetic spatio-temporal patterns observed A. Derighetti, Ecole polytechnique fédérale de Lausanne, of Technology, Austria (Eds.) in control mechanisms of crucial phases of their life Lausanne, Switzerland (reproduction, ageing, epidemic spread,...) are due Probability in Complex Physical to the combination of physico-chemical phenomena Convolution Operators on Groups like diffusion, convection, chemotaxy, haptotaxy,... Systems This volume is devoted to a systematic study of the The aim of the book is to present basic mathematical In Honour of Erwin Bolthausen and Jürgen Banach algebra of the convolution operators of a tools underlying the mathematical models used to Gärtner explain the spatio-temporal patterns associated to locally compact group. Inspired by classical Fourier the observed phenomenology, and parallelly some analysis we consider operators on Lp spaces, arriving Probabilistic approaches have played a prominent examples of modelling and simulation of these at a description of these operators and Lp versions of role in the study of complex physical systems for phenomena (even through non classical ways like the theorems of Wiener and Kaplansky-Helson. more than thirty years. This volume collects twenty multiagent or individual-centered systems). More on www.springer.com/978-3-642-20655-9 articles on various topics in this field, including self- interacting random walks and polymer models in More on www.springer.com/978-3-642-19547-1 Usually dispatched within 3 to 5 business days random and non-random environments, branching Due: May 24, 2012 2011. XII, 171 p. (Lecture Notes of the Unione Matematica processes, Parisi formulas and metastability in spin 2012. X, 340 p. 150 illus., 50 in color. (Springer Proceedings Italiana, Vol. 11) Softcover glasses, and hydrodynamic limits for gradient Gibbs in Mathematics, Vol. 14) Hardcover 978-3-642-20655-9 models. The majority of these articles contain original 978-3-642-19547-1 ▶$49.95 results at the forefront of contemporary research; springer.com 27 some of them include review aspects and summarize requiring a single-source assessment of current developments. 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Di Nunno, University of Oslo, Norway; B. Øksendal, University of Oslo, Norway (Eds.) Advanced Mathematical Methods for Finance This book presents innovations in the mathematical foundations of financial analysis and numerical methods for finance and applications to the modeling of risk. The topics selected include measures of risk, M.O. Deville, Swiss Federal Institute of Technology EPFL, credit contagion, insider trading, information in Lausanne, Switzerland; Th.B. Gatski, Old Dominion finance, stochastic control and its applications to University, Norfolk, VA, USA portfolio choices and liquidation, models of liquidity, pricing, and hedging. The models presented are based Mathematical Modeling for on the use of Brownian motion, Lévy processes and E. DiBenedetto, Vanderbilt University, Nashville, TN, USA; U. Complex Fluids and Flows jump diffusions. Moreover, fractional Brownian Gianazza, University of Pavia, Italy; V. Vespri, University of motion and ambit processes are also introduced at Florence, Italy Mathematical Modeling for Complex Fluids various levels. The chosen blend of topics gives an and Flows provides researchers and engineering overview of the frontiers of mathematics for finance. Harnack's Inequality for practitioners encountering fluid flows with state- New results, new methods and new models are all Degenerate and Singular of-the-art knowledge in continuum concepts and introduced in different forms according to the subject. associated fluid dynamics. In doing so it supplies Additionally, the existing literature on the topic Parabolic Equations the means to design mathematical models of these is reviewed. The diversity of the topics makes the While degenerate and singular parabolic equations flows that adequately express the engineering physics book suitable for graduate students, researchers and have been researched extensively for the last 25 years, involved. It exploits the implicit link between the practitioners in the areas of financial modeling and the Harnack inequality for nonnegative solutions turbulent flow of classical Newtonian fluids and quantitative finance. The chapters will also be of to these equations has received relatively little the laminar and turbulent flow of non-Newtonian interest to experts in the financial market interested attention. Recent progress has been made on the fluids such as those required in food processing and in new methods and products. This volume presents Harnack inequality to the point that the theory is polymeric flows.The book develops a descriptive the results of the European ESF research networking now reasonably complete—except for the singular mathematical model articulated through continuum program Advanced Mathematical Methods for subcritical range—both for the p-Laplacian and mechanics concepts for these non-Newtonian, Finance. the porous medium equations. 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The work and their treatment with the Boltzmann equation. $119.00 ▶ is mathematical in nature; its aim is to introduce a Both solution and modeling strategies for turbulent novel set of tools and techniques that deepen our flows are laid out using continuum concepts, understanding of the notions of degeneracy and including a description of constructing polynomial D.A. Di Pietro, IFP Energies nouvelles, Rueil-Malmaison, singularity in partial differential equations. Although representations and accounting for non-inertial and France; A. Ern, Université Paris Est, Marne-la-Vallée, France related in spirit to a monograph by the first author in curvature effects.Ranging from fundamental concepts this subject, this book is a self-contained treatment to practical methodology, and including discussion Mathematical Aspects of with a different perspective. Here the focus is entirely of emerging technologies, this book is ideal for those Discontinuous Galerkin Methods on the Harnack estimates and on their applications; the authors use the Harnack inequality to reprove This book introduces the basic ideas for building a number of known regularity results. This book is discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical 28 springer.com aimed at researchers and advanced graduate students difficult and their solutions must arise from creative Schwarz’s inequality for positive selfadjoint operators who work in this fascinating field. and clever insights rather than tedious calculations.In as well as some results for the spectrum of this class More on www.springer.com/978-1-4614-1583-1 preparation for the distinguished International of operators are presented. This text introduces the Mathematical Olympiad (IMO) competition, each reader to the fundamental results for polynomials in Usually dispatched within 3 to 5 business days participating country selects the top six high school a linear operator, continuous functions of selfadjoint 2012. XIII, 278 p. 6 illus. (Springer Monographs in students every year through a series of national operators as well as the step functions of selfadjoint Mathematics) Hardcover olympiads. These students are invited to participate in operators. The spectral decomposition for this class of 978-1-4614-1583-1 the IMO, usually held in July. The IMO is a two-day operators, which play a central role in the rest of the ▶$99.00 contest where each day competitors are given three book and its consequences are introduced. At the end problems which they work on independently. The of the chapter, some classical operator inequalities IMO host country appoints a special committee to are presented as well.Recent new results that deal L. Diening, LMU Munich, Germany; P. Harjulehto, University which each country submits up to six problems. From with different aspects of the famous Jensen operator of Helsinki, Finland; P. Hästö, University of Oulu, Finland; M. this composite “longlist” of problems, a “shortlist” inequality are explored through the second chapter. Ruzicka, University of Freiburg, Germany of 25-30 problems is created. The jury, consisting These include but are not limited to the operator of one professor from each country, makes the final version of the Dragomir-Ionescu inequality, the Lebesgue and Sobolev Spaces selection from the shortlist a few days before the IMO Slater type inequalities for operators and its inverses, begins.The IMO has sparked a burst of creativity Jensen’s inequality for twice differentiable functions with Variable Exponents among enthusiasts to create new and interesting whose second derivatives satisfy some upper and The field of variable exponent function spaces has mathematics problems. It can be safely said that lower bound conditions and Jensen’s type inequalities witnessed an explosive growth in recent years. the IMO and shortlisted problems are among the for log-convex functions. Hermite-Hadamard’s The standard reference article for basic properties well-crafted problems created in a given year. This type inequalities for convex functions and the is already 20 years old. Thus this self-contained book attempts to gather all of these problems with corresponding results for operator convex functions monograph collecting all the basic properties of their solutions. In addition, the book contains all are also presented.The Čebyšev, (Chebyshev) variable exponent Lebesgue and Sobolev spaces the available longlist problems, for a total of more inequality that compares the integral/discrete mean is timely and provides a much-needed accessible than 2000 problems. From the reviews of the first of the product with the product of the integral/ reference work utilizing consistent notation and edition:"The International Mathematical Olympiad, discrete means is famous in the literature devoted terminology. Many results are also provided with or IMO is the premier international competition for to Mathematical Inequalities. The sister inequality new and improved proofs. The book also presents a talented high school mathematics students. … This due to Grüss which provides error bounds for the number of applications to PDE and fluid dynamics. book collects statements and solutions of all of the magnitude of the difference between the integral problems ever set in the IMO, together with many mean of the product and the product of the integral More on www.springer.com/978-3-642-18362-1 problems proposed for the contest. … serves as a means has also attracted much interest since it has Usually dispatched within 3 to 5 business days vast repository of problems at the Olympiad level, been discovered in 1935 with more than 200 papers 2011. IX, 509 p. 10 illus. (Lecture Notes in Mathematics, Vol. useful both to students … and to faculty looking published so far. The last part of the book is devoted 2017) Softcover for hard elementary problems. No library will want to the operator versions of these famous results for 978-3-642-18362-1 to be without a copy, nor will anyone involved in continuous functions of selfadjoint operators on ▶$119.00 mathematics competitions …" — (Fernando Q. complex Hilbert spaces. Various particular cases Gouvêa, MathDL, March, 2006) of interest and related results are presented as well. More on www.springer.com/978-1-4419-9853-8 This book is intended for use by both researchers in various fields of Linear Operator Theory and Usually dispatched within 3 to 5 business days Mathematical Inequalities, domains which have 2011. XIV, 809 p. 124 illus. (Problem Books in Mathematics) grown exponentially in the last decade, as well as Hardcover by postgraduate students and scientists applying 978-1-4419-9853-8 inequalities in their specific areas. ▶$89.95 More on www.springer.com/978-1-4614-1520-6 Usually dispatched within 3 to 5 business days 2012. XII, 121 p. 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D. Djukić, University of Toronto, ON, Canada; V. Janković, Belgrade University, Belgrade, Serbia; I. Matić, Duke University, Durham, NC, USA; N. Petrović, Texas A&M University at Qatar, Science Department, Doha, Qatar The IMO Compendium A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2009 Second Edition S.S. Dragomir, Victoria University, Melbourne ,VIC, Australia The IMO Compendium is the ultimate collection of Operator Inequalities of the challenging high school level mathematics problems. It is an invaluable resource, not only for students Jensen, Čebyšev and Grüss Type preparing for competitions, but for anyone who loves The main aim of this book is to present recent results S.S. Dragomir, Victoria University, Melbourne, VIC, Austraila and appreciates math. Training for mathematical concerning inequalities of the Jensen, Čebyšev and olympiads is enjoyed by talented students throughout Grüss type for continuous functions of bounded Operator Inequalities of the world. Olympiads have become one of the selfadjoint operators on complex Hilbert spaces. In primary ways to recognize and develop talented youth Ostrowski and Trapezoidal Type the introductory chapter, the author portrays with a potential to excel in areas that require abstract fundamental facts concerning bounded selfadjoint Inequalities of Ostrowski and Trapezoidal Type thinking. Although the problems appearing at IMO operators on complex Hilbert spaces. The generalized for Functions of Selfadjoint Operators on Hilbert do not involve advanced mathematics, they must be springer.com 29

Spaces presents recent results concerning Ostrowski Approximation algorithms are organized into together and to discuss new developments in and the and Trapezoidal type inequalities for continuous chapters based on the design techniques for the interaction between these fields. Correspondingly, functions of bounded Selfadjoint operators on algorithms, enabling the reader to study algorithms of the articles in this book cover a wide area of topics, complex Hilbert spaces. The first chapter recalls some the same nature with ease, and providing an improved ranging from topics in (classical) algebraic geometry fundamental facts concerning bounded Selfadjoint understanding of the design and analysis techniques through complex geometry, including (holomorphic) operators on complex Hilbert spaces. The generalized for approximation algorithms. Instructors benefit symplectic and poisson geometry, to differential Schwarz’s inequality for positive Selfadjoint operators from this approach allowing for an easy way to geometry (with an emphasis on curvature flows) and as well as some results for the spectrum of this present the ideas and techniques of algorithms with a topology. class of operators are presented. The author also unified approach. More on www.springer.com/978-3-642-20299-5 introduces and explores the fundamental results More on www.springer.com/978-1-4614-1700-2 for polynomials in a linear operator, continuous Usually dispatched within 3 to 5 business days functions of selfadjoint operators that will play a Usually dispatched within 3 to 5 business days 2011. IX, 420 p. 5 illus. (Springer Proceedings in central role throughout the book. The following Mathematics, Vol. 8) Hardcover 2012. XI, 440 p. 101 illus. (Springer Optimization and chapter is devoted to the Ostrowski’s type inequalities, 978-3-642-20299-5 Its Applications, Vol. 62) Hardcover which provide sharp error estimates in approximating ▶$149.00 978-1-4614-1700-2 the value of a function by its integral mean and can $74.95 be used to obtain a priory error bounds for different ▶ quadrature rules in approximating the Riemann integral by different Riemann sums. The author also presents recent results extending Ostrowski inequality R. Durrett, Duke University, Durham, NC, USA; Th.M. Liggett, in various directions for continuous functions of University of California, Los Angeles, CA, USA; F. Spitzer, A.-S. selfadjoint operators in complex Hilbert spaces. Sznitman, ETH Zürich, Switzerland The final chapter illustrates recent results obtained in extending trapezoidal type inequality in various Interacting Particle Systems at directions for continuous functions of selfadjoint Saint-Flour operators in complex Hilbert spaces. Applications for mid-point inequalities and some elementary functions Founded in 1971, the Saint-Flour Probability of operators as also provided. This book is intended Summer School is organised every year by the for use by researchers in various fields of Linear mathematics department of the Université Blaise Operator Theory and Mathematical Inequalities. As Pascal at Clermont-Ferrand, France, and held in the well as postgraduate students and scientists applying pleasant surroundings of an 18th century seminary G. Edgar, The Ohio State University, Columbus, OH, USA inequalities in their specific areas. building in the city of Saint-Flour, located in the French Massif Central, at an altitude of 900 m.It Measure, Topology, and Fractal More on www.springer.com/978-1-4614-1778-1 attracts a mixed audience of up to 70 PhD students, Geometry Usually dispatched within 3 to 5 business days January 31, instructors and researchers interested in probability 2012 theory, statistics, and their applications, and lasts For the Second Edition of this highly regarded 2012. VI, 120 p. (SpringerBriefs in Mathematics) Softcover 2 weeks. Each summer it provides, in three high- textbook, Gerald Edgar has made numerous additions 978-1-4614-1778-1 level courses presented by international specialists, a and changes, in an attempt to provide a clearer ▶$49.95 comprehensive study of some subfields in probability and more focused exposition. The most important theory or statistics. The participants thus have the addition is an increased emphasis on the packing opportunity to interact with these specialists and measure, so that now it is often treated on a par with also to present their own research work in short the Hausdorff measure. The topological dimensions lectures.The lecture courses are written up by their were rearranged for Chapter 3, so that the covering authors for publication in the LNM series. dimension is the major one, and the inductive dimensions are the variants. A "reduced cover More on www.springer.com/978-3-642-25297-6 class" notion was introduced to help in proofs for Due: December 12, 2011 Method I or Method II measures. Research results 2012. VIII, 326 p. With Reprint of lectures originally since 1990 that affect these elementary topics have published in the Lecture Notes in Mathematics volumes been taken into account. Some examples have been 1608 (1995), 1464 (1991), 589 (1977), and 390 (1974).. added, including Barnsley leaf and Julia set, and (Probability at Saint-Flour, Vol.) Softcover most of the figures have been re-drawn. From 978-3-642-25297-6 reviews of the First Edition: "...there has been a ▶$49.95 deluge of books, articles and television programmes D.-Z. Du, University of Texas, Dallas, TX, USA; K.-I. Ko, Stony about the beautiful mathematical objects, drawn by Brook University, NY, USA; X. Hu, Chinese Academy of computers using recursive or iterative algorithms, Sciences, Beijing, China W. Ebeling, Leibniz Universität Hannover, Germany; K. which Mandelbrot christened fractals. Gerald Edgar's Hulek, Leibniz Universität Hannover, Germany; K. Smoczyk, book is a significant addition to this deluge. Based Design and Analysis of Leibniz Universität Hannover, Germany (Eds.) on a course given to talented high-school students Approximation Algorithms at Ohio University in 1988, it is, in fact, an advanced Complex and Differential undergraduate textbook about the mathematics When precise algorithmic solutions are difficult Geometry of fractal geometry, treating such topics as metric to compute, the use of approximation algorithms spaces, measure theory, dimension theory, and even can help. Design and Analysis of Approximation Conference held at Leibniz Universität some algebraic topology...the book also contains Algorithms is a textbook for a graduate course in Hannover, September 14 – 18, 2009 many good illustrations of fractals..." - Mathematics theoretical computer science taught globally in This volume contains the Proceedings of the Teaching "The book can be recommended to universities. It can also be used as a reference work conference "Complex and Differential Geometry students who seriously want to know about the for researchers in the area of design and analysis 2009", held at Leibniz Universität Hannover, mathematical foundation of fractals, and to lecturers algorithms. There are few texts available for this September 14 - 18, 2009. It was the aim of this who want to illustrate a standard course in metric standard course, and those that do exist mainly conference to bring specialists from differential topology by interesting examples." - Christoph follow a problem-oriented format. This text follows geometry and (complex) algebraic geometry Bandt, Mathematical Reviews "...not only intended a structured, technique-oriented presentation. to fit mathematics students who wish to learn fractal 30 springer.com geometry from its beginning but also students in detailed but full of evocations, an all-embracing look computer science who are interested in the subject. at the world of mathematics and culture [For such students] the author gives the required More on www.springer.com/978-88-470-2426-7 topics from metric topology and measure theory on an elementary level. The book is written in a very Due: April 16, 2012 clear style and contains a lot of exercises which should 2012. X, 290 p. 50 illus. in color. Hardcover be worked out." - H.Haase, Zentralblatt 978-88-470-2426-7 approx. $89.95 More on www.springer.com/978-0-387-74748-4 ▶ Currently out of stock.

2008. XVI, 272 p. 169 illus., 20 in color. A. Engel, Johann Wolfgang Goethe-Universität, Frankfurt, (Undergraduate Texts in Mathematics) Hardcover Germany M. Emmer, University "La Sapienza", Rome, Italy (Ed.) 978-0-387-74748-4 Problem-Solving Strategies ▶$54.95 Mathematics and Culture III Problem-Solving Strategies is a unique collection This work contains the proceedings of the of competition problems from over twenty major "Mathematics and Culture" conference held in Venice national and international mathematical competitions in March 2002. The conference aims to act as a bridge for high school students. The discussion of problem across the various aspects of human knowledge. solving strategies is extensive. It is written for trainers While keeping mathematics as its core, it is aimed and participants of contests of all levels up to the at anyone endowed with cultural curiosity and highest level: IMO, Tournament of the Towns, and interests, whether within or (even more so) outside the noncalculus parts of the Putnam Competition. mathematics. This volume therefore covers music, It will appeal to high school teachers conducting cinema, art, theatre and literature, with topics ranging a mathematics club who need a range of simple to from Tibet to comics. complex problems and to those instructors wishing More on www.springer.com/978-3-540-34259-5 to pose a "problem of the week", "problem of the Due: April 28, 2012 month", and "research problem of the year" to their students, thus bringing a creative atmosphere into M. Einsiedler, ETH Zurich, Switzerland; Th. Ward, University their classrooms with continuous discussions of of East Anglia, UK 2012. XII, 280 p. 128 illus. With CD-ROM. Hardcover mathematical problems. This volume is a must- Ergodic Theory 978-3-540-34259-5 have for instructors wishing to enrich their teaching ▶$59.95 with some interesting non-routine problems and with a view towards Number Theory for individuals who are just interested in solving This text is a rigorous introduction to ergodic theory, difficult and challenging problems. Each chapter developing the machinery of conditional measures starts with typical examples illustrating the central and expectations, mixing, and recurrence. Beginning concepts and is followed by a number of carefully by developing the basics of ergodic theory and selected problems and their solutions. Most of the progressing to describe some recent applications to solutions are complete, but some merely point to the number theory, this book goes beyond the standard road leading to the final solution. Very few problems texts in this topic. Applications include Weyl's have no solutions. Readers interested in increasing polynomial equidistribution theorem, the ergodic the effectiveness of the book can do so by working proof of Szemeredi's theorem, the connection on the examples in addition to the problems thereby between the continued fraction map and the modular increasing the number of problems to over 1300. In surface, and a proof of the equidistribution of addition to being a valuable resource of mathematical horocycle orbits. Ergodic Theory with a view towards problems and solution strategies, this volume is the Number Theory will appeal to mathematicians with most complete training book on the market. some standard background in measure theory and M. Emmer, University La Sapienza, Roma, Italy (Ed.) More on www.springer.com/978-0-387-98219-9 functional analysis. No background in ergodic theory Usually dispatched within 3 to 5 business days or Lie theory is assumed, and a number of exercises Imagine Math 1998. X, 406 p. 223 illus. (Problem Books in Mathematics) and hints to problems are included, making this Between Culture and Mathematics Softcover the perfect companion for graduate students and 978-0-387-98219-9 researchers in ergodic theory, homogenous dynamics Imagine mathematics, imagine with the help of $74.95 or number theory. mathematics, imagine new worlds, new geometries, ▶ new forms. The volumes in the series “Imagine More on www.springer.com/978-0-85729-020-5 Math” are intended to contribute to grasping how Usually dispatched within 3 to 5 business days much that is interesting and new is happening in B. Engquist, University of Texas at Austin, TX, USA; O. the relationships between mathematics, imagination Runborg, Royal Institute of Technology, Stockholm, Sweden; 2011. XXX, 467 p. 52 illus. (Graduate Texts in and culture. With a look at the past, at figures and Y.-H.R. Tsai, University of Austin at Texas, TX, USA (Eds.) Mathematics, Vol. 259) Hardcover events, that help to understand the phenomena of 978-0-85729-020-5 today.It is no coincidence that this volume contains Numerical Analysis of Multiscale ▶$74.95 an homage to the great Italian artist of the 1700s, Computations Andrea Pozzo, and his perspective views. Theatre, art and architecture are the topics of choice, along Proceedings of a Winter Workshop at the Banff with music, literature and cinema. No less important International Research Station 2009 are applications of mathematics to medicine and This book is a snapshot of current research economics.The treatment is rigorous but captivating, in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numerical algorithms as well as practical computational advice for analysing single and springer.com 31 multiphysics models containing a variety of scales in time and space. Complex fluids, porous media flow and oscillatory dynamical systems are treated in some extra depth, as well as tools like analytical and numerical homogenization, and the fast multipole method. More on www.springer.com/978-3-642-21942-9 Usually dispatched within 3 to 5 business days 2012. X, 420 p. 108 illus., 42 in color. (Lecture Notes in Computational Science and Engineering, Vol. 82) Hardcover 978-3-642-21942-9 ▶$149.00 A. Etheridge, University of Oxford, UK A. Figà Talamanca, Università di Firenze, Italy (Ed.) Some Mathematical Models from Harmonic Analysis and Group Population Genetics Representations École d'Été de Probabilités de Saint-Flour Lectures given at a Summer School of the Centro XXXIX-2009 Internazionale Matematico Estivo (C.I.M.E.) held This work reflects sixteen hours of lectures delivered in Cortona (Arezzo), Italy, June 24 - July 9, 1980 by the author at the 2009 St Flour summer school Lectures: A. Auslander, R. Tolimeri: Nilpotent in probability. It provides a rapid introduction to a groups and abelian varieties.- M Cowling: Unitary range of mathematical models that have their origins and uniformly bounded representations of some in theoretical population genetics. The models fall simple Lie groups.- M. Duflo: Construction into two classes: forwards in time models for the de representations unitaires d’un groupe de evolution of frequencies of different genetic types Lie.- R. Howe: On a notion of rank for unitary in a population; and backwards in time (coalescent) R.H. Enns, Simon Fraser University, Burnaby, BC, Canada representations of the classical groups.- V.S. models that trace out the genealogical relationships Varadarajan: Eigenfunction expansions of semisimple It's a Nonlinear World between individuals in a sample from the population. Lie groups.- R. Zimmer: Ergodic theory, group Some, like the classical Wright-Fisher model, date representations and rigidity.- Seminars: A. Koranyi: Drawing examples from mathematics, physics, right back to the origins of the subject. Others, like the Some applications of Gelfand pairs in classical chemistry, biology, engineering, economics, medicine, multiple merger coalescents or the spatial Lambda- analysis. Fleming-Viot process are much more recent. All share politics, and sports, this book illustrates how More on www.springer.com/978-3-642-11115-0 nonlinear dynamics plays a vital role in our world. a rich mathematical structure. Biological terms are Examples cover a wide range from the spread and explained, the models are carefully motivated and Due: February 28, 2012 possible control of communicable diseases, to the lack tools for their study are presented systematically. 2011. 484 p. (C.I.M.E. Summer Schools, Vol. 82) Softcover of predictability in long-range weather forecasting, More on www.springer.com/978-3-642-16631-0 978-3-642-11115-0 $69.95 to competition between political groups and nations. Usually dispatched within 3 to 5 business days ▶ After an introductory chapter that explores what it means to be nonlinear, the remainder of Part I 2011. VIII, 119 p. (École d'Été de Probabilités de Saint-Flour, Vol. 2012) Softcover covers nonlinear mathematical concepts such as 978-3-642-16631-0 Forthcoming fixed points, limit cycles, fractals, chaos, bifurcations, $49.95 and solitons, and nonlinear diagnostic tools such ▶ F. Finster, Universität Regensburg, Germany; O. Müller, as fixed point analysis, bifurcation diagrams, and Universität Regensburg, Germany; M. Nardmann, Universität Lyapunov exponents, to name a few. Part II of the Hamburg, Germany; J. Tolksdorf, Max-Planck-Institut für text presents illustrative examples of nonlinear S. Ferrara, Cern, Geneva, Switzerland; R. Fioresi, University of Mathematik in den Naturwissenschaften, Leipzig, Germany; E. Zeidler, Max-Planck-Institut für Mathematik in den dynamics that are highly relevant to the contemporary Bologna, Italy; V.S. Varadarajan, UCLA Los Angeles CA, USA Naturwissenschaften, Leipzig, Germany (Eds.) world. At the end of each chapter, a wide variety (Eds.) of problems are presented which extend the ideas developed in the chapter as well as allow the reader Supersymmetry in Mathematics Quantum Field Theory and to explore other aspects of our nonlinear world. The and Physics Gravity mathematical level of the text assumes good working UCLA Los Angeles, USA 2010 Conceptual and Mathematical Advances in the knowledge of basic calculus and prior exposure to Search for a Unified Framework ordinary differential equations and the wave and Supersymmetry was created by the physicists in the diffusion equations. The book may be used at the 1970's to give a unified treatment of fermions and One of the most challenging problems of undergraduate or graduate level to prepare science bosons, the basic constituents of matter. Since then its contemporary theoretical physics is the and engineering students for problems in the "real mathematical structure has been recognized as that of mathematically rigorous construction of a world" or for self-study by practicing scientists and a new development in geometry, and mathematicians theory which describes gravitation and the other engineers. The more casual reader can simply read the have busied themselves with exploring this aspect. fundamental physical interactions within a common book for intellectual enjoyment. This volume collects recent advances in this field, framework. The physical ideas which grew from attempts to develop such a theory require highly More on www.springer.com/978-0-387-75338-6 both from a physical and a mathematical point of view, with an accent on a rigorous treatment of the advanced mathematical methods and radically new Usually dispatched within 3 to 5 business days various questions raised. physical concepts. This book presents different approaches to a rigorous unified description of More on www.springer.com/978-3-642-21743-2 2011. XII, 384 p. 145 illus., 8 in color. (Springer quantum fields and gravity. It contains a carefully Undergraduate Texts in Mathematics and Technology) Usually dispatched within 3 to 5 business days selected cross-section of lively discussions which Hardcover 2011. X, 273 p. (Lecture Notes in Mathematics, Vol. 2027) took place in autumn 2010 at the fifth conference 978-0-387-75338-6 Softcover "Quantum field theory and gravity - Conceptual $59.95 ▶ 978-3-642-21743-2 and mathematical advances in the search for a ▶$59.95 unified framework" in Regensburg, Germany. In 32 springer.com the tradition of the other proceedings covering this Wiskunde & Informatica, Amsterdam, The Netherlands; L. commutative algebra and algebraic geometry with a series of conferences, a special feature of this book is Davies, Universität Duisburg-Essen, Germany (Eds.) combinatorial flavour. the exposition of a wide variety of approaches, with More on www.springer.com/978-3-642-19491-7 the intention to facilitate a comparison. The book is Mathematical Methods for Usually dispatched within 3 to 5 business days mainly addressed to mathematicians and physicists Signal and Image Analysis and who are interested in fundamental questions of 2011. XIV, 174 p. 63 illus., 37 in color. (Abel Symposia, Vol. 6) mathematical physics. It allows the reader to obtain a Representation Hardcover broad and up-to-date overview of a fascinating active 978-3-642-19491-7 Mathematical Methods for Signal and Image Analysis research area. ▶$124.00 and Representation presents the mathematical More on www.springer.com/978-3-0348-0042-6 methodology for generic image analysis tasks. Due: February 29, 2012 In the context of this book an image may be any 2012. XIV, 380 p. 49 illus. Hardcover m-dimensional empirical signal living on an n- 978-3-0348-0042-6 dimensional smooth manifold (typically, but not ▶approx. $139.00 necessarily, a subset of spacetime). The existing literature on image methodology is rather scattered and often limited to either a deterministic or a statistical point of view. In contrast, this book brings together these seemingly different points of view in order to stress their conceptual relations and formal analogies.Furthermore, it does not focus on specific applications, although some are detailed for the sake of illustration, but on the methodological frameworks on which such applications are built, making it an ideal companion for those seeking a L. Formaggia, Politecnico di Milano, Italia; F. Saleri, Politecnico di Milano, Italia; A. Veneziani, Politecnico di rigorous methodological basis for specific algorithms Milano, Italia as well as for those interested in the fundamental methodology per se.Covering many topics at the Solving Numerical PDEs: forefront of current research, including anisotropic diffusion filtering of tensor fields, this book will be Problems, Applications, Exercises F. Flandoli, University of Pisa, Italy of particular interest to graduate and postgraduate students and researchers in the fields of computer This book aims at introducing students to the Random Perturbation of PDEs and vision, medical imaging and visual perception. numerical approximation of Partial Differential Equations (PDEs). One of the difficulties of this Fluid Dynamic Models More on www.springer.com/978-1-4471-2352-1 subject is to identify the right trade-off between École d’Été de Probabilités de Saint-Flour XL – Due: February 29, 2012 theoretical concepts and their use in practice. 2010 2012. XII, 344 p. 100 illus., 50 in color. (Computational With that collection of examples and exercises we This volume deals with the random perturbation of Imaging and Vision, Vol. 41) Hardcover try to address this issue by illustrating "standard" PDEs which lack well-posedness, mainly because 978-1-4471-2352-1 examples which focus on basic concepts of Numerical of their non-uniqueness, in some cases because of ▶$149.95 Analysis, as well as problems derived from practical blow-up. The aim is to show that noise may restore applications which the student is encouraged to uniqueness or prevent blow-up. This is not a general formalize in terms of PDEs, analyze and solve. The latter examples are derived from the experience of the or easy-to-apply rule, and the theory presented in the G. Fløystad, University of Bergen, Norway; T. Johnsen, authors in research project developed in collaboration book is in fact a series of examples with a few unifying University of Tromsø, Norway; A.L. Knutsen, University of with scientists of different fields (biology, medicine, ideas. The role of additive and bilinear multiplicative Bergen, Norway (Eds.) noise is described and a variety of examples are etc.) and industry. We wanted this book to be useful included, from abstract parabolic evolution equations Combinatorial Aspects of both to readers more interested in the theoretical with non-Lipschitz nonlinearities to particular aspects, and also to those more concerned with the fluid dynamic models, like the dyadic model, linear Commutative Algebra and numerical implementation. To this aim, solutions transport equations and motion of point vortices. Algebraic Geometry to the exercises have been subdivided in three parts. The first concerns the mathematical analysis of the More on www.springer.com/978-3-642-18230-3 The Abel Symposium 2009 problem, the second its numerical approximation Usually dispatched within 3 to 5 business days The Abel Symposium 2009 "Combinatorial aspects and the third part is devoted to implementation 2011. IX, 176 p. 10 illus. (École d'Été de Probabilités de Saint- of Commutative Algebra and Algebraic Geometry", aspects and the analysis of the results. The book Flour, Vol. 2015) Softcover held at Voss, Norway, featured talks by leading consists of three parts. The first deals with basic 978-3-642-18230-3 researchers in the field. This is the proceedings material and results provided as useful reference for ▶$49.95 of the Symposium, presenting contributions on the other sections. In particular, we recall the basics syzygies, tropical geometry, Boij-Söderberg theory, of functional analysis and the finite element method. Schubert calculus, and quiver varieties. The volume The second part deals with steady elliptic problems, solved with finite elements or finite differences, Forthcoming also includes an introductory survey on binomial ideals with applications to hypergeometric series, while in the third part we address time-dependent L. Florack, Eindhoven University of Technology, The combinatorial games and chemical reactions. The problems, including linear hyperbolic systems and Netherlands; R. Duits, Eindhoven University of Technology, contributions pose interesting problems, and offer up- Navier-Stokes equations. Two appendices discuss The Netherlands; G. Jongbloed, Eindhoven University of to-date research on some of the most active fields of some practical implementation issues and three- Technology, The Netherlands; M.-C. van Lieshout, Centrum dimensional applications. Each section contains a springer.com 33 brief introduction to the subject to make this book self book self contained. Modelers in the fields of finance, Czech Republic; R. Herbin, Université Aix-Marseille, France; contained. insurance, network science and environmental studies F. Hubert, Université Aix-Marseille, France (Eds.) will find this book to be an essential reference. More on www.springer.com/978-88-470-2411-3 Finite Volumes for Complex Due: March 28, 2012 More on www.springer.com/978-1-4419-9472-1 Usually dispatched within 3 to 5 business days Applications VI Problems & 2012. X, 434 p. (La Matematica per il 3+2) Softcover 2011. IX, 123 p. 1 illus. (Springer Series in Operations Perspectives 978-88-470-2411-3 Research and Financial Engineering) Hardcover FVCA 6, International Symposium, Prague, June ▶$69.95 978-1-4419-9472-1 6-10, 2011 ▶$99.00 Finite volume methods are used for F. Forstnerič, University of Ljubljana, Slovenia various applications in fluid dynamics, magnetohydrodynamics, structural analysis Stein Manifolds and Holomorphic or nuclear physics. A closer look reveals many interesting phenomena and mathematical or Mappings numerical difficulties, such as true error analysis and The Homotopy Principle in Complex Analysis adaptivity, modelling of multi-phase phenomena or fitting problems, stiff terms in convection/ None. The Ergebnisse volumes do not have back diffusion equations and sources. To overcome cover texts. existing problems and to find solution methods for More on www.springer.com/978-3-642-22249-8 future applications requires many efforts and always Usually dispatched within 3 to 5 business days new developments. The goal of The International 2011. XII, 489 p. 27 illus. (Ergebnisse der Mathematik und Symposium on Finite Volumes for Complex ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Applications VI is to bring together mathematicians, Mathematics, Vol. 56) Hardcover A. Fowler, MACSI, Department of Mathematics & Statistics, physicists and engineers dealing with Finite Volume 978-3-642-22249-8 University of Limerick, Limerick, Ireland Techniques in a wide context. This book, divided in ▶$189.00 two volumes, brings a critical look at the subject (new Mathematical Geoscience ideas, limits or drawbacks of methods, theoretical as well as applied topics). Mathematical Geoscience is an expository textbook More on www.springer.com/978-3-642-20670-2 which aims to provide a comprehensive overview of a number of different subjects within the Earth Usually dispatched within 3 to 5 business days and environmental sciences. Uniquely, it treats 2011. XVII, 1065 p. 106 illus. in color. (Springer Proceedings its subjects from the perspective of mathematical in Mathematics, Vol. 4) Hardcover modelling with a level of sophistication that is 978-3-642-20670-2 appropriate to their proper investigation. The ▶$219.00 material ranges from the introductory level, where it can be used in undergraduate or graduate courses, to research questions of current interest. The chapters end with notes and references, which provide an entry point into the literature, as well as allowing S. Foss, Heriot-Watt University, Edinburgh, UK; D. discursive pointers to further research avenues. The Korshunov, Sobolev Institute of Mathematics, Novosibirsk, introductory chapter provides a condensed synopsis RU; S. Zachary, Heriot-Watt University, Edinburgh, UK of applied mathematical techniques of analysis, as used in modern applied mathematical modelling. An Introduction to Heavy-Tailed There follows a succession of chapters on climate, and Subexponential Distributions ocean and atmosphere dynamics, rivers, dunes, landscape formation, groundwater flow, mantle Heavy-tailed probability distributions are an convection, magma transport, glaciers and ice sheets, important component in the modeling of many and sub-glacial floods. This book introduces a whole stochastic systems. They are frequently used to range of important geoscientific topics in one single E. Freitag, Universität Heidelberg, Heidelberg, Germany accurately model inputs and outputs of computer volume and serves as an entry point for a rapidly and data networks and service facilities such as call expanding area of genuine interdisciplinary research. Complex Analysis 2 By addressing the interplay between mathematics centers. They are an essential for describing risk Riemann Surfaces, Several Complex Variables, processes in finance and also for insurance premia and the real world, this book will appeal to graduate pricing, and such distributions occur naturally students, lecturers and researchers in the fields of Abelian Functions, Higher Modular Functions in models of epidemiological spread. The class applied mathematics, the environmental sciences and The book provides a complete presentation of includes distributions with power law tails such engineering. complex analysis, starting with the theory of Riemann as the Pareto, as well as the lognormal and certain More on www.springer.com/978-0-85729-699-3 surfaces, including uniformization theory and a Weibull distributions. This monograph defines the detailed treatment of the theory of compact Riemann Usually dispatched within 3 to 5 business days classes of long-tailed and subexponential distributions surfaces, the Riemann-Roch theorem, Abel's theorem in one dimension and provides a complete and and Jacobi's inversion theorem. This motivates a 2011. XIX, 883 p. 211 illus., 6 in color. comprehensive description of their properties. (Interdisciplinary Applied Mathematics, Vol. 36) Hardcover short introduction into the theory of several complex New results are presented in a simple, coherent 978-0-85729-699-3 variables, followed by the theory of Abelian functions and systematic way. This leads to a comprehensive $89.95 up to the theta theorem. The last part of the book exposition of tail properties of sums of independent ▶ random variables whose distributions belong to the long-tailed and subexponential class.The book includes a discussion of and references to J. Fořt, FME, CTU Prague, Czech Republic; J. Fürst, FME, contemporary areas of applications and also contains CTU Prague, Czech Republic; J. Halama, FME, CTU Prague, preliminary mathematical material which makes the 34 springer.com provides an introduction into the theory of higher Forthcoming in particular new sections have been added on modular functions. rational interpolation, interpolation using H^{\nfty} M. Frémond, Università di Roma "Tor Vergata", Italy More on www.springer.com/978-3-642-20553-8 functions, and tensor products of models.Review from first edition:“…the approach pursued by the Usually dispatched within 3 to 5 business days Phase Change in Mechanics author is of unconventional beauty and the material Predictive theories of phenomena involving covered by the book is unique.” (Mathematical 2011. XIII, 506 p. 51 illus. (Universitext) Softcover Reviews, A. Böttcher) 978-3-642-20553-8 phase change with applications in engineering are investigated in this volume, e.g. solid-liquid phase $84.95 More on www.springer.com/978-1-4614-0337-1 ▶ change, volume and surface damage, and phase Usually dispatched within 3 to 5 business days change involving temperature discontinuities. Many other phase change phenomena such 2012. XVI, 411 p. (Universitext) Softcover as solid-solid phase change in shape memory 978-1-4614-0337-1 alloys and vapor-liquid phase change are also $74.95 explored. Modeling is based on continuum thermo- ▶ mechanics. This involves a renewed principle of virtual power introducing the power of the microscopic motions responsible for phase change. W. Fulton, University of Chicago, IL, USA; J. Harris, Harvard This improvement yields a new equation of motion University, Cambridge, MA, USA related to microscopic motions, beyond the classical equation of motion for macroscopic motions. The Representation Theory new theory sensibly improves the phase change A First Course modeling. For example, when warm rain falls on frozen soil, the dangerous black ice phenomenon More on www.springer.com/978-0-387-97495-8 M.N. Fried, Ben-Gurion University of the Negev, Program for can be comprehensively predicted. In addition, novel Usually dispatched within 3 to 5 business days Science and Technology Education, Marcus Family Campus, equations predict the evolution of clouds, which are Building 72, Beer-Sheva 84105, Israel themselves a mixture of air, liquid water and vapor. 1991. XV, 551 p. 144 illus. (Readings in Mathematics, More on www.springer.com/978-3-642-24608-1 Vol. 129) Softcover Edmond Halley’s Reconstruction 978-0-387-97495-8 Due: February 29, 2012 of the Lost Book of Apollonius’s ▶$59.95 2012. XIII, 303 p. 66 illus., 27 in color. (Lecture Notes of the Conics Unione Matematica Italiana, Vol. 13) Softcover Translation and Commentary 978-3-642-24608-1 ▶$89.95 Forthcoming Apollonius’s Conics was one of the greatest works of advanced mathematics in antiquity. The work P. Fung, The Hong Kong University of Science; R. Rapp, University of Mainz, Germany; S. Sharoff, University of Leeds, comprised eight books, four of which have come United Kingdom; P. Zweigenbaum, STIM – DPA/DS, Hôpital down to us in their original Greek and three in Broussais, Paris, France (Eds.) Arabic. By the time the Arabic translations were produced, the eighth book had already been lost. BUCC: Building and Using In 1710, Edmond Halley, then Savilian Professor of Geometry at Oxford, produced an edition of Comparable Corpora the Greek text of the Conics of Books I-IV, a translation into Latin from the Arabic versions of The 1990s saw a paradigm change in the use of Books V-VII, and a reconstruction of Book VIII. corpus-driven methods in NLP. In the field of Motivated by such questions as what role did multilingual NLP (such as machine translation and Halley's reconstruction play in the mathematical terminology mining) this implied the use of parallel world of the late 17th and early 18th century? and corpora. However, parallel resources are relatively what did Halley see himself learning from engaging scarce: many more texts are produced daily by native with mathematicians such as Apollonius?, Michael P.A. Fuhrmann, Ben Gurion University, Israel speakers of any given language than translated. This Fried’s work provides the first complete English situation resulted in a natural drive towards the use of translation of Halley’s reconstruction of Book VIII A Polynomial Approach to Linear comparable corpora, i.e. non-parallel texts in the same with supplementary notes on the text. The volume Algebra domain or genre. Nevertheless, this research direction also contains an introduction discussing aspects of has not produced a single authoritative source suitable Apollonius’s Conics, an investigation of Edmond A Polynomial Approach to Linear Algebra is a text for researchers and students coming to the field. The Halley's understanding of the nature of his venture which is heavily biased towards functional methods. proposed volume will provide such a reference source, into ancient mathematics, and appendices giving brief In using the shift operator as a central object, it makes identifying the state of the art in the field as well as accounts of Apollonius’s approach to conic sections linear algebra a perfect introduction to other areas future trends. and his mathematical techniques.This book will be of of mathematics, operator theory in particular. This More on www.springer.com/978-3-642-20127-1 great interest to students and researchers interested technique is very powerful as becomes clear from the Due: April 11, 2012 in the history of ancient Greek mathematics and analysis of canonical forms (Frobenius, Jordan). It 2012. 40 illus. (Theory and Applications of Natural Language should be emphasized that these functional methods mathematics in the early modern period. Processing) Hardcover are not only of great theoretical interest, but lead More on www.springer.com/978-1-4614-0145-2 978-3-642-20127-1 to computational algorithms. Quadratic forms are approx. $149.00 Usually dispatched within 3 to 5 business days treated from the same perspective, with emphasis ▶ 2012. X, 132 p. 64 illus. (Sources and Studies in the History of on the important examples of Bezoutian and Hankel Mathematics and Physical Sciences, Vol.) Hardcover forms. These topics are of great importance in applied 978-1-4614-0145-2 areas such as signal processing, numerical linear ▶$124.00 algebra, and control theory. Stability theory and system theoretic concepts, up to realization theory, are treated as an integral part of linear algebra. This new edition has been updated throughout, springer.com 35

mathematical properties of boundary-value problems related to the Navier-Stokes equations. These properties include existence, uniqueness and regularity of solutions in bounded as well as unbounded domains. Whenever the domain is unbounded, the asymptotic behavior of solutions is also investigated. This book is the new edition of the original two volume book, under the same title, published in 1994.In this new edition, the two volumes have merged into one and two more chapters on steady generalized oseen flow in exterior domains and steady Navier–Stokes flow in three- A. Galbis, Universidad de Valencia, Burjasot, Spain; M. dimensional exterior domains have been added. J. Gallier, University of Pennsylvania, Philadelphia, PA, USA Maestre, Universidad de Valencia, Burjasot, Spain Most of the proofs given in the previous edition were also updated.An introductory first chapter describes Discrete Mathematics Vector Analysis Versus Vector all relevant questions treated in the book and lists This book gives an introduction to discrete and motivates a number of significant and still open Calculus mathematics for beginning undergraduates and starts questions. It is written in an expository style so as to with a chapter on the rules of mathematical reasoning. The aim of this book is to facilitate the use of Stokes' be accessible also to non-specialists. Each chapter This book begins with a presentation of the rules of Theorem in applications. The text takes a differential is preceded by a substantial, preliminary discussion logic as used in mathematics where many examples geometric point of view and provides for the student of the problems treated, along with their motivation of formal and informal proofs are given. With this a bridge between pure and applied mathematics by and the strategy used to solve them. Also, each logical framework firmly in place, the book describes carefully building a formal rigorous development chapter ends with a section dedicated to alternative the major axioms of set theory and introduces the of the topic and following this through to concrete approaches and procedures, as well as historical natural numbers. The rest of the book deals with applications in two and three variables. Several notes. The book contains more than 400 stimulating functions and relations, directed and undirected practical methods and many solved exercises are exercises, at different levels of difficulty, that will graphs and an introduction to combinatorics, partial provided. This book tries to show that vector analysis help the junior researcher and the graduate student orders and complete induction. There is a section and vector calculus are not always at odds with one to gradually become accustomed with the subject. on public key cryptography and RSA, with complete another. Key topics include:-vectors and vector Finally, the book is endowed with a vast bibliography proofs of Fermat's little theorem and the correctness fields;-line integrals;-regular k-surfaces;-flux of a that includes more than 500 items. Each item brings of the RSA scheme, as well as explicit algorithms vector field;-orientation of a surface;-differential a reference to the section of the book where it is to perform modular arithmetic. The last chapter forms;-Stokes' theorem;-divergence theorem. This cited. The book will be useful to researchers and provides more graph theory where Eulerian and book is intended for upper undergraduate students graduate students in mathematics in particular Hamiltonian cycles are discussed. This book also who have completed a standard introduction to mathematical fluid mechanics and differential includes network flows, matchings, covering, bipartite differential and integral calculus for functions of equations. Review of First Edition, First Volume:“The graphs, planar graphs and state the graph minor several variables. The book can also be useful to emphasis of this book is on an introduction to the theorem of Seymour and Robertson. The book is engineering and physics students who know how to mathematical theory of the stationary Navier-Stokes highly illustrated and each chapter ends with a list handle the theorems of Green, Stokes and Gauss, but equations. It is written in the style of a textbook of problems of varying difficulty. Undergraduates in would like to explore the topic further. and is essentially self-contained. The problems are mathematics and computer science will find this book presented clearly and in an accessible manner. Every More on www.springer.com/978-1-4614-2199-3 useful. chapter begins with a good introductory discussion Due: March 31, 2012 of the problems considered, and ends with interesting More on www.springer.com/978-1-4419-8046-5 notes on different approaches developed in the Usually dispatched within 3 to 5 business days 2012. XII, 328 p. 79 illus., 59 in color. (Universitext) literature. Further, stimulating exercises are proposed. Softcover 978-1-4614-2199-3 (Mathematical Reviews, 1995) 2011. XIII, 465 p. 220 illus., 20 in color. (Universitext) Softcover $74.95 More on www.springer.com/978-0-387-09619-3 ▶ 978-1-4419-8046-5 Usually dispatched within 3 to 5 business days ▶$74.95 2011. XIV, 1018 p. 4 illus. (Springer Monographs in Mathematics) Hardcover 978-0-387-09619-3 ▶$149.00

G.P. Galdi, University of Pittsburgh, PA, USA An Introduction to the J. Gallier, University of Pennsylvania, Philadelphia, PA, USA Mathematical Theory of the Geometric Methods and Navier-Stokes Equations Applications Steady-State Problems For Computer Science and Engineering The book provides a comprehensive, detailed This book is an introduction to the fundamental and self-contained treatment of the fundamental concepts and tools needed for solving problems of a 36 springer.com geometric nature using a computer. It attempts to fill the framework provided by the Kazhdan-Lusztig author, and historical background are cited whenever the gap between standard geometry books, which are theory of cells, the authors develop an analogue of possible. This work may be used as a study guide primarily theoretical, and applied books on computer James' (1970) "characteristic-free'' approach to the for the Putnam exam, as a text for many different graphics, computer vision, robotics, or machine representation theory of Iwahori-Hecke algebras in problem-solving courses, and as a source of problems learning. This book covers the following topics: affine general.Presenting a systematic and unified treatment for standard courses in undergraduate mathematics. geometry, projective geometry, Euclidean geometry, of representations of Hecke algebras at roots of unity, Putnam and Beyond is organized for self-study by convex sets, SVD and principal component analysis, this book is unique in its approach and includes new undergraduate and graduate students, as well as manifolds and Lie groups, quadratic optimization, results that have not yet been published in book form. teachers and researchers in the physical sciences who basics of differential geometry, and a glimpse of It also serves as background reading to further active wish to expand their mathematical horizons. computational geometry (Voronoi diagrams and areas of current research such as the theory of affine More on www.springer.com/978-0-387-25765-5 Delaunay triangulations). Some practical applications Hecke algebras and Cherednik algebras.The main of the concepts presented in this book include results of this book are obtained by an interaction of Usually dispatched within 3 to 5 business days computer vision, more specifically contour grouping, several branches of mathematics, namely the theory 2007. XVI, 798 p. 50 illus. Softcover motion interpolation, and robot kinematics. In this of Fock spaces for quantum affine Lie algebras and 978-0-387-25765-5 extensively updated second edition, more material on Ariki's theorem, the combinatorics of crystal bases, convex sets, Farkas’s lemma, quadratic optimization the theory of Kazhdan-Lusztig bases and cells, and ▶$69.95 and the Schur complement have been added. The computational methods.This book will be of use to chapter on SVD has been greatly expanded and researchers and graduate students in representation now includes a presentation of PCA. The book is theory as well as any researchers outside of the field E.H. Georgoulis, University of Leicester, UK; A. Iske, well illustrated and has chapter summaries and a with an interest in Hecke algebras. University of Hamburg, Germany; J. Levesley, University of Leicester, UK (Eds.) large number of exercises throughout. It will be More on www.springer.com/978-0-85729-715-0 of interest to a wide audience including computer scientists, mathematicians, and engineers. Reviews Usually dispatched within 3 to 5 business days Approximation Algorithms for of first edition:"Gallier's book will be a useful 2011. XII, 401 p. 6 illus. (Algebra and Applications, Vol. 15) Complex Systems source for anyone interested in applications of Hardcover geometrical methods to solve problems that arise 978-0-85729-715-0 Proceedings of the 6th International Conference in various branches of engineering. It may help to ▶$129.00 on Algorithms for Approximation, Ambleside, develop the sophisticated concepts from the more UK, 31st August - 4th September 2009 advanced parts of geometry into useful tools for This book collects up-to-date papers from world applications." (Mathematical Reviews, 2001)"...it experts in a broad variety of relevant applications of will be useful as a reference book for postgraduates approximation theory, including dynamical systems, wishing to find the connection between their current multiscale modelling of fluid flow, metrology, and problem and the underlying geometry." (The geometric modelling to mention a few. The 14 Australian Mathematical Society, 2001) papers in this volume document modern trends More on www.springer.com/978-1-4419-9960-3 in approximation through recent theoretical Usually dispatched within 3 to 5 business days developments, important computational aspects and multidisciplinary applications. The book is 2011. XXVII, 680 p. 98 illus. (Texts in Applied arranged in seven invited surveys, followed by seven Mathematics, Vol. 38) Hardcover contributed research papers. The surveys of the 978-1-4419-9960-3 R. Gelca, Texas Tech University, Lubbock, TX, USA; T. first seven chapters are addressing the following ▶$89.95 Andreescu, University of Texas at Dallas, Richardson, TX, USA relevant topics: emergent behaviour in large electrical networks, algorithms for multivariate piecewise Putnam and Beyond constant approximation, anisotropic triangulation methods in adaptive image approximation, form Putnam and Beyond takes the reader on a journey assessment in coordinate metrology, discontinuous through the world of college mathematics, focusing Galerkin methods for linear problems, a numerical on some of the most important concepts and results analyst's view of the lattice Boltzmann method, in the theories of polynomials, linear algebra, real approximation of probability measures on manifolds. analysis in one and several variables, differential Moreover, the diverse contributed papers of the equations, coordinate geometry, trigonometry, remaining seven chapters reflect recent developments elementary number theory, combinatorics, and in approximation theory, approximation practice and probability. Using the W.L. Putnam Mathematical their applications. Graduate students who wish to Competition for undergraduates as an inspiring discover the state of the art in a number of important symbol to build an appropriate math background directions of approximation algorithms will find for graduate studies in pure or applied mathematics, this a valuable volume. Established researchers from the reader is eased into transitioning from problem- M. Geck, Department of Mathematical Sciences, King's statisticians through to fluid modellers will find solving at the high school level to the university College, University of Aberdeen, UK; N. Jacon, UFR Sciences interesting new approaches to solving familiar but and beyond, that is, to mathematical research. et Techniques, Besançon, France challenging problems. This book grew out of the Key features of Putnam and Beyond * Preliminary sixth in the conference series on "Algorithms for Representations of Hecke material provides an overview of common methods Approximation", which took place from 31st August of proof: argument by contradiction, mathematical to September 4th 2009 in Ambleside in the Lake Algebras at Roots of Unity induction, pigeonhole principle, ordered sets, and District of the United Kingdom. invariants. * Each chapter systematically presents a More on www.springer.com/978-3-642-16875-8 The modular representation theory of Iwahori- single subject within which problems are clustered Hecke algebras and this theory's connection to in every section according to the specific topic. * The Usually dispatched within 3 to 5 business days groups of Lie type is an area of rapidly expanding exposition is driven by more than 1100 problems 2011. X, 307 p. 128 illus. (Springer Proceedings in interest; it is one that has also seen a number of and examples chosen from numerous sources from Mathematics, Vol. 3) Hardcover breakthroughs in recent years. In classifying the around the world; many original contributions 978-3-642-16875-8 irreducible representations of Iwahori-Hecke algebras come from the authors. * Complete solutions to all ▶$149.00 at roots of unity, this book is a particularly valuable problems are given at the end of the book. The source, addition to current research in this field. Using springer.com 37

such as: boundary layer phenomena for viscous fluids, issues. But the purpose of these notes, beyond treating population dynamics,, dead core phenomena, etc. the pinning models in full detail, is also to convey It addresses researchers and post-graduate students the gist, or at least the flavor, of the "overall picture," working at the interplay between mathematics which is, in many respects, unfamiliar territory for and other fields of science and technology and mathematicians. is a comprehensive introduction to the theory of More on www.springer.com/978-3-642-21155-3 nonlinear partial differential equations and its main principles also presents their real-life applications in Usually dispatched within 3 to 5 business days various contexts: mathematical physics, chemistry, 2011. XI, 130 p. 12 illus. (École d'Été de Probabilités de Saint- mathematical biology, and population genetics. Based Flour, Vol. 2025) Softcover on the authors' original work, this volume provides 978-3-642-21155-3 an overview of the field, with examples suitable for ▶$49.95 G. Geymonat, Polit. Torino, Italy (Ed.) researchers but also for graduate students entering research. The method of presentation appeals Constructive Aspects of to readers with diverse backgrounds in partial J.C. Gibbings, University of Liverpool, UK Functional Analysis differential equations and functional analysis. Each chapter includes detailed heuristic arguments, Dimensional Analysis Lectures given at a Summer School of the Centro providing thorough motivation for the material Internazionale Matematico Estivo (C.I.M.E.) held developed later in the text. The content demonstrates For experiments, dimensional analysis enables the in Erice (Trapani), Italy, June 27-July 7, 1971 in a firm way that partial differential equations can design, checks the validity, orders the procedure be used to address a large variety of phenomena and synthesises the data. Additionally it can provide A. Balakrishnan: A constructive approach to occurring in and influencing our daily lives. The relationships between variables where standard optimal control.- R. Glowinski: Méthodes itératives extensive reference list and index make this book analysis is not available. This widely valuable analysis duales pour la minimisation de fonctionnelles a valuable resource for researchers working in a for engineers and scientists is here presented to the convexes.- J.L. Lions: Approximation numérique des variety of fields and who are interested in phenomena student, the teacher and the researcher. It is the first inéquations d’évolution.- G. Marchuk: Introduction modeled by nonlinear partial differential equations. complete modern text that covers developments over to the methods of numerical analysis.- U. Mosco: the last three decades while closing all outstanding An introduction to the approximate solution of More on www.springer.com/978-3-642-22663-2 logical gaps. Dimensional Analysis also lists the variational inequalities.- I. Singer: Best approximation Usually dispatched within 3 to 5 business days logical stages of the analysis, so showing clearly the in normed linear spaces.- G. Strang: A Fourier 2012. XVIII, 391 p. 10 illus. (Springer Monographs in care to be taken in its use while revealing the very analysis of the finite element variational method.- Mathematics) Hardcover few limitations of application. As the conclusion of M. Zerner: Caractéristiques d’approximation des 978-3-642-22663-2 that logic, it gives the author's original proof of the compacts dans les espaces fonctionnels et problèmes ▶$124.00 fundamental and only theorem. Unlike past texts, aux limites elliptiques. Dimensional Analysis includes examples for which More on www.springer.com/978-3-642-10982-9 the answer does not already exist from standard Usually dispatched within 3 to 5 business days analysis. It also corrects the many errors present in the existing literature by including accurate solutions. 2011. 854 p. (C.I.M.E. Summer Schools, Vol. 57) Softcover Dimensional Analysis is written for all branches of 978-3-642-10982-9 engineering and science as a teaching book covering $69.95 ▶ both undergraduate and postgraduate courses, as a guide for the lecturer and as a reference volume for the researcher. More on www.springer.com/978-1-84996-316-9 Usually dispatched within 3 to 5 business days 2011. XIV, 297 p. 84 illus. Hardcover 978-1-84996-316-9 $229.00 G. Giacomin, Université Paris Diderot, Paris, France ▶ Disorder and Critical Phenomena P. Gillibert, Charles University in Prague, Czech Republic; F. Through Basic Probability Models Wehrung, CNRS, Université de Caen, France École d’Été de Probabilités de Saint-Flour XL – 2010 From Objects to Diagrams for M. Ghergu, University College Dublin, Ireland; V.D. Rӑdulescu, Romanian Academy, Bucharest, Romania Understanding the effect of disorder on critical Ranges of Functors phenomena is a central issue in statistical mechanics. Nonlinear PDEs In probabilistic terms: what happens if we perturb a This work introduces tools from the field of category system exhibiting a phase transition by introducing theory that make it possible to tackle a number Mathematical Models in Biology, Chemistry and of representation problems that have remained Population Genetics a random environment? The physics community has approached this very broad question by aiming at unsolvable to date (e.g. the determination of the range The emphasis throughout the present volume general criteria that tell whether or not the addition of a given functor). The basic idea is: if a functor lifts is on the practical application of theoretical of disorder changes the critical properties of a many objects, then it also lifts many (poset-indexed) mathematical models helping to unravel the model: some of the predictions are truly striking diagrams. underlying mechanisms involved in processes from and mathematically challenging. We approach this More on www.springer.com/978-3-642-21773-9 mathematical physics and biosciences. It has been domain of ideas by focusing on a specific class of Usually dispatched within 3 to 5 business days conceived as a unique collection of abstract methods models, the "pinning models," for which a series of 2011. CLVIII, 10 p. 19 illus. (Lecture Notes in Mathematics, dealing especially with nonlinear partial differential recent mathematical works has essentially put all Vol. 2029) Softcover equations (either stationary or evolutionary) that are the main predictions of the physics community on 978-3-642-21773-9 applied to understand concrete processes involving firm footing; in some cases, mathematicians have $49.95 some important applications related to phenomena even gone beyond, settling a number of controversial ▶ 38 springer.com

the implementation of several of the most important numerous exercises, and detailed cross-references to models used in financial engineering. The next simplify a non-linear reading of the material. part describes techniques for improving simulation More on www.springer.com/978-0-387-09444-1 accuracy and efficiency. The final third of the book addresses special topics: estimating price sensitivities, Due: March 31, 2012 valuing American options, and measuring market 2012. 350 p. 10 illus. (Graduate Texts in Mathematics, risk and credit risk in financial portfolios. The Tentative volume 935) Hardcover most important prerequisite is familiarity with the 978-0-387-09444-1 mathematical tools used to specify and analyze approx. $59.95 continuous-time models in finance, in particular the ▶ key ideas of stochastic calculus. Prior exposure to the G. Glaeser, University of Applied Arts, Vienna, Austria; K. basic principles of option pricing is useful but not Polthier, Free University of Berlin, Germany essential. The book is aimed at graduate students in A Mathematical Picture Book financial engineering, researchers in Monte Carlo simulation, and practitioners implementing models How can one visualize a curve that fills the entire in industry. Mathematical Reviews, 2004: "... this book plane or all of space? Can a polyhedron be smoothly is very comprehensive, up-to-date and useful tool turned inside out? What is the projective plane? for those who are interested in implementing Monte What does four-dimensional space look like? Can Carlo methods in a financial context." soap bubbles exist that are not spherical? How can More on www.springer.com/978-0-387-00451-8 one better understand the structure of vortices Usually dispatched within 3 to 5 business days and currents? In this book you will experience mathematics from the visual point of view, where 2003. XIV, 602 p. 70 illus. (Stochastic Modelling and fascinating images, many of them appearing in Applied Probability, Vol. 53) Hardcover J.S. Golan, University of Haifa, Israel print for the first time, provide answers to the above 978-0-387-00451-8 questions. Every picture is accompanied by a brief $74.95 explanatory text along with numerous references ▶ The Linear Algebra a Beginning and web links for further reading. This book is Graduate Student Ought to Know intended for all friends of mathematics— students, teachers, amateurs, and professionals—who want to Forthcoming Linear algebra is a living, active branch of mathematics which is central to almost all other areas see something beyond dry text and endless formulas. H. Glöckner, University of Paderborn, Germany; K.-H. Neeb, of mathematics, both pure and applied, as well as It will provide inspiration for further pursuit of topics TU Darmstadt, Germany in mathematics that may previously have seemed to computer science, to the physical, biological, and inaccessible. You will get to know mathematics from Infinite-dimensional Lie Groups. social sciences, and to engineering. It encompasses a totally new and colorful viewpoint. Enjoy the beauty an extensive corpus of theoretical results as well as and fascination of mathematics in over 300 pages General Theory and Main a large and rapidly-growing body of computational richly illustrated with more than 1000 figures on the Examples techniques. Unfortunately, in the past decade, the following topics: • Polyhedral Models • Geometry in content of linear algebra courses required to complete the Plane • Problems New and Old • Formulas and Symmetries play a decisive role in the natural sciences an undergraduate degree in mathematics has been Numbers • Functions and Limits • Curves and Knots and throughout mathematics. Infinite-dimensional depleted to the extent that they fail to provide a • Geometry and Topology of Surfaces • Minimal Lie theory deals with symmetries depending on sufficient theoretical or computational background. Surfaces and Soap Bubbles • Tilings and Packings • infinitely many parameters. Infinite-dimensional Lie Students are not only less able to formulate or even Space Forms and Dimension • Graphs and Incidence Groups provides a comprehensive introduction to follow mathematical proofs, they are also less able Geometry • Flexible Shapes • Fractals • Maps and this important subject by developing a global infinite- to understand the mathematics of the numerical Mappings • Forms and Processes in Nature and dimensional Lie theory on the basis that a Lie group is algorithms they need for applications. Certainly, the Technology simply a manifold modeled on a locally convex space, material presented in the average undergraduate course is insufficient for graduate study.This book More on www.springer.com/978-3-642-14647-3 equipped with a group structure with smooth group operations. The focus is on the local and global level, is intended to fill the gap which has developed by Due: January 8, 2012 as well as on the translation mechanisms allowing providing enough theoretical and computational 2012. XII, 339 p. 1000 illus. in color. Hardcover or preventing passage between Lie groups and Lie material to allow the advanced undergraduate 978-3-642-14647-3 algebras. Starting from scratch, the reader is led from or beginning graduate student to overcome this ▶$74.95 the basics of the theory through to the frontiers of deficiency and be able to work independently or current research. This introductory volume subtitled, in advanced courses. The book is intended to be General Theory and Main Examples, examines the used either as a self-study guide, a textbook for a P. Glasserman, Columbia University, New York, NY, USA structure theory of infinite-dimensional Lie groups course in advanced linear algebra, or as a reference by developing a broad framework of Lie theory and book. It is also designed to prepare a student for Monte Carlo Methods in Financial illustrating the general results through a detailed the linear algebra portion of prelim exams or PhD discussion of the major classes of Lie groups: linear qualifying exams.The volume is self-contained to the Engineering Lie groups, groups of (smooth) maps, groups of extent that it does not assume any previous formal knowledge of linear algebra, though the reader is Monte Carlo simulation has become an essential diffeomorphisms, and direct limit groups. From assumed to have been exposed, at least informally, tool in the pricing of derivative securities and in these, most other relevant groups can be obtained to some of the basic ideas and techniques, such as risk management. These applications have, in turn, as extensions or Lie subgroups. Together with manipulation of small matrices and the solution stimulated research into new Monte Carlo methods its companion volume subtitled, Geometry and of small systems of linear equations over the real and renewed interest in some older techniques. This Topology, these essentially self-contained texts numbers. More importantly, it assumes a seriousness book develops the use of Monte Carlo methods provide all necessary background as regards generally of purpose, considerable motivation, and a modicum in finance and it also uses simulation as a vehicle locally convex spaces, finite-dimensional Lie theory of mathematical sophistication on the part of the for presenting models and ideas from financial and differential geometry, with modest prerequisites reader.In the latest edition, new major theorems have engineering. It divides roughly into three parts. The limited to a basic knowledge of abstract algebra, point been added, as well as many new examples. There first part develops the fundamentals of Monte Carlo set topology, differentiable manifolds, and functional are over 130 additional exercises and many of the methods, the foundations of derivatives pricing, and analysis in Banach spaces. The clear exposition includes careful explanations, illustrative examples, previous exercises have been revised or rewritten. In springer.com 39 addition, a large number of additional biographical notes and thumbnail portraits of mathematicians have been included. More on www.springer.com/978-94-007-2635-2 Due: January 31, 2012

2012. XI, 549 p. 205 illus. Softcover 978-94-007-2635-2 ▶$69.95

E.A. González-Velasco, Department of Mathematical B. Goodwine, University of Notre Dame, South Bend, IN, USA Sciences, University of Massachusetts at Lowell, Lowell, MA 01854, USA Engineering Differential Journey through Mathematics Equations Creative Episodes in Its History Theory and Applications This book offers an accessible and in-depth look This book is a comprehensive treatment of at some of the most important episodes of two engineering undergraduate differential equations thousand years of mathematical history. Beginning as well as linear vibrations and feedback control. with trigonometry and moving on through While this material has traditionally been separated logarithms, complex numbers, infinite series, and into different courses in undergraduate engineering calculus, this book profiles some of the lesser known curricula. This text provides a streamlined and D. Goldfeld, Columbia University, NY, USA; J. Jorgenson, The but crucial contributors to modern day mathematics. efficient treatment of material normally covered City College of New York, NY, USA; P. Jones, Yale University, in three courses. Ultimately, engineering students New Haven, CT, USA; D. Ramakrishnan, California Institute It is unique in its use of primary sources as well as its accessibility; a knowledge of first-year calculus is study mathematics in order to be able to solve of Technology, Pasadena, CA, USA; K.A. Ribet, University of problems within the engineering realm. Engineering California at Berkeley, CA, USA; J. Tate, Harvard University, the only prerequisite. But undergraduate and graduate Differential Equations: Theory and Applications Cambridge, MA, USA (Eds.) students alike will appreciate this glimpse into the fascinating process of mathematical creation.The guides students to approach the mathematical Number Theory, Analysis and history of math is an intercontinental journey, and theory with much greater interest and enthusiasm this book showcases brilliant mathematicians from by teaching the theory together with applications. Geometry Greece, Egypt, and India, as well as Europe and the Additionally, it includes an abundance of detailed In Memory of Serge Lang Islamic world. Several of the primary sources have examples. Appendices include numerous C and FORTRAN example programs. This book is intended Serge Lang was an iconic figure in mathematics, never before been translated into English. Their interpretation is thorough and readable, and offers for engineering undergraduate students, particularly both for his own important work and for the aerospace and mechanical engineers and students in indelible impact he left on the field of mathematics, an excellent background for teachers of high school mathematics as well as anyone interested in the other disciplines concerned with mechanical systems on his students, and on his colleagues. Over the analysis and control. Prerequisites include basic and course of his career, Lang traversed a tremendous history of math.Features of this book include:-Dozens of diagrams and photographs of original sources- advanced calculus with an introduction to linear amount of mathematical ground. As he moved from algebra. subject to subject, he found analogies that led to Original translation of Rafael Bombelli's contribution important questions in such areas as number theory, to the study of complex numbers-A detailed history More on www.springer.com/978-1-4419-7918-6 arithmetic geometry and the theory of negatively of the calculus as it was being written, and a new Usually dispatched within 3 to 5 business days curved spaces. Lang's conjectures will keep many analysis of Leibniz's writings on the subject-The mathematicians occupied far into the future. In the first English translation of the first published proof 2011. XVI, 748 p. 313 illus. Hardcover spirit of Lang’s vast contribution to mathematics, of the fundamental theorem of Calculus, given by 978-1-4419-7918-6 this memorial volume contains articles by prominent James Gregory in 1668-An accessible discussion ▶$89.95 mathematicians in a variety of areas, namely number of James Gregory's work, including his invention theory, analysis and geometry, representing Lang’s of Taylor series forty years before Taylor-An original own breadth of interests. A special introduction by English translation of extended portions of works John Tate includes a brief and engaging account by José Anastácio da Cunha, a little known but of Serge Lang’s life.Contributors to the volume:D. important contributor to the convergence of series AbramovichA. AgasheD. BertrandE. BrennerA. and the differential calculus, some of whose ideas BuiumG. ChintaA. ConstantinJ. DodziukM. were later attributed to Cauchy van FrankenhuijsenW. GoldringB.H. GrossP.E. More on www.springer.com/978-0-387-92153-2 GunnellsP. IngramJ. JorgensonA. KarlssonN.M. Usually dispatched within 3 to 5 business days KatzM. KimH. KisilevskyD.Y. KleinbockB. KolevJ. 2011. XI, 466 p. 146 illus. Hardcover KramerS. LangJ. LubinG.A. MargulisJ. McGowanP. 978-0-387-92153-2 MichelM. R. MurtyV.K. MurtyM. NakamayeC. $79.95 O’NeilJ.A. ParsonP. PerryA.-M. von PippichF. ▶ PopD. RamakrishnanK.A. RibetD.E. RohrlichJ.H. SilvermanA. SintonW.A. SteinL. SzpiroJ. TateT.J. I.G. Graham, Th.Y. Hou, O. Lakkis, R. Scheichl (Eds.) TuckerM.-F. VignérasP. VojtaM. Waldschmidt More on www.springer.com/978-1-4614-1259-5 Numerical Analysis of Multiscale Due: January 31, 2012 Problems 2012. XX, 704 p. 6 illus. Hardcover The 91st London Mathematical Society Durham 978-1-4614-1259-5 Symposium took place from July 5th to 15th 2010, ▶$219.00 with more than 100 international participants attending. The Symposium focused on Numerical 40 springer.com

Analysis of Multiscale Problems and this book describing the fluid dynamics are examined in contains 10 invited articles from some of the combination with models for mass and surfactant meeting's key speakers, covering a range of topics transport. The book pursues a comprehensive of contemporary interest in this area. Articles cover approach: important modeling issues are treated, the analysis of forward and inverse PDE problems appropriate weak formulations are derived, level in heterogeneous media, high-frequency wave set and finite element discretization techniques are propagation, atomistic-continuum modeling and analyzed, efficient iterative solvers are investigated, high-dimensional problems arising in modeling implementational aspects are considered and the uncertainty. Novel upscaling and preconditioning results of numerical experiments are presented. The techniques, as well as applications to turbulent multi- book is aimed at M Sc and PhD students and other phase flow, and to problems of current interest in researchers in the fields of Numerical Analysis and materials science are all addressed. As such this book Computational Engineering Science interested in the presents the current state-of-the-art in the numerical H.-D. Gronau, University of Rostock; H.-H. Langmann, numerical treatment of two-phase incompressible analysis of multiscale problems and will be of interest Bundeswettbewerb Mathematik, Bonn; D. Schleicher, Jacobs flows. University, Bremen (Eds.) to both practitioners and mathematicians working in More on www.springer.com/978-3-642-19685-0 those fields. 50th IMO - 50 Years of Usually dispatched within 3 to 5 business days More on www.springer.com/978-3-642-22060-9 International Mathematical 2011. XVII, 480 p. 90 illus., 35 in color. (Springer Series in Due: January 28, 2012 Computational Mathematics, Vol. 40) Hardcover Olympiads 978-3-642-19685-0 2012. X, 363 p. 111 illus., 25 in color. (Lecture ▶$124.00 Notes in Computational Science and Engineering, Vol. 83) In July 2009 Germany hosted the 50th International Hardcover Mathematical Olympiad (IMO). For the very 978-3-642-22060-9 first time the number of participating countries ▶$74.95 exceeded 100, with 104 countries from all continents. Celebrating the 50th anniversary of the IMO provides an ideal opportunity to look back over the past five decades and to review its development to become a worldwide event. This book is a report about the 50th IMO as well as the IMO history. A lot of data about all the 50 IMOs are included. We list the most successful contestants, the results of the 50 Olympiads and the 112 countries that have ever taken part. It is impressive to see that many of the world’s leading research mathematicians were among the most successful IMO participants in their youth. Six of them gave presentations at a special celebration: K.-G. Grosse-Erdmann, Université de Mons, Belgium; A. Peris Bollobás, Gowers, Lovász, Smirnov, Tao and Yoccoz. Manguillot, Universitat Politècnica de València, Spain This book is aimed at students in the IMO age group and all those who have interest in this worldwide Linear Chaos G. Grioli, Università di Padova, Italy; C. Truesdell, Johns leading competition for highschool students. Hopkins University, Baltimore, USA (Eds.) It is commonly believed that chaos is linked to non- More on www.springer.com/978-3-642-14564-3 linearity, however many (even quite natural) linear Non-linear Continuum Theories Usually dispatched within 3 to 5 business days dynamical systems exhibit chaotic behavior. The Lectures given at a Summer School of the Centro study of these systems is a young and remarkably 2011. VII, 241 p. 131 illus. in color. Softcover active field of research, which has seen many Internazionale Matematico Estivo (C.I.M.E.) held 978-3-642-14564-3 landmark results over the past two decades. Linear in Bressanone (Bolzano), Italy, May 31-June 9, ▶$29.95 dynamics lies at the crossroads of several areas of 1965 mathematics including operator theory, complex B. Coleman, M.E. Gurtin: Thermodynamics and wave analysis, ergodic theory and partial differential propagation in Elastic and Viscoelastic media.- L. equations. At the same time its basic ideas can be De Vito: Sui fondamenti della meccanica di sistemi easily understood by a wide audience.Written by continui (II).- G. Fichera: Problemi elastostatici two renowned specialists, Linear Chaos provides a con ambigue condizioni al contorno.- G. Grioli: welcome introduction to this theory. Split into two Sistemi a trasformazioni reversibili.- W. Noll: the parts, part I presents a self-contained introduction foundations of mechanics.- R.A. Toupin: Elasticity to the dynamics of linear operators, while part II and electromagnetic.- C.C. Wang: Subfluids. covers selected, largely independent topics from linear dynamics. More than 350 exercises and many More on www.springer.com/978-3-642-11032-0 illustrations are included, and each chapter contains Usually dispatched within 3 to 5 business days a further ‘Sources and Comments’ section.The only 2011. 358 p. (C.I.M.E. Summer Schools, Vol. 36) Softcover prerequisites are a familiarity with metric spaces, 978-3-642-11032-0 the basic theory of Hilbert and Banach spaces and ▶$49.95 S. Gross, University of Bonn, Germany; A. Reusken, RWTH fundamentals of complex analysis. More advanced Aachen, Germany tools, only needed occasionally, are provided in two appendices. A self-contained exposition, this Numerical Methods for Two- book will be suitable for self-study and will appeal phase Incompressible Flows to advanced undergraduate or beginning graduate students. It will also be of use to researchers in other This book is the first monograph providing an introduction to and an overview of numerical methods for the simulation of two-phase incompressible flows. The Navier-Stokes equations springer.com 41 areas of mathematics such as partial differential Forthcoming early pioneering work in computing and espionage, equations, dynamical systems and ergodic theory. where his contribution was vital to the American Cold V. Guedj, Université Paul Sabatier, Toulouse, France (Ed.) More on www.springer.com/978-1-4471-2169-5 War effort, to his observations on core contemporary issues such as the stability of the world’s financial Usually dispatched within 3 to 5 business days Complex Monge–Ampère system.Gustafson’s crucial role in top-secret military Equations and Geodesics in the intelligence, which saw him tracking Russian 2011. XII, 388 p. 28 illus. (Universitext) Softcover submarines, intercepting electronic intelligence and 978-1-4471-2169-5 Space of Kähler Metrics writing the software for America’s first spy satellite, is ▶$69.95 The purpose of these lecture notes is to provide related here for the first time. His narrative includes an introduction to the theory of complex Monge– fascinating encounters with Nobel laureates and Ampère operators (definition, regularity issues, figures of historical importance, the European post- geometric properties of solutions, approximation) doctoral fellowships that expanded his perspectives on compact Kähler manifolds (with or without on science and life, and hair-raising stories from boundary).These operators are of central use in his early rock-climbing days including brushes several fundamental problems of complex differential with death then and later, such as being struck by geometry (Kähler–Einstein equation, uniqueness lightning and knocked unconscious near a mountain of constant scalar curvature metrics), complex top. Gustafson’s wide-ranging mathematical analysis and dynamics. The topics covered include, accomplishments have led to invitations and travel the Dirichlet problem (after Bedford–Taylor), throughout the world, and he tells of the great—and Monge–Ampère foliations and laminated currents, at times strange—personalities he has met along the polynomial hulls and Perron envelopes with no way. His unique journey has included hard knocks G. Grätzer, University of Manitoba, Winnipeg, MB, Canada analytic structure, a self-contained presentation of and beautiful women, who have, as he likes to say, Krylov regularity results, a modernized proof of the added to the great adventure. More Math Into LaTeX Calabi–Yau theorem (after Yau and Kolodziej), an More on www.springer.com/978-3-642-22557-4 introduction to infinite dimensional riemannian This new edition of Math Into Latex continues to be Due: January 28, 2012 geometry, geometric structures on spaces of Kähler the standard introduction and complete reference metrics (after Mabuchi, Semmes and Donaldson), 2012. XVI, 176 p. 26 illus., 18 in color. Hardcover for writing articles and books containing math generalizations of the regularity theory of Caffarelli– 978-3-642-22557-4 formulas. In this fully revised fourth edition, the Kohn–Nirenberg–Spruck (after Guan, Chen and ▶$59.95 focus is on important updates in latex for articles Blocki) and Bergman approximation of geodesics and books as well as detailed information on (after Phong–Sturm and Berndtsson).Each chapter creating transparencies and computer projections, can be read independently and is based on a series both for the classroom and professional meetings. of lectures by R. Berman, Z. Blocki, S. Boucksom, The text maintains its user-friendly, example- F. Delarue, R. Dujardin, B. Kolev and A. Zeriahi, based visual approach, gently easing readers into delivered to non-experts. The book is thus addressed the secrets of latex with The Short Course. Basic to any mathematician with some interest in one of ideas through sample articles and documents are the following fields, complex differential geometry, introduced. Key features include a visual guide and complex analysis, complex dynamics, fully non-linear detailed presentation of multiline math formulas, PDE's and stochastic analysis. instructions on installing Latex on the Mac and PC, and instructions on preparing books for publishers. More on www.springer.com/978-3-642-23668-6 Key features of More Math into Latex, 4th edition: Due: December 31, 2011 - Installation instructions for PC and Mac users - 2012. VIII, 310 p. 4 illus. (Lecture Notes in Mathematics, Vol. An example-based, visual approach and a gentle 2038) Softcover S.J. Gustafson, University of British Columbia, Vancouver, BC, introduction with the Short Course - A detailed 978-3-642-23668-6 Canada; I.M. Sigal, University of Toronto, ON, Canada exposition of multiline math formulas with a Visual ▶$89.95 Guide - A unified approach to Tex, Latex, and the AMS enhancements - A quick introduction to Mathematical Concepts of creating presentations with computer projections Quantum Mechanics From earlier reviews of Math into Latex: "There are several Latex guides, but this one wins hands The book gives a streamlined introduction to down for the elegance of its approach and breadth quantum mechanics while describing the basic of coverage." -Amazon.com Best of 2000, Editor’s mathematical structures underpinning this discipline. choice "A novice reader will be able to learn the Starting with an overview of key physical experiments most essential features of Latex sufficient to begin illustrating the origin of the physical foundations, the typesetting papers within a few hours of time…An book proceeds with a description of the basic notions experienced Tex user, on the other hand, will find a of quantum mechanics and their mathematical systematic and detailed discussion of Latex features." content.It then makes its way to topics of current -Report on Mathematical Physics "A very helpful and interest, specifically those in which mathematics useful tool for all scientists and engineers." -Review of plays an important role. The more advanced topics Astronomical Tools presented include many-body systems, modern K. Gustafson, University of Colorado, Boulder, CO, USA perturbation theory, path integrals, the theory of More on www.springer.com/978-0-387-32289-6 resonances, quantum statistics, mean-field theory, Usually dispatched within 3 to 5 business days The Crossing of Heaven second quantization, the theory of radiation (non- 2007. XXXIV, 619 p. 44 illus. Softcover Memoirs of a Mathematician relativistic quantum electrodynamics), and the 978-0-387-32289-6 renormalization group.With different selections As one of the most prolific mathematicians of our ▶$64.95 of chapters, the book can serve as a text for an time, Karl Gustafson has been a central figure in introductory, intermediate, or advanced course in the astonishing technological revolution of the last quantum mechanics. The last four chapters could half-century—a revolution which has transformed human life. This, his own account of his journey through those decades, takes the reader from his 42 springer.com also serve as an introductory course in quantum field Germany; M. Striebel, University of Wuppertal, Germany theory. (Eds.) More on www.springer.com/978-3-642-21865-1 Progress in Industrial Usually dispatched within 3 to 5 business days Mathematics at ECMI 2010 2011. XIII, 382 p. 37 illus. (Universitext) Softcover ECMI, the European Consortium for Mathematics 978-3-642-21865-1 in Industry, is the European brand associated with ▶$74.95 applied mathematics for industry and organizes highly successful biannual conferences. In this series, the ECMI 2010, the 16th European Conference on Mathematics for Industry, was held in the historic B. Gärtner, ETH Zurich, Switzerland; J. Matousek, Charles city hall of Wuppertal in Germany. It covered the University, Prague, Czech Republic mathematics of a wide range of applications and methods, from circuit and electromagnetic device Approximation Algorithms and simulation to model order reduction for chip design, Semidefinite Programming uncertainties and stochastics, production, fluids, life and environmental sciences, and dedicated and Semidefinite programs constitute one of the largest versatile methods.These proceedings of ECMI 2010 classes of optimization problems that can be emphasize mathematics as an innovation enabler for solved with reasonable efficiency - both in theory industry and business, and as an absolutely essential and practice. They play a key role in a variety of pre-requiste for Europe on its way to becoming the research areas, such as combinatorial optimization, leading knowledge-based economy in the world. B. Gustafsson, Uppsala University, Sweden approximation algorithms, computational More on www.springer.com/978-3-642-25099-6 complexity, graph theory, geometry, real algebraic Fundamentals of Scientific geometry and quantum computing. This book is Due: February 28, 2012 Computing an introduction to selected aspects of semidefinite 2012. XIV, 541 p. 193 illus., 70 in color. (The European programming and its use in approximation Consortium for Mathematics in Industry, Vol. 17) Hardcover The book of nature is written in the language of algorithms. It covers the basics but also a significant 978-3-642-25099-6 mathematics -- Galileo Galilei How is it possible amount of recent and more advanced material. There ▶$179.00 to predict weather patterns for tomorrow, with are many computational problems, such as access solely to today’s weather data? 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Indeed, assuming usually much too complicated to solve, either by the the Unique Games Conjecture, a plausible but smartest mathematician or the largest supercomputer. as yet unproven hypothesis, it was shown that This problem is overcome by constructing an for these problems, known algorithms based on approximation: a numerical model with a simpler semidefinite programming deliver the best possible structure can be translated into a program that tells approximation ratios among all polynomial-time the computer how to carry out the simulation.This algorithms. This book follows the “semidefinite book conveys the fundamentals of mathematical side” of these developments, presenting some of models, numerical methods and algorithms. Opening the main ideas behind approximation algorithms L.J. Halbeisen, Universität Zürich, Switzerland with a tutorial on mathematical models and analysis, based on semidefinite programming. It develops the it proceeds to introduce the most important classes basic theory of semidefinite programming, presents Combinatorial Set Theory of numerical methods, with finite element, finite one of the known efficient algorithms in detail, With a Gentle Introduction to Forcing difference and spectral methods as central tools. The and describes the principles of some others. It also concluding section describes applications in physics includes applications, focusing on approximation This book provides a self-contained introduction and engineering, including wave propagation, heat algorithms. to modern set theory and also opens up some more advanced areas of current research in this field. The conduction and fluid dynamics. Also covered are the More on www.springer.com/978-3-642-22014-2 principles of computers and programming, including first part offers an overview of classical set theory Due: January 28, 2012 MATLAB®. wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated More on www.springer.com/978-3-642-19494-8 2012. XI, 251 p. 23 illus. Hardcover technique of forcing, originally developed by Usually dispatched within 3 to 5 business days 978-3-642-22014-2 Paul Cohen, is explained in great detail. With this ▶$59.95 technique, one can show that certain statements, like 2011. XIII, 324 p. 144 illus., 43 in color. (Texts in the continuum hypothesis, are neither provable nor Computational Science and Engineering, Vol. 8) Hardcover disprovable from the axioms of set theory. In the last 978-3-642-19494-8 Forthcoming part, some topics of classical set theory are revisited ▶$59.95 and further developed in the light of forcing.The M. Günther, University of Wuppertal, Germany; A. Bartel, notes at the end of each chapter put the results in a University of Wuppertal, Germany; M. Brunk, University of historical context, and the numerous related results Wuppertal, Germany; S. Schöps, University of Wuppertal, and the extensive list of references lead the reader to the frontier of research.This book will appeal to all mathematicians interested in the foundations of springer.com 43 mathematics, but will be of particular use to graduates of beer really affected by the type of water used? in this field. and Processed foods: good or bad? Readers will be More on www.springer.com/978-1-4471-2172-5 captivated by this superbly written book, especially so as their guides are Professor Richard Hartel, Usually dispatched within 3 to 5 business days December professor of Food Engineering at UW-Madison, 31, 2011 along with his daughter, AnnaKate Hartel. Professor 2012. XVI, 453 p. 15 illus. (Springer Monographs in Hartel has for the last four years penned a witty and Mathematics) Hardcover illuminating column on all aspects of food science for 978-1-4471-2172-5 the Capital Times of Madison, and his weekly wisdom ▶$124.00 has now been collected into a single publication. 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The Netherlands This happened under the strictures of a closed society Algebraic Geometry that put severe restrictions on academics (despite Late Style – Yuri I. Manin Looking diplomatic détente) right up to the fall of the Iron Robin Hartshorne studied algebraic geometry with Back on a Life in Mathematics Curtain in 1989. Yuri Manin’s brilliance, and his Oscar Zariski and David Mumford at Harvard, unswerving integrity, helped him evade the pitfalls of and with J.-P. Serre and A. Grothendieck in Paris. This biographical documentary follows Yuri Soviet-era academia. His full cooperation with this After receiving his Ph.D. from Princeton in 1963, Ivanovich Manin’s stellar career in the ‘golden years’ documentary allows the world a fascinating glimpse Hartshorne became a Junior Fellow at Harvard, then of Moscow mathematics during the 1960s and 1970s. into an era of scientific enquiry that is as celebrated taught there for several years. In 1972 he moved He was one of the key players in the development of as it is underreported. It is about the exceptional life to California where he is now Professor at the algebraic geometry, at a time when a constellation of of a mathematician in unusual times, whose passion University of California at Berkeley. He is the author brilliant minds — of which Manin's was but one — for his subject, as well as his breadth of thinking, of "Residues and Duality" (1966), "Foundations of were conducting outstanding mathematical research. allowed him to forge his own freedom. Internationally Projective Geometry (1968), "Ample Subvarieties of This happened under the strictures of a closed society recognized for his contribution to mathematics, Algebraic Varieties" (1970), and numerous research that put severe restrictions on academics (despite Manin’s many prizes include the Lenin Prize in 1967, titles. His current research interest is the geometry diplomatic détente) right up to the fall of the Iron the Brouwer Gold Medal in 1984 and the Georg of projective varieties and vector bundles. He has Curtain in 1989. Yuri Manin’s brilliance, and his Cantor Medal in 2002. been a visiting professor at the College de France and at Kyoto University, where he gave lectures unswerving integrity, helped him evade the pitfalls of More on www.springer.com/978-3-642-24522-0 Soviet-era academia. His full cooperation with this in French and in Japanese, respectively. Professor Due: March 9, 2012 documentary allows the world a fascinating glimpse Hartshorne is married to Edie Churchill, educator into an era of scientific enquiry that is as celebrated and psychotherapist, and has two sons. He has as it is underreported. It is about the exceptional life 2012. 16 p. 13 illus., 7 in color. DVD. (Springer travelled widely, speaks several foreign languages, and of a mathematician in unusual times, whose passion VideoMATH) is an experienced mountain climber. He is also an for his subject, as well as his breadth of thinking, 978-3-642-24522-0 accomplished amateur musician: he has played the allowed him to forge his own freedom. Internationally ▶$39.95 flute for many years, and during his last visit to Kyoto recognized for his contribution to mathematics, he began studying the shakuhachi. Manin’s many prizes include the Lenin Prize in 1967, More on www.springer.com/978-0-387-90244-9 the Brouwer Gold Medal in 1984 and the Georg Usually dispatched within 3 to 5 business days Cantor Medal in 2002. More on www.springer.com/978-3-642-24482-7 1977. 496 p. 25 illus. (Graduate Texts in Mathematics, Vol. 52) Hardcover Due: March 9, 2012 978-0-387-90244-9 ▶$74.95 2012. Approx. 15 p. DVD. (Springer VideoMATH) 978-3-642-24482-7 ▶$39.95

R.W. Hartel, University of Wisconsin, Madison, WI, USA; A. Hartel, Northland College, Ashland, WI, USA Food Bites The Science of the Foods We Eat Food Bites is an easy-to-read, often humorous book on the scientific basis of the foods we eat, and answers those pesky, niggling questions such as: Is the quality 44 springer.com

of a new topic and some basic examples. The author around the duality and double fibration, which is then demonstrates the use of new commands realized through the masterful treatment of a variety through three categories of problems - the first of examples. The book is written by an expert, who category highlights those essential parts of the text has made fundamental contributions to the area.” — that demonstrate the use of new commands in Boris Rubin, Louisiana State University Mathematica whilst solving each problem presented; More on www.springer.com/978-1-4419-6054-2 - the second comprises problems that further demonstrate the use of commands previously Usually dispatched within 3 to 5 business days introduced to tackle different situations; and - 2011. XIII, 301 p. 28 illus. Hardcover the third presents more challenging problems for 978-1-4419-6054-2 further study. The intention is to enable the reader to learn from the codes, thus avoiding long and ▶$74.95 exhausting explanations. While based on a computer R. Hartshorne, University of California, Berkeley, CA, USA algebra course taught to undergraduate students of mathematics, science, engineering and finance, the C. Herdeiro, Universidade de Aveiro, Portugal; R. Picken, Deformation Theory book also includes chapters on calculus and solving Technical University of Lisbon, Portugal (Eds.) equations, and graphics, thus covering all the basic The basic problem of deformation theory in algebraic XIX International Fall Workshop geometry involves watching a small deformation of topics in Mathematica. With its strong focus upon one member of a family of objects, such as varieties, programming and problem solving, and an emphasis on Geometry and Physics or subschemes in a fixed space, or vector bundles on on using numerical problems that do not need any a fixed scheme. In this new book, Robin Hartshorne particular background in mathematics, this book The aim of this series of meetings is to provide a studies first what happens over small infinitesimal is also ideal for self-study and as an introduction context for exchanging ideas among researchers of deformations, and then gradually builds up to to researchers who wish to use Mathematica as a different fields in Differential Geometry, Applied more global situations, using methods pioneered by computational tool. Mathematica®: A Problem- Mathematics and Physics; in general, among all Kodaira and Spencer in the complex analytic case, Centered Approach comes with a free 30 day trial of people interested in the application of geometric and adapted and expanded in algebraic geometry the Wolfram Mathematica(R) software. methods and techniques to the study of physical by Grothendieck. Topics include: * deformations More on www.springer.com/978-1-84996-250-6 problems. over the dual numbers; * smoothness and the Usually dispatched within 3 to 5 business days More on www.springer.com/978-0-7354-0918-7 infinitesimal lifting property; * Zariski tangent space Online orders shipping within 2-3 days and obstructions to deformation problems; * pro- 2010. XX, 180 p. 63 illus., 50 in color. (Springer 2011. 184 p. (Mathematical and Statistical Physics, Vol. representable functors of Schlessinger; * infinitesimal Undergraduate Mathematics Series, Vol. 53) Softcover 1360) Softcover study of moduli spaces such as the Hilbert scheme, 978-1-84996-250-6 978-0-7354-0918-7 Picard scheme, moduli of curves, and moduli of ▶$49.95 $139.00 stable vector bundles. The author includes numerous ▶ exercises, as well as important examples illustrating various aspects of the theory. This text is based on a graduate course taught by the author at the University of California, Berkeley. More on www.springer.com/978-1-4419-1595-5 Usually dispatched within 3 to 5 business days

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S. Helgason, MIT, Cambridge, MA, USA N. Herrmann, Leibniz Universität Hannover, Germany Integral Geometry and Radon The Beauty of Everyday Transforms Mathematics In this text, integral geometry deals with Radon’s Imagine that you’ve finally found a parking space problem of representing a function on a manifold after a long and harrowing search, but are now in terms of its integrals over certain submanifolds encountering some difficulty in trying to enter this —hence the term the Radon transform. Examples space. Wouldn’t it be great if you knew a formula that and far-reaching generalizations lead to fundamental allowed you to enter the space without difficulty? Are problems such as: (i) injectivity, (ii) inversion you annoyed because your soda can doesn’t remain formulas, (iii) support questions, (iv) applications upright during a picnic? Would you like to know why R. Hazrat, Department of Pure Mathematics, Queen's (e.g., to tomography, partial differential equations and University Belfast, Belfast, UK a mirror swaps right and left, but not top and bottom? group representations). For the case of the plane, the Are you looking for a mathematical speech to toast inversion theorem and the support theorem have had your mother-in-law’s 85th birthday? Or do you want Mathematica®: A Problem- major applications in medicine through tomography to give your heart away mathematically? Dr. Norbert and CAT scanning. While containing some recent Centered Approach Herrmann provides amusing and entertaining research, the book is aimed at beginning graduate solutions to these and many other problems that we Mathematica®: A Problem-Centered Approach students for classroom use or self-study. A number of encounter in everyday situations.“A book for teachers, introduces the vast array of features and powerful exercises point to further results with documentation. mathematical functions of Mathematica using a From the reviews: “Integral Geometry is a fascinating multitude of clearly presented examples and worked- area, where numerous branches of mathematics meet out problems. Each section starts with a description together. The contents of the book is concentrated springer.com 45 students of mathematics, and anybody who likes unusual and amusing calculations.” More on www.springer.com/978-3-642-22103-3 Usually dispatched within 3 to 5 business days 2012. XIII, 138 p. 35 illus. Softcover 978-3-642-22103-3 ▶$19.95

O. Hijab, Department of Mathematics, Temple University, J. Hilgert, University of Paderborn, Germany; K.-H. Neeb, Philadelphia, PA 19122 USA Friedrich-Alexander Universität Erlangen-Nürnburg, Germany Introduction to Calculus and Structure and Geometry of Lie Classical Analysis Groups This text is intended for an honors calculus course or for an introduction to analysis. Involving rigorous This text is designed as an introduction to Lie analysis, computational dexterity, and a breadth of groups and their actions on manifolds, one that is applications, it is ideal for undergraduate majors. This accessible both to a broad range of mathematicians J. Herzog, Universität Duisburg-Essen, Essen, Germany; T. third edition includes corrections as well as some and to graduate students. Building on the authors' Hibi, Osaka University, Toyonaka, Osaka, Japan additional material.Some features of the text:* The Lie-Gruppen und Lie-Algebren textbook from text is completely self-contained and starts with the 1991, it presents the fundamental principles of Monomial Ideals real number axioms;* The integral is defined as the Lie groups while incorporating the past 20 years area under the graph, while the area is defined for of the authors' teaching and research, and giving This book demonstrates current trends in research every subset of the plane;* There is a heavy emphasis due emphasis to the role played by differential on combinatorial and computational commutative on computational problems, from the high-school geometry in the field. The text is entirely self algebra with a primary emphasis on topics related quadratic formula to the formula for the derivative of contained, and provides ample guidance to students to monomial ideals. Providing a useful and quick the zeta function at zero;* There are applications from with the presence of many exercises and selected introduction to areas of research spanning these many parts of analysis, e.g., convexity, the Cantor hints.The work begins with a study of matrix groups, fields, Monomial Ideals is split into three parts. Part set, continued fractions, the AGM, the theta and zeta which serve as examples to concretely and directly I offers a quick introduction to the modern theory of functions, transcendental numbers, the Bessel and illustrate the correspondence between groups and Gröbner bases as well as the detailed study of generic gamma functions, and many more;* Traditionally their Lie algebras. In the second part of the book, initial ideals. Part II supplies Hilbert functions and transcendentally presented material, such as infinite the authors investigate the basic structure and resolutions and some of the combinatorics related products, the Bernoulli series, and the zeta functional representation theory of finite dimensional Lie to monomial ideals including the Kruskal—Katona equation, is developed over the reals;* There are algebras, such as the rough structure theory relevant theorem and algebraic aspects of Alexander duality. 385 problems with all the solutions at the back of to the theorems of Levi and Malcev, the fine structure Part III discusses combinatorial applications of the text.Review from the first edition:"This is a very of semisimple Lie algebras (root decompositions), monomial ideals, providing a valuable overview of intriguing, decidedly unusual, and very satisfying and questions related to representation theory. In some of the central trends in algebraic combinatorics. treatment of calculus and introductory analysis. It's the third part of the book, the authors turn to global Main subjects include edge ideals of finite graphs, full of quirky little approaches to standard topics issues, most notably the interplay between differential powers of ideals, algebraic shifting theory and an that make one wonder over and over again, 'Why is geometry and Lie theory. Finally, the fourth part introduction to discrete polymatroids. Theory it never done like this?'"-John Allen Paulos, author of the book deals with the structure theory of Lie is complemented by a number of examples and of Innumeracy and A Mathematician Reads the groups, including some refined applications of the exercises throughout, bringing the reader to a deeper Newspaper exponential function, various classes of Lie groups, understanding of concepts explored within the text. and structural issues for general Lie groups. To Self-contained and concise, this book will appeal More on www.springer.com/978-1-4419-9487-5 round out the book's content, several appendices to a wide range of readers, including PhD students Usually dispatched within 3 to 5 business days appear at the end of this last part.Containing a on advanced courses, experienced researchers, and wealth of useful information, including new results, combinatorialists and non-specialists with a basic 2011. XII, 364 p. 66 illus. (Undergraduate Texts in Structure and Geometry of Lie Groups provides a knowledge of commutative algebra. Since their Mathematics) Hardcover unique perspective on the study of Lie groups and is first meeting in 1985, Juergen Herzog (Universität 978-1-4419-9487-5 a valuable addition to the literature. Prerequisites are Duisburg-Essen, Germany) and Takayuki Hibi ▶$74.95 generally kept to a minimum, and various pedagogical (Osaka University, Japan), have worked together on features make it an excellent supplemental text for a number of research projects, of which recent results graduate students. However, the work also contains are presented in this monograph. much that will be of interest to more advanced More on www.springer.com/978-0-85729-105-9 audiences, and can serve as a useful research reference in the field. Usually dispatched within 3 to 5 business days More on www.springer.com/978-0-387-84793-1 2011. XVI, 305 p. 5 illus. (Graduate Texts in Usually dispatched within 3 to 5 business days Mathematics, Vol. 260) Hardcover 2012. X, 744 p. 4 illus. (Springer Monographs in 978-0-85729-105-9 Mathematics) Hardcover ▶$74.95 978-0-387-84793-1 ▶$129.00 46 springer.com

and developed as required. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: * classical cryptographic constructions, such as Diffie-Hellmann key exchange, discrete logarithm- based cryptosystems, the RSA cryptosystem, and digital signatures; * fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; * an in- depth treatment of important recent cryptographic innovations, such as elliptic curves, elliptic curve M. Hindry, Université Paris 7 Denis Diderot, Paris, France F. Hirsch, University of Evry, France; C. Profeta, University of and pairing-based cryptography, lattices, lattice- Nancy, France; B. Roynette, University of Nancy, France; M. based cryptography, and the NTRU cryptosystem. Arithmetics Yor, Institut Universitaire de France, Paris This book is an ideal introduction for mathematics and computer science students to the mathematical Number theory is a branch of mathematics which foundations of modern cryptography. The book draws its vitality from a rich historical background. Peacocks and Associated includes an extensive bibliography and index; It is also traditionally nourished through interactions Martingales, with Explicit supplementary materials are available online. with other areas of research, such as algebra, algebraic geometry, topology, complex analysis and Constructions More on www.springer.com/978-0-387-77993-5 harmonic analysis. More recently, it has made a We call peacock an integrable process which is Usually dispatched within 3 to 5 business days spectacular appearance in the field of theoretical increasing in the convex order; such a notion plays computer science and in questions of communication, an important role in Mathematical Finance. A deep 2008. XVI, 524 p. 29 illus. (Undergraduate Texts in cryptography and error-correcting codes.Providing Mathematics) Hardcover theorem due to Kellerer states that a process is a an elementary introduction to the central topics in 978-0-387-77993-5 peacock if and only if it has the same one-dimensional number theory, this book spans multiple areas of $54.95 marginals as a martingale. Such a martingale is ▶ research. The first part corresponds to an advanced then said to be associated to this peacock.In this Special offer valid until December 31, 2011 ▶$29.50 undergraduate course. All of the statements given monograph, we exhibit numerous examples of in this part are of course accompanied by their peacocks and associated martingales with the help proofs, with perhaps the exception of some results of different methods: construction of sheets, time appearing at the end of the chapters. A copious list reversal, time inversion, self-decomposability, SDE, of exercises, of varying difficulty, are also included Skorokhod embeddings… They are developed in here. The second part is of a higher level and is eight chapters, with about a hundred of exercises. relevant for the first year of graduate school. It contains an introduction to elliptic curves and a More on www.springer.com/978-88-470-1907-2 chapter entitled “Developments and Open Problems”, Online orders shipping within 2-3 days which introduces and brings together various themes 2011. 430 p. 11 illus., 6 in color. (Bocconi & Springer Series) oriented toward ongoing mathematical research. Hardcover Given the multifaceted nature of number theory, 978-88-470-1907-2 the primary aims of this book are to:- provide an ▶$129.00 overview of the various forms of mathematics useful for studying numbers- demonstrate the necessity H. Holden, Norwegian University of Science and Technology, of deep and classical themes such as Gauss sums- Trondheim, Norway; N.H. Risebro, University of Oslo, highlight the role that arithmetic plays in modern Blindern, Norway applied mathematics- include recent proofs such as the polynomial primality algorithm- approach Front Tracking for Hyperbolic subjects of contemporary research such as elliptic curves- illustrate the beauty of arithmeticThe Conservation Laws prerequisites for this text are undergraduate level Hyperbolic conservation laws are central in the theory algebra and a little topology of Rn. It will be of use of nonlinear partial differential equations and in to undergraduates, graduates and phd students, and science and technology. The reader is given a self- may also appeal to professional mathematicians as a contained presentation using front tracking, which reference text. is also a numerical method. The multidimensional More on www.springer.com/978-1-4471-2130-5 J. Hoffstein, Brown University, Providence, RI, USA; J. Pipher, scalar case and the case of systems on the line are Usually dispatched within 3 to 5 business days Brown University, Providence, RI, USA; J.H. Silverman, Brown treated in detail. A chapter on finite differences is University, Providence, RI, USA included.From the reviews:"It is already one of the 2011. XVIII, 322 p. 5 illus. (Universitext) Softcover few best digests on this topic. The present book is an 978-1-4471-2130-5 An Introduction to Mathematical excellent compromise between theory and practice. ▶$74.95 Students will appreciate the lively and accurate style." Cryptography D. Serre, MathSciNet "I have read the book with great This self-contained introduction to modern pleasure, and I can recommend it to experts as well cryptography emphasizes the mathematics behind as students. It can also be used for reliable and very the theory of public key cryptosystems and digital exciting basis for a one-semester graduate course." S. signature schemes. The book focuses on these key Noelle, Book review, German Math. Soc."Making it topics while developing the mathematical tools an ideal first book for the theory of nonlinear partial needed for the construction and security analysis differential equations...an excellent reference for a of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced springer.com 47 graduate course on nonlinear conservation laws." M. cultural heritage. As such, one of my goals is to Forthcoming Laforest, Comp. Phys. Comm. open up these aspects of the field; another is to B. Howard, Boston College, Chestnut Hill, MA, USA; T. Yang, extend an invitation to mathematics in general. It More on www.springer.com/978-3-642-23910-6 University of Wisconsin, Madison, WI, USA is an unfortunate fact that today, at a time when Usually dispatched within 3 to 5 business days mathematics and knowledge of mathematics are more Intersections of Hirzebruch– important than ever, phrases like math avoidance and 2011. XII, 361 p. 40 illus. (Applied Mathematical math anxiety are very much in the public vocabulary. Zagier Divisors and CM Cycles Sciences, Vol. 152) Softcover Making a serious effort to heal these ills is an essential 978-3-642-23910-6 This monograph treats one case of a series of task. Thus the book also aims at an informed public, $74.95 conjectures by S. Kudla, whose goal is to show that ▶ interested in making a new beginning in math.For Fourier of Eisenstein series encode information about the 2nd edition, some of the historical material giving the Arakelov intersection theory of special cycles on historical context has been expanded and numerous Shimura varieties of orthogonal and unitary type. A.S. Holevo, Steklov Mathematical Institute, Moscow, Russia illustrations have been added. The main difference is Here, the Eisenstein series is a Hilbert modular form however the inclusion of a large number of exercises of weight one over a real quadratic field, the Shimura Probabilistic and Statistical with some suggestions for solutions.For excerpts from variety is a classical Hilbert modular surface, and reviews from the first edition have a look at http:// Aspects of Quantum Theory the special cycles are complex multiplication points www.springer.com/978-3-540-41949-5. and the Hirzebruch–Zagier divisors. By developing This book is devoted to aspects of the foundations More on www.springer.com/978-3-642-14440-0 new techniques in deformation theory, the authors of Quantum Mechanics in which probabilistic and Usually dispatched within 3 to 5 business days successfully compute the Arakelov intersection statistical concepts play an essential role. The main multiplicities of these divisors, and show that they part of the book concerns the quantitative statistical 2010. XIX, 551 p. 295 illus., 85 in color. Hardcover agree with the Fourier coefficients of derivatives of theory of quantum measurement, based on the notion 978-3-642-14440-0 Eisenstein series. of Positive Operator-valued Measures. During the $84.95 past years there has been substantial progress in ▶ More on www.springer.com/978-3-642-23978-6 this direction, stimulated to a great extent by new Due: February 29, 2012 applications such as Quantum Optics, Quantum 2012. VIII, 140 p. (Lecture Notes in Mathematics, Vol. 2041) Communication and high-precision experiments. Softcover The questions of statistical interpretation, quantum 978-3-642-23978-6 symmetries, theory of canonical commutation ▶$49.95 relations and Gaussian states, uncertainty relations, as well as new fundamental bounds concerning the accuracy of quantum measurements, are discussed in this book in an accessible yet rigorous way. Compared B. Hu, University of Notre Dame, USA to the first edition, there is a new Supplement devoted to the hidden variable issue. Comments and the Blow-up Theories for Semilinear bibliography have also been extended and updated. Parabolic Equations More on www.springer.com/978-88-7642-375-8 There is an enormous amount of work in the Online orders shipping within 2-3 days A. Holme, University of Bergen, Norway literature about the blow-up behavior of evolution 2011. 334 p. (Monographs (Scuola Normale Superiore), Vol. equations. It is our intention to introduce the theory 1) Softcover A Royal Road to Algebraic by emphasizing the methods while seeking to avoid 978-88-7642-375-8 Geometry massive technical computations. To reach this goal, ▶$39.95 we use the simplest equation to illustrate the methods; This book is about modern algebraic geometry. these methods very often apply to more general The title A Royal Road to Algebraic Geometry is equations. inspired by the famous anecdote about the king More on www.springer.com/978-3-642-18459-8 asking Euclid if there really existed no simpler way Usually dispatched within 3 to 5 business days for learning geometry, than to read all of his work Elements. Euclid is said to have answered: “There 2011. X, 127 p. 2 illus. (Lecture Notes in Mathematics, Vol. is no royal road to geometry!” The book starts by 2018) Softcover explaining this enigmatic answer, the aim of the book 978-3-642-18459-8 being to argue that indeed, in some sense there is a ▶$49.95 royal road to algebraic geometry. From a point of departure in algebraic curves, the exposition moves on to the present shape of the field, culminating with Alexander Grothendieck’s theory of schemes. Contemporary homological tools are explained. The A. Holme, University of Bergen, Norway reader will follow a directed path leading up to the main elements of modern algebraic geometry. When Geometry the road is completed, the reader is empowered to Our Cultural Heritage start navigating in this immense field, and to open up the door to a wonderful field of research. The greatest This book contains selected topics from the history scientific experience of a lifetime! of geometry, with "modern" proofs of some of the More on www.springer.com/978-3-642-19224-1 results, as well as a fully modern treatment of selected basic issues in geometry. It is geared towards the Usually dispatched within 3 to 5 business days needs of future mathematics teachers. All too often the geometry which goes into the syllabus for these 2012. XIII, 364 p. 27 illus. Hardcover students presents the material in a pedantic and 978-3-642-19224-1 formalistic style, suppressing its dynamic character ▶$74.95 and its role as part of the foundation of our common 48 springer.com

for the stability analysis of delayed dynamical structure of Verma modules and Fock modules, systems with parametric excitation. Delay- the classification of (unitarizable) Harish-Chandra differential equations often come up in different modules, tilting equivalence, and the rational vertex fields of engineering, such as feedback control operator algebras associated to the so-called minimal systems, machine tool vibrations, and balancing/ series representations.Covering a wide range of stabilization with reflex delay. The behavior of material, this book has three appendices which such systems is often counter-intuitive and closed provide background information required for some form analytical formulas can rarely be given even of the chapters. Fundamental results are organized in for the linear stability conditions. The same holds a unified way and existing proofs refined. For for parametrically excited systems. If parametric instance in chapter three, a generalization of Jantzen excitation is coupled with the delay effect, then the filtration is reformulated in an algebraic manner, and governing equation is a delay-differential equation geometric interpretation is provided. Statements, W.T. Ingram, Missouri University of Science and Technology, with time-periodic coefficients, and the stability widely believed to be true, are collated, and results Rolla, MO, USA; W.S. Mahavier, Emory University, Atlanta, properties are even more intriguing. The semi- which are known but not verified are proven, such as GA, USA discretization method is a simple but efficient method the corrected structure theorem of Fock modules in that is based on the discretization with respect chapter eight.This book will be of interest to a wide Inverse Limits to the delayed term and the periodic coefficients range of mathematicians and physicists from the level From Continua to Chaos only. This discretization results in a system of of graduate students to researchers. Inverse limits provide a powerful tool for constructing ordinary differential equations that can be solved More on www.springer.com/978-0-85729-159-2 using standard techniques, which are part of basic complicated spaces from simple ones. They also can Usually dispatched within 3 to 5 business days turn the study of a dynamical system consisting of engineering curriculums. The method can effectively 2011. XVIII, 474 p. 15 illus. (Springer Monographs in a space and a self-map into a study of a (likely more be used to construct stability charts in the space of system parameters. These charts provide a useful tool Mathematics) Hardcover complicated) space and a self-homeomorphism. In 978-0-85729-159-2 four chapters along with an appendix containing for engineers, since they present an overview on the ▶$124.00 background material the authors develop the effects of system parameters on the local dynamics theory of inverse limits. The book begins with an of the system. The book presents the application introductory study of inverse limits on [0,1] before of the method to different engineering problems, moving to a general treatment of the subject. Special such as dynamics of turning and milling processes A. Isaev, The Australian National University, Canberra, topics in continuum theory complete the book. with constant and with varying spindle speeds, stick Australia Although it is not a book on dynamics, the influence balancing with reflex delay, force control processes of dynamics can be seen throughout; for instance, in the presence of feedback delay, and stabilization Spherical Tube Hypersurfaces using time-periodic control gains.The book is it includes studies of inverse limits with maps from We examine Levi non-degenerate tube hypersurfaces families of maps that are of interest to dynamicists designed for graduate and PhD students as well as researchers working in the field of delayed dynamical in complex linear space which are "spherical," that such as the logistic and the tent families. This book is, locally CR-equivalent to the real hyperquadric. will serve as a useful reference to graduate students systems with application to mechanical, electrical and chemical engineering, control theory, biomechanics, Spherical hypersurfaces are characterized by the and researchers in continuum theory and dynamical condition of the vanishing of the CR-curvature form, systems. Researchers working in applied areas who population dynamics, neuro-physiology, and climate research. so such hypersurfaces are flat from the CR-geometric are discovering inverse limits in their work will also viewpoint. On the other hand, such hypersurfaces benefit from this book. More on www.springer.com/978-1-4614-0334-0 are also of interest from the point of view of affine More on www.springer.com/978-1-4614-1796-5 Usually dispatched within 3 to 5 business days geometry. Thus our treatment of spherical tube Usually dispatched within 3 to 5 business days 2011. X, 174 p. 81 illus. (Applied Mathematical Sciences, Vol. hypersurfaces in this book is two-fold: CR-geometric 178) Hardcover and affine-geometric. As the book shows, spherical 2012. XV, 217 p. 49 illus. (Developments in Mathematics, 978-1-4614-0334-0 tube hypersurfaces possess remarkable properties. Vol. 25) Hardcover 978-1-4614-1796-5 ▶$79.95 For example, every such hypersurface is real-analytic and extends to a closed real-analytic spherical tube $99.00 ▶ hypersurface in complex space. One of our main goals is to provide an explicit affine classification of closed spherical tube hypersurfaces whenever possible. In this book we offer a comprehensive exposition of the theory of spherical tube hypersurfaces, starting with the idea proposed in the pioneering work by P. Yang (1982) and ending with the new approach put forward by G. Fels and W. Kaup (2009). More on www.springer.com/978-3-642-19782-6 Usually dispatched within 3 to 5 business days 2011. XII, 230 p. (Lecture Notes in Mathematics, Vol. 2020) Softcover K. Iohara, Université Claude Bernard Lyon, Villeurbanne, 978-3-642-19782-6 France; Y. Koga, University of Fukui, Japan ▶$59.95 T. Insperger, Budapest University of Technology and Economics, Hungary; G. Stépán, Budapest University of Representation Theory of the Technology and Economics, Hungary Virasoro Algebra Semi-Discretization for Time- The Virasoro algebra is an infinite dimensional Delay Systems Lie algebra that plays an increasingly important Stability and Engineering Applications role in mathematics and theoretical physics. This book describes some fundamental facts about The book presents the recently introduced and the representation theory of the Virasoro algebra already widely cited semi-discretization method in a self-contained manner. Topics include the springer.com 49

destructive evaluation (NDE), this book explores in detail the mathematical modeling and inverse problems encountered when using ultrasound to investigate heterogeneous microstructured materials. The outstanding features of the text are firstly, a clear description of both linear and nonlinear mathematical models derived for modelling the propagation of ultrasonic deformation waves, and secondly, the provision of solutions to the corresponding inverse problems that determine the physical parameters of the models. The data are related to nonlinearities at both a macro- and micro- level, as well as to J. Jacod, Université Paris VI, France; P. Protter, Columbia dispersion. The authors’ goal has been to construct F.E.A. Johnson, University College London, UK University, New York, NY, USA algorithms that allow us to determine the parameters Syzygies and Homotopy Theory Discretization of Processes within which we are required to characterize microstructure. To achieve this, the authors not only The most important invariant of a topological In applications, and especially in mathematical use conventional harmonic waves, but also propose a space is its fundamental group. When this is finance, random time-dependent events are often novel methodology based on using solitary waves in trivial, the resulting homotopy theory is well modeled as stochastic processes. Assumptions NDE. The book analyzes the uniqueness and stability researched and familiar. In the general case, however, are made about the structure of such processes, of the solutions, in addition to providing numerical homotopy theory over nontrivial fundamental and serious researchers will want to justify those examples. groups is much more problematic and far less well assumptions through the use of data. As statisticians More on www.springer.com/978-3-642-21583-4 understood.Syzygies and Homotopy Theory explores are wont to say, “In God we trust; all others must Usually dispatched within 3 to 5 business days the problem of nonsimply connected homotopy bring data.” This book establishes the theory of how in the first nontrivial cases and presents, for the 2011. IX, 160 p. 30 illus., 3 in color. (Springer Monographs in to go about estimating not just scalar parameters first time, a systematic rehabilitation of Hilbert's Mathematics) Hardcover about a proposed model, but also the underlying 978-3-642-21583-4 method of syzygies in the context of non-simply structure of the model itself. Classic statistical tools connected homotopy theory. The first part of the ▶$99.00 are used: the law of large numbers, and the central book is theoretical, formulated to allow a general limit theorem. Researchers have recently developed finitely presented group as a fundamental group. creative and original methods to use these tools in The innovation here is to regard syzygies as stable sophisticated (but highly technical) ways to reveal modules rather than minimal modules. Inevitably new details about the underlying structure. For the this forces a reconsideration of the problems of first time in book form, the authors present these noncancellation; these are confronted in the second, latest techniques, based on research from the last 10 practical, part of the book. In particular, the second years. They include new findings. This book will be of part of the book considers how the theory works special interest to researchers, combining the theory out in detail for the specific examples Fn ´F where of mathematical finance with its investigation using Fn is a free group of rank n and F is finite. Another market data, and it will also prove to be useful in a innovation is to parametrize the first syzygy in terms broad range of applications, such as to mathematical of the more familiar class of stably free modules. biology, chemical engineering, and physics. Furthermore, detailed description of these stably More on www.springer.com/978-3-642-24126-0 free modules is effected by a suitable modification of the method of Milnor squares.The theory developed Usually dispatched within 3 to 5 business days M. Jarden, Ramat Aviv, Tel Aviv, Israel within this book has potential applications in various 2012. XIV, 596 p. (Stochastic Modelling and Applied branches of algebra, including homological algebra, Probability, Vol. 67) Hardcover Algebraic Patching ring theory and K-theory. Syzygies and Homotopy 978-3-642-24126-0 Assuming only basic algebra and Galois theory, the Theory will be of interest to researchers and also to $129.00 ▶ book develops the method of "algebraic patching" graduate students with a background in algebra and to realize finite groups and, more generally, to solve algebraic topology. finite split embedding problems over fields. The More on www.springer.com/978-1-4471-2293-7 method succeeds over rational function fields of Usually dispatched within 3 to 5 business days December one variable over "ample fields". Among others, it 31, 2011 leads to the solution of two central results in "Field 2012. XXIV, 294 p. 1 illus. (Algebra and Applications, Vol. 17) Arithmetic": (a) The absolute Galois group of a Hardcover countable Hilbertian pac field is free on countably 978-1-4471-2293-7 many generators; (b) The absolute Galois group of ▶$99.00 a function field of one variable over an algebraically closed field $C$ is free of rank equal to the cardinality of $C$. More on www.springer.com/978-3-642-15127-9 Usually dispatched within 3 to 5 business days J. Janno, Tallinn University of Technology, Estonia; J. 2011. X, 290 p. (Springer Monographs in Mathematics) Engelbrecht, Tallinn University of Technology, Estonia Hardcover 978-3-642-15127-9 Microstructured Materials: ▶$99.00 Inverse Problems Complex, microstructured materials are widely used in industry and technology and include alloys, ceramics and composites. Focusing on non- 50 springer.com

anyway to be covered by a book so small.The book's central concept is the “tropical convexity” introduced by Develin and Sturmfels, which is a version of “tropical linear algebra”. This is used in the book as a general language to study classical subjects in combinatorial optimization including shortest paths, the assignment problem, the even dicycle problem, flow-type problems, and others. This book focuses on the polyhedral and combinatorial aspects of tropical geometry while requiring less prerequisites in algebraic geometry and commutative algebra, thus making the book more accessible to a wider audience. S.-M. Jung, Hongik University, Jochiwon, Republic of South J. Jost, Max Planck Institute for Mathematics in the Sciences, The main requirement beyond general mathematical Korea Leipzig, Germany maturity is a basic knowledge in polytope theory. Riemannian Geometry and More on www.springer.com/978-1-4419-8365-7 Hyers-Ulam-Rassias Stability of Geometric Analysis Due: March 27, 2012 Functional Equations in Nonlinear This established reference work continues to lead its 2012. XX, 180 p. 50 illus. Hardcover Analysis 978-1-4419-8365-7 readers to some of the hottest topics of contemporary This textbook at the advanced undergraduate/ approx. $49.95 mathematical research. The previous edition already ▶ graduate level will complement the books of D.H. introduced and explained the ideas of the parabolic Hyers, G. Isac, and Th.M. Rassias (© Birkhauser methods that had found a spectacular success in 1998) and of S. Czerwik (2002) by integrating and the work of Perelman at the examples of closed presenting the primary developments applying to geodesics and harmonic forms. It also discussed almost all the classical results of the Hyers-Ulam- further examples of geometric variational problems Rassias stability.The self-contained text is presented from quantum field theory, another source of in an easy to understand fashion and all the necessary profound new ideas and methods in geometry. materials and information are included in order The 6th edition includes a systematic treatment of to appeal to a diverse audience with interests in eigenvalues of Riemannian manifolds and several difference and functional equations and functional other additions. Also, the entire material has been analysis. Highlights of the text include discussions of reorganized in order to improve the coherence of the the method of invariant means and the fixed point book.From the reviews: "This book provides a very method, the stability problems for the exponential readable introduction to Riemannian geometry and functional equations, Hyers-Ulam stability, Hyers- geometric analysis. ... With the vast development of Ulam-Rassias stability, Pexider equation, and the mathematical subject of geometric analysis, the S. Jukna, Vilnius University, Lithuania superstability of the exponential function. present textbook is most welcome." Mathematical More on www.springer.com/978-1-4419-9636-7 Reviews"...the material ... is self-contained. Each Boolean Function Complexity chapter ends with a set of exercises. Most of the Advances and Frontiers Usually dispatched within 3 to 5 business days paragraphs have a section ‘Perspectives’, written with Boolean circuit complexity is the combinatorics the aim to place the material in a broader context and 2011. XVI, 364 p. 1 illus. (Springer Optimization and of computer science and involves many intriguing explain further results and directions." Zentralblatt Its Applications, Vol. 48) Hardcover problems that are easy to state and explain, even for MATH 978-1-4419-9636-7 the layman. This book is a comprehensive description ▶$74.95 More on www.springer.com/978-3-642-21297-0 of basic lower bound arguments, covering many Usually dispatched within 3 to 5 business days of the gems of this “complexity Waterloo” that have been discovered over the past several decades, 2011. XIII, 611 p. 16 illus., 4 in color. (Universitext) right up to results from the last year or two. Many Softcover open problems, marked as Research Problems, are 978-3-642-21297-0 mentioned along the way. The problems are mainly ▶$84.95 of combinatorial flavor but their solutions could have great consequences in circuit complexity and computer science. The book will be of interest to Forthcoming graduate students and researchers in the fields of computer science and discrete mathematics. M. Joswig, Fachbereich Mathematik, Algorithmische More on www.springer.com/978-3-642-24507-7 diskrete Mathematik, Technische Universität Darmstadt, 64293 Darmstadt, Germany Due: January 31, 2012 Essentials of Tropical 2012. XV, 619 p. 70 illus. (Algorithms and S. Kalliadasis, Department of Chemical Engineering, Imperial Combinatorics, Vol. 27) Hardcover College London, London, UK; C. Ruyer-Quil, Laboratoire Combinatorics 978-3-642-24507-7 FAST, Université Pierre et Marie Curie (Paris 6), Paris, ▶$84.95 France; B. Scheid, TIPs - Fluid Physics Unit, Université Libre The goal of this book is to explain, at the graduate de Bruxelles, Brussels, Belgium; M.G. Velarde, Instituto student level, how tropical geometry can be accessed Pluridisciplinar, Universidad Complutense, Madrid, Spain via geometric combinatorics. This way the book offers a viable path to a topic of very active research. At Falling Liquid Films the same time the reader learns how a number of seemingly unrelated combinatorial results fall into Falling Liquid Films gives a detailed review of state- place, once viewed through the “tropical lens”. No of-the-art theoretical, analytical and numerical attempt is made to cover the entire field of tropical methodologies, for the analysis of dissipative wave geometry, which has been evolving too rapidly dynamics and pattern formation on the surface of a springer.com 51 film falling down a planar inclined substrate. This like to learn more about this subject, to start their prototype is an open-flow hydrodynamic instability, research in this area or to study the properties of that represents an excellent paradigm for the study concrete mechanical systems subjected to random of complexity in active nonlinear media with energy perturbations. supply, dissipation and dispersion. It will also be More on www.springer.com/978-3-642-23279-4 of use for a more general understanding of specific events characterizing the transition to spatio-temporal Usually dispatched within 3 to 5 business days chaos and weak/dissipative turbulence. Particular 2012. XVII, 339 p. 4 illus. (Stochastic Modelling and Applied emphasis is given to low-dimensional approximations Probability, Vol. 66) Hardcover for such flows through a hierarchy of modeling 978-3-642-23279-4 approaches, including equations of the boundary- ▶$129.00 layer type, averaged formulations based on weighted residuals approaches and long-wave expansions. A. Kirsch, Karlsruhe Institute of Technology (KIT), Karlsruhe, Whenever possible the link between theory and Germany experiment is illustrated, and, as a further bridge between the two, the development of order-of- An Introduction to the magnitude estimates and scaling arguments is used Mathematical Theory of Inverse to facilitate the understanding of basic, underlying physics. This monograph will appeal to advanced Problems graduate students in applied mathematics, science This book introduces the reader to the area of inverse or engineering undertaking research on interfacial problems. The study of inverse problems is of vital fluid mechanics or studying fluid mechanics as part interest to many areas of science and technology such of their program. It will also be of use to researchers as geophysical exploration, system identification, working on both applied, fundamental theoretical nondestructive testing and ultrasonic tomography. and experimental aspects of thin film flows, as well The aim of this book is twofold: in the first part, as engineers and technologists dealing with processes H. Kielhöfer, University of Augsburg , Augsburg, Germany the reader is exposed to the basic notions and involving isothermal or heated films. This monograph difficulties encountered with ill-posed problems. is largely self-contained and no background on Bifurcation Theory Basic properties of regularization methods for linear interfacial fluid mechanics is assumed. An Introduction with Applications to Partial ill-posed problems are studied by means of several More on www.springer.com/978-1-84882-366-2 Differential Equations simple analytical and numerical examples. The second part of the book presents three special nonlinear Usually dispatched within 3 to 5 business days In the past three decades, bifurcation theory has inverse problems in detail - the inverse spectral 2012. XV, 440 p. 129 illus. (Applied Mathematical Sciences, matured into a well-established and vibrant branch of problem, the inverse problem of electrical impedance Vol. 176) Hardcover mathematics. This book gives a unified presentation tomography (EIT), and the inverse scattering 978-1-84882-366-2 in an abstract setting of the main theorems in problem. The corresponding direct problems are ▶$124.00 bifurcation theory, as well as more recent and lesser studied with respect to existence, uniqueness and known results. It covers both the local and global continuous dependence on parameters. Then some theory of one-parameter bifurcations for operators theoretical results as well as numerical procedures acting in infinite-dimensional Banach spaces, and for the inverse problems are discussed. In this new shows how to apply the theory to problems involving edition, the Factorization Method is included as one partial differential equations. In addition to existence, of the prominent members in this monograph. Since qualitative properties such as stability and nodal the Factorization Method is particularly simple for structure of bifurcating solutions are treated in depth. the problem of EIT and this field has attracted a lot This volume will serve as an important reference of attention during the past decade a chapter on EIT for mathematicians, physicists, and theoretically- has been added in this monograph. The book is highly inclined engineers working in bifurcation theory and illustrated and contains many exercises. This together its applications to partial differential equations. The with the choice of material and its presentation in the second edition is substantially and formally revised book are new, thus making it particularly suitable for and new material is added. Among this is bifurcation graduate students in mathematics and engineering. with a two-dimensional kernel with applications, the R. Khasminskii, Wayne State University, Detroit, MI, USA buckling of the Euler rod, the appearance of Taylor More on www.springer.com/978-1-4419-8473-9 vortices, the singular limit process of the Cahn- Usually dispatched within 3 to 5 business days Stochastic Stability of Differential Hilliard model, and an application of this method to more complicated nonconvex variational problems. 2011. XIV, 307 p. (Applied Mathematical Sciences, Equations Vol. 120) Hardcover More on www.springer.com/978-1-4614-0501-6 978-1-4419-8473-9 Since the publication of the first edition of the present Usually dispatched within 3 to 5 business days volume in 1980, the stochastic stability of differential ▶$99.00 equations has become a very popular subject of 2012. IX, 398 p. 48 illus. (Applied Mathematical research in mathematics and engineering. To date Sciences, Vol. 156) Hardcover exact formulas for the Lyapunov exponent, the 978-1-4614-0501-6 criteria for the moment and almost sure stability, and ▶$74.95 for the existence of stationary and periodic solutions of stochastic differential equations have been widely used in the literature. In this updated volume readers will find important new results on the moment Lyapunov exponent, stability index and some other fields, obtained after publication of the first edition, and a significantly expanded bibliography.This volume provides a solid foundation for students in graduate courses in mathematics and its applications. It is also useful for those researchers who would 52 springer.com

Cybernetics and Information Technology, National Mining Germany; R.F. Swarttouw, Free University Amsterdam, The University, 49005 Dnepropetrovsk, Ukraine Netherlands Regression Analysis Under A Hypergeometric Orthogonal Priori Parameter Restrictions Polynomials and Their q- Construction of various models of objects under Analogues uncertainty is one of the most important problems in The very classical orthogonal polynomials named modern decision making theory. Regression models after Hermite, Laguerre and Jacobi, satisfy many are some of the most prevalent tools for modeling common properties. For instance, they satisfy a under uncertainty and are widely applied in different second-order differential equation with polynomial branches of science such as in industrial research, coefficients and they can be expressed in terms of a D.A. Klyushin, Kyiv National Taras Shevchenko University, agriculture, medicine, and business and economics. hypergeometric function. Replacing the differential Ukraine; S.I. Lyashko, Kyiv National Taras Shevchenko Regression Analysis Under A Priori Parameter equation by a second-order difference equation University, Ukraine; D.A. Nomirovskii, Kyiv National Taras Restrictions will be of interest to a broad spectrum results in (discrete) orthogonal polynomial solutions Shevchenko University, Ukraine; Y.I. Petunin, Kyiv National of readers in applied mathematics, mathematical Taras Shevchenko University, Ukraine; V.V. Semenov, Kyiv with similar properties. Generalizations of these statistics, identification theory, systems analysis, National Taras Shevchenko University, Ukraine difference equations, in terms of Hahn's q-difference econometrics, finance, optimization, and other operator, lead to both continuous and discrete scientific disciplines. Requiring a background in Generalized Solutions of Operator orthogonal polynomials with similar properties. algebra, probability theory, mathematical statistics, For instance, they can be expressed in terms of Equations and Extreme Elements and mathematical programming, this work may (basic) hypergeometric functions. Based on Favard's also be a useful supplement for advanced graduate theorem, the authors first classify all families of The abstract models for many problems in science courses in estimation theory, regression analysis, orthogonal polynomials satisfying a second-order and engineering take the form of an operator mathematical statistics, econometrics, mathematical differential or difference equation with polynomial equation; the resolution of these problems often programming and optimal control, and stochastic coefficients. Together with the concept of duality this requires determining the existence and uniqueness of optimization. The material contained in this leads to the families of hypergeometric orthogonal solutions to these equations. Generalized Solutions of monograph successfully combines interesting polynomials belonging to the Askey scheme. For Operator Equations and Extreme Elements presents theoretical results with methods and algorithms each family they list the most important properties a general functional analytic approach to solving for solving practical problems. It focuses on the and they indicate the (limit) relations. Furthermore operator equations in a general form. This unique construction of regression models with linear and the authors classify all q-orthogonal polynomials and valuable monograph presents recently obtained non-linear constraint inequalities and is the first satisfying a second-order q-difference equation results in the study of the generalized solutions book in which the theoretical results lying in the based on Hahn's q-operator. Together with the of operator equations and extreme elements in background of construction and studying regression concept of duality this leads to the families of basic linear topological spaces. The results are clearly models with inequality constraints on parameters hypergeometric orthogonal polynomials which can and thoroughly presented and offer new methods are presented systematically and solidly. Problems be arranged in a q-analogue of the Askey scheme. of identifying these solutions and studying their are described and studied in a clear, precise, and Again, for each family they list the most important properties. These methods are based on a priori rigorous method and include: calculation of estimates properties, the (limit) relations between the various estimations and a general topological approach for regression parameters, determination of their families and the limit relations (for q --> 1) to the to construct generalized solutions of linear and asymptotic properties and accuracy of estimation, classical hypergeometric orthogonal polynomials nonlinear operator equations. This volume is point and interval prediction by the regression, belonging to the Askey scheme. These (basic) intended for mathematicians, graduate students parameters of which are estimated under inequality hypergeometric orthogonal polynomials have several and researchers studying functional analysis, constraints. The authors’ approach lends itself to applications in various areas of mathematics and operator theory, and the theory of optimal control. numerous applications in various practical problems, (quantum) physics such as approximation theory, Prerequisites include knowledge of basic functional several of which are discussed in detail. analysis. asymptotics, birth and death processes, probability More on www.springer.com/978-1-4614-0573-3 and statistics, coding theory and combinatorics. More on www.springer.com/978-1-4614-0618-1 Usually dispatched within 3 to 5 business days Usually dispatched within 3 to 5 business days More on www.springer.com/978-3-642-05013-8 2012. XIII, 233 p. 4 illus. (Springer Optimization and Its Usually dispatched within 3 to 5 business days 2012. XXI, 202 p. (Springer Optimization and Its Applications, Vol. 54) Hardcover Applications, Vol. 55) Hardcover 978-1-4614-0573-3 2010. XIX, 578 p. 2 illus. (Springer Monographs in 978-1-4614-0618-1 Mathematics) Hardcover ▶$99.00 ▶$99.00 978-3-642-05013-8 ▶$129.00

R. Koekoek, Delft University of Technology, Delft, P.S. Knopov, Department of Mathematical Methods of The Netherlands; P.A. Lesky, University of Stuttgart, Operation Research, V.M. Glushkov Institute of Cybernetics, National Academy of Science of Ukraine, 03187 Kiev, Ukraine; A.S. Korkhin, Department of Economical springer.com 53

to think rigorously. Many historical vignettes illustrate the concepts and acquaint the reader with how mathematicians think and what they care about.In modern times, strict rules for generating and recording proof have been established. At the same time, many new vectors and forces have had an influence over the way mathematics is practiced. Certainly the computer plays a fundamental role in many mathematical investigations.But there are also fascinating social forces that have affected the way that we now conceive of proof. Daniel Gorenstein’s program to classify the finite simple V. Koltchinskii, Georgia Institute of Technology, Atlanta GA, Y. Kosmann-Schwarzbach, Ecole Polytechnique, Palaiseau, groups, Thomas Hales’s resolution of the Kepler USA France sphere-packing problem, Louis de Branges’s proof of the Bieberbach conjecture, and Thurston’s treatment Oracle Inequalities in Empirical Groups and Symmetries of the geometrization program are but some examples Risk Minimization and Sparse From Finite Groups to Lie Groups of mathematical proofs that were generated in ways inconceivable 100 years ago. Krantz treats all of Recovery Problems Unlike many other texts, this book deals with the them---and more---in some detail; he names the École d’Été de Probabilités de Saint-Flour theory of representations of finite groups, compact players and tells all the secrets.Many of the proofs groups, linear Lie groups and their Lie algebras, XXXVIII-2008 treated in this book are described in some detail, concisely and in one volume. Key Topics: • Brisk with figures and explanatory equations. The reader The purpose of these lecture notes is to provide an review of the basic definitions of group theory, with is given a dose of modern mathematics, and how introduction to the general theory of empirical risk examples • Representation theory of finite groups: mathematicians think. Both the joy and the sorrow minimization with an emphasis on excess risk bounds character theory • Representations of compact groups of mathematical exploration are communicated and oracle inequalities in penalized problems. In using the Haar measure • Lie algebras and linear dynamically and energetically in this exciting new recent years, there have been new developments in Lie groups • Detailed study of SO(3) and SU(2), book. this area motivated by the study of new classes of and their representations • Spherical harmonics • methods in machine learning such as large margin Representations of SU(3), roots and weights, with More on www.springer.com/978-0-387-48908-7 classification methods (boosting, kernel machines). quark theory as a consequence of the mathematical Usually dispatched within 3 to 5 business days The main probabilistic tools involved in the analysis properties of this symmetry group This book is 2011. XVII, 264 p. 88 illus., 5 in color. Hardcover of these problems are concentration and deviation illustrated with portraits and a few historical remarks. 978-0-387-48908-7 inequalities by Talagrand along with other methods With only linear algebra and calculus as prerequisites, ▶$39.95 of empirical processes theory (symmetrization Groups and Symmetries: From Finite Groups to Lie inequalities, contraction inequality for Rademacher Groups is accessible to advanced undergraduates in sums, entropy and generic chaining bounds). Sparse mathematics and physics, and will still be of interest recovery based on l_1-type penalization and low to beginning graduate students. Exercises for each rank matrix recovery based on the nuclear norm chapter and a collection of problems with complete penalization are other active areas of research, where solutions make this an ideal text for the classroom and the main problems can be stated in the framework for independent study. of penalized empirical risk minimization, and More on www.springer.com/978-0-387-78865-4 concentration inequalities and empirical processes Usually dispatched within 3 to 5 business days tools have proved to be very useful. More on www.springer.com/978-3-642-22146-0 2010. XVI, 196 p. 44 illus. (Universitext) Softcover Usually dispatched within 3 to 5 business days 978-0-387-78865-4 2011. IX, 254 p. (École d'Été de Probabilités de Saint-Flour, ▶$49.95 Vol. 2033) Softcover 978-3-642-22146-0 H. Kunze, University of Guelph, ON, Canada; D. La Torre, University of Milan, Italy; F. Mendivil, Acadia University, $59.95 ▶ Wolfville, NS, Canada; E.R. Vrscay, University of Waterloo, ON, Canada Fractal-Based Methods in Analysis The idea of modeling the behavior of phenomena at multiple scales has become a useful tool in both pure and applied mathematics. Fractal-based techniques lie at the heart of this area, as fractals are inherently multiscale objects; they very often describe nonlinear phenomena better than traditional mathematical S.G. Krantz, Washington University, St. Louis, MO, USA models. In many cases they have been used for solving inverse problems arising in models described by The Proof is in the Pudding systems of differential equations and dynamical systems. "Fractal-Based Methods in Analysis" draws The Changing Nature of Mathematical Proof together, for the first time in book form, methods Krantz’s book covers the full history and evolution of and results from almost twenty years of research in the proof concept. The notion of rigorous thinking this topic, including new viewpoints and results in has evolved over time, and this book documents that many of the chapters. For each topic the theoretical development. It gives examples both of decisive framework is carefully explained using examples and developments in the technique of proof and also applications. The second chapter on basic iterated of magnificent blunders that taught us about how function systems theory is designed to be used as the 54 springer.com basis for a course and includes many exercises. This this area of research and will be of great interest chapter, along with the three background appendices to graduate students and researchers studying on topological and metric spaces, measure theory, the minisum hypersphere problems as well as and basic results from set-valued analysis, make the mathematicians interested in geometric optimization. book suitable for self-study or as a source book for a More on www.springer.com/978-1-4419-9806-4 graduate course. The other chapters illustrate many extensions and applications of fractal-based methods Usually dispatched within 3 to 5 business days to different areas. This book is intended for graduate 2011. VIII, 116 p. 24 illus. (Springer Optimization and Its students and researchers in applied mathematics, Applications, Vol. 51) Hardcover engineering and social sciences. Herb Kunze is a 978-1-4419-9806-4 Professor in the Department of Mathematics and ▶$99.00 Statistics, University of Guelph. Davide La Torre is an Associate Professor in the Department of J.C. Lagarias, University of Michigan, Ann Arbor, MI, USA Economics, Business and Statistics, University of (Ed.) Milan. Franklin Mendivil is a Professor in the Department of Mathematics and Statistics, Acadia The Kepler Conjecture University. Edward R. Vrscay is a Professor in the The Hales-Ferguson Proof Department of Applied Mathematics, Faculty of The Kepler conjecture, one of geometry's oldest Mathematics, University of Waterloo. A major focus unsolved problems, was formulated in 1611 by of their research is fractals and their applications. Johannes Kepler and mentioned by Hilbert in his More on www.springer.com/978-1-4614-1890-0 famous 1900 problem list. The Kepler conjecture Usually dispatched within 3 to 5 business days states that the densest packing of three-dimensional 2012. XV, 408 p. 72 illus. Hardcover Euclidean space by equal spheres is attained by the 978-1-4614-1890-0 “cannonball" packing. In a landmark result, this was proved by Thomas C. Hales and Samuel P. ▶$124.00 G. Labinaz, Queen's University, Kingston, ON, Canada; M. Ferguson, using an analytic argument completed Guay, Queen's University, Kingston, ON, Canada with extensive use of computers.This book centers Viability of Hybrid Systems around six papers, presenting the detailed proof of the Kepler conjecture given by Hales and Ferguson, A Controllability Operator Approach published in 2006 in a special issue of Discrete & The problem of viability of hybrid systems is Computational Geometry. Further supporting considered in this work. A model for a hybrid material is also presented: a follow-up paper of system is developed including a means of including Hales et al (2010) revising the proof, and describing three forms of uncertainty: transition dynamics, progress towards a formal proof of the Kepler structural uncertainty, and parametric uncertainty. conjecture. For historical reasons, this book also A computational basis for viability of hybrid systems includes two early papers of Hales that indicate his is developed and applied to three control law classes. original approach to the conjecture.The editor's An approach is developed for robust viability based two introductory chapters situate the conjecture on two extensions of the controllability operator. The in a broader historical and mathematical context. M.-C. Körner, Institut für Numerische und Angewandte three-tank example is examined for both the viability These chapters provide a valuable perspective and Mathematik, Georg-August-Universität Göttingen, problem and robust viability problem.The theory is are a key feature of this work.Thomas C. Hales, Göttingen 37083, Germany applied through simulation to an active magnetic Mellon Professor of Mathematics at the University bearing system and to abatch polymerization process of Pittsburgh, began his efforts to solve the Kepler Minisum Hyperspheres showing that viability can be satisfied in practice. conjecture before 1992. He is a pioneer in the use of The problem of viable attainability is examined based computer proof techniques, and he continues work on This volume presents a self-contained introduction on the controllability operator approach introduced a formal proof of the Kepler conjecture as the aim of to the theory of minisum hyperspheres. The minisum by Nerode and colleagues. Lastly, properties of the the Flyspeck Project (F, P and K standing for Formal hypersphere problem is a generalization of the controllability operator are presented. Proof of Kepler).Samuel P. Ferguson completed his famous Fermat-Torricelli problem. The problem doctorate in 1997 under the direction of Hales at the asks for a hypersphere minimizing the weighted More on www.springer.com/978-94-007-2520-1 University of Michigan. In 1995, Ferguson began to sum of distances to a given point set. In the general Usually dispatched within 3 to 5 business days work with Hales and made significant contributions framework of finite dimensional real Banach spaces, 2012. VII, 242 p. 31 illus., 4 in color. (Intelligent Systems, to the proof of the Kepler conjecture. His doctoral the minisum hypersphere problem involves defining Control and Automation: Science and Engineering, Vol. 55) work established one crucial case of the proof, which a hypersphere and calculating the distance between Hardcover appeared as a singly authored paper in the detailed points and hyperspheres. The theory of minisum 978-94-007-2520-1 proof.Jeffrey C. Lagarias, Professor of Mathematics hyperspheres is full of interesting open problems ▶$129.00 at the University of Michigan, Ann Arbor, was a co- which impinge upon the larger field of geometric guest editor, with Gábor Fejes-Tóth, of the special optimization.This work provides an overview of issue of Discrete & Computational Geometry that the history of minisum hyperspheres as well as originally published the proof. describes the best techniques for analyzing and solving minisum hypersphere problems. Related areas More on www.springer.com/978-1-4614-1128-4 of geometric and nonlinear optimization are also Usually dispatched within 3 to 5 business days discussed. Key features of Minisum Hyperspheres 2011. XIV, 456 p. 93 illus., 12 in color. Softcover include: -assorted applications of the minisum 978-1-4614-1128-4 hypersphere problem- a discussion on the existence ▶$74.95 of a solution to the problem with respect to Euclidean and other norms- several proposed extensions to the problem, including a highlight of positive and negative weights and extensive facilities extensionsThis work is the first book devoted to springer.com 55

numbers. The asymptotic behavior of the s-numbers aspects are fast solvers in elastoplasticity, symbolic of Hardy operators acting between Lebesgue spaces analysis for boundary problems, symbolic treatment is determined here in a wide variety of cases. The of operators, computer algebra, and finite element proof methods involve the geometry of Banach spaces methods, a symbolic approach to finite difference and generalized trigonometric functions; there are schemes, cylindrical algebraic decomposition and connections with the theory of the p-Laplacian. local Fourier analysis, and white noise analysis for More on www.springer.com/978-3-642-18267-9 stochastic partial differential equations. Further numerical-symbolic topics range from applied Usually dispatched within 3 to 5 business days and computational geometry to computer algebra 2011. XI, 220 p. 10 illus. (Lecture Notes in Mathematics, Vol. methods used for total variation energy minimization. 2016) Softcover 978-3-642-18267-9 More on www.springer.com/978-3-7091-0793-5 Y.-C. Lai, Arizona State University, Tempe, AZ, USA; T. Tél, ▶$59.95 Usually dispatched within 3 to 5 business days November Eötvös Loránd University , Budapest, Hungary 30, 2011 2012. VIII, 358 p. 50 illus., 13 in color. (Texts & Monographs Transient Chaos in Symbolic Computation) Softcover 3rd Edition Complex Dynamics on Finite Time Scales 978-3-7091-0793-5 S. Lang, Yale University, New Haven, CT, USA ▶$99.00 This book represents the first comprehensive treatment of Transient Chaos. It gives an overview Algebra of the subject based on three decades of intensive research. One special emphasis is on applications, "Lang's Algebra changed the way graduate algebra and the fact that certain interesting dynamical is taught, retaining classical topics but introducing phenomena can be understood only in the framework language and ways of thinking from category of transient chaos. Specific topics treated include basic theory and homological algebra. It has affected all concepts and characterization of transient chaos, subsequent graduate-level algebra books." NOTICES crises, fractal basin boundaries, chaotic scattering, OF THE AMS "The author has an impressive knack noise-induced chaos, chaotic advections and the for presenting the important and interesting ideas spreading of pollutants in fluid flows, quantum of algebra in just the right way, and he never gets chaotic scattering, spatiotemporal chaotic transients bogged down in the dry formalism which pervades and turbulence, controlling transient chaos, and some parts of algebra." MATHEMATICAL REVIEWS analysis of transient chaotic time series, etc. Materials This book is intended as a basic text for a one-year H.P. Langtangen, Simula Research Laboratory, Lysaker, in the book reflect the most recent advances in the course in algebra at the graduate level, or as a useful Norway field. Case studies and examples are included in each reference for mathematicians and professionals who chapter with relevant experimental evidence wherever use higher-level algebra. It successfully addresses A Primer on Scientific appropriate. The book is intended for researchers the basic concepts of algebra. For the revised third and graduate students in Physics, Engineering, edition, the author has added exercises and made Programming with Python Applied Mathematics, and Biomedical Sciences. Ying- numerous corrections to the text. The book serves as a first introduction to computer Cheng Lai is a Professor of Electrical Engineering and More on www.springer.com/978-0-387-95385-4 programming of scientific applications, using Professor of Physics at Arizona State University, USA the high-level Python language. The exposition and a Sixth Century Chair in Electrical Engineering Usually dispatched within 3 to 5 business days is example- and problem-oriented, where the at the University of Aberdeen, UK. Tamás Tél is a applications are taken from mathematics, Professor of Physics at Eötvös University, Budapest, 2002. XV, 918 p. (Graduate Texts in Mathematics, Vol. 211) Hardcover numerical calculus, statistics, physics, biology, Hungary. 978-0-387-95385-4 and finance. The book teaches "Matlab-style" and More on www.springer.com/978-1-4419-6986-6 ▶$79.95 procedural programming as well as object-oriented Usually dispatched within 3 to 5 business days programming. High school mathematics is a required background, and it is advantageous to study classical 2011. XIV, 497 p. (Applied Mathematical Sciences, Vol. 173) Hardcover and numerical one-variable calculus in parallel 978-1-4419-6986-6 with reading this book. Besides learning how to program computers, the reader will also learn how ▶$89.95 to solve mathematical problems, arising in various branches of science and engineering, with the aid of numerical methods and programming. By J. Lang, The Ohio State University, Columbus, USA; D. blending programming, mathematics and scientific Edmunds, University of Sussex, Brighton, United Kingdom applications, the book lays a solid foundation for Eigenvalues, Embeddings and practicing computational science. More on www.springer.com/978-3-642-18365-2 Generalised Trigonometric Online orders shipping within 2-3 days Functions U. Langer, Johannes Kepler University, Linz, Austria; P. Paule, 2011. XXX, 706 p. 72 illus., 28 in color. (Texts in The main theme of the book is the study, from Johannes Kepler University, Linz, Austria (Eds.) Computational Science and Engineering, Vol. 6) Hardcover the standpoint of s-numbers, of integral operators 978-3-642-18365-2 of Hardy type and related Sobolev embeddings. Numerical and Symbolic Scientific ▶$59.95 In the theory of s-numbers the idea is to attach to every bounded linear map between Banach Computing spaces a monotone decreasing sequence of non- Progress and Prospects negative numbers with a view to the classification The book presents the state of the art, new results, of operators according to the way in which these and it also includes articles pointing to future numbers approach a limit: approximation numbers developments. Most of the articles center around provide an especially important example of such the theme of partial differential equations. Major 56 springer.com

Albuquerque, NM, USA; R.D. Nair, National Center for Atmospheric Research, Boulder, CO, USA (Eds.) Numerical Techniques for Global Atmospheric Models This book surveys recent developments in numerical techniques for global atmospheric models. It is based upon a collection of lectures prepared by leading experts in the field. The chapters reveal the multitude of steps that determine the global atmospheric model design. They encompass the choice of the equation H.P. Langtangen, Simula Research Laboratory, Lysaker, C. Laurent-Thiébaut, Université Joseph Fourier, Saint Martin set, computational grids on the sphere, horizontal Norway d'Héres, France and vertical discretizations, time integration methods, filtering and diffusion mechanisms, conservation Python Scripting for Holomorphic Function Theory in properties, tracer transport, and considerations for Computational Science Several Variables designing models for massively parallel computers. A reader interested in applied numerical methods but Now in its revised and updated 4th edition, this An Introduction also the many facets of atmospheric modeling should book teaches computational scientists how to This book provides an introduction to complex find this book of particular relevance. develop tailored, flexible, and human-efficient analysis in several variables. The viewpoint of More on www.springer.com/978-3-642-11639-1 working environments built from small programs integral representation theory together with Grauert's Usually dispatched within 3 to 5 business days written in the easy-to-learn, high-level Python bumping method offers a natural extension of single language.As in the previous edition, the focus is on variable techniques to several variables analysis and 2011. XVI, 556 p. (Lecture Notes in Computational Science highly relevant examples and applications. These leads rapidly to important global results. Applications and Engineering, Vol. 80) Hardcover 978-3-642-11639-1 include binding together existing applications and focus on global extension problems for CR functions, tools, for example, for automating simulation, data such as the Hartogs-Bochner phenomenon and ▶$74.95 analysis, and visualization.The book also covers removable singularities for CR functions. Three steering simulations and computational experiments; appendices on differential manifolds, sheaf theory equipping old programs with graphical user and functional analysis make the book self-contained. Forthcoming interfaces; making computational Web applications; Each chapter begins with a detailed abstract, clearly W.J. Layton, University of Pittsburgh, PA, USA; L. Rebholz, and creating interactive interfaces with a Maple/ demonstrating the structure and relations of following Clemson University, SC, USA Matlab-like syntax to numerical applications in C/ chapters. New concepts are clearly defined and C++ or Fortran.The highly regarded author, Hans theorems and propositions are proved in detail. Petter Langtangen, demonstrates that scripting with Historical notes are also provided at the end of each Approximate Deconvolution Python helps the programmer achieve much greater chapter. Clear and succinct, this book will appeal to Models of Turbulence productivity, increases the reliability of scientific post-graduate students, young researchers seeking work and lets programmers have more fun - on Unix, Analysis, Phenomenology and Numerical an introduction to holomorphic function theory in Analysis Windows and Macintosh.The fourth edition corrects, several variables and lecturers seeking a concise book updates and improves the implementation of a range on the subject. This volume presents a mathematical development of tools that have seen significant changes in recent of a recent approach to the modeling and simulation More on www.springer.com/978-0-85729-029-8 years. The open source software tools and examples of turbulent flows based on methods for the associated with the book are also improved. Usually dispatched within 3 to 5 business days approximate solution of inverse problems. The More on www.springer.com/978-3-642-21962-7 resulting Approximate Deconvolution Models 2011. XIII, 252 p. (Universitext) Softcover Due: March 29, 2012 or ADMs have some advantages over more 978-0-85729-029-8 commonly used turbulence models – as well as some ▶$59.95 2012. XXVI, 760p. 70 illus. in color. (Texts in disadvantages. Our goal in this book is to provide Computational Science and Engineering, Vol. 3) Hardcover a clear and complete mathematical development of 978-3-642-21962-7 ADMs, while pointing out the difficulties that remain. ▶$89.95 In order to do so, we present the analytical theory of ADMs, along with its connections, motivations and complements in the phenomenology of and algorithms for ADMs. More on www.springer.com/978-3-642-24408-7 Due: February 28, 2012 2012. VIII, 188 p. 22 illus., 11 in color. (Lecture Notes in Mathematics, Vol. 2042) Softcover 978-3-642-24408-7 ▶$49.95

P.H. Lauritzen, National Center for Atmospheric Research, Boulder, CO, USA; C. Jablonowski, University of Michigan, Ann Arbor, MI, USA; M.A. Taylor, Sandia National Laboratory, springer.com 57

can carry, such as Riemannian metrics, symplectic structures, and foliations. The book is aimed at students who already have a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis. John M. Lee is Professor of Mathematics at the University of Washington in Seattle, where he regularly teaches graduate courses on the topology and geometry of manifolds. He was the recipient of the American Mathematical Society's Centennial Research Fellowship and he is the author of two previous Springer books, Introduction Y. Le Jan, Université Paris-Sud, Orsay, France J.M. Lee, University of Washington, Seattle, WA, USA to Topological Manifolds (2000) and Riemannian Manifolds: An Introduction to Curvature (1997). Markov Paths, Loops and Fields Introduction to Topological More on www.springer.com/978-0-387-95448-6 École d'Été de Probabilités de Saint-Flour Manifolds Usually dispatched within 3 to 5 business days XXXVIII – 2008 This book is an introduction to manifolds at the The purpose of these notes is to explore some simple beginning graduate level. It contains the essential 2003. XVII, 628 p. 157 illus. (Graduate Texts in relations between Markovian path and loop measures, topological ideas that are needed for the further Mathematics, Vol. 218) Softcover 978-0-387-95448-6 the Poissonian ensembles of loops they determine, study of manifolds, particularly in the context their occupation fields, uniform spanning trees, of differential geometry, algebraic topology, and ▶$64.95 determinants, and Gaussian Markov fields such related fields. Its guiding philosophy is to develop as the free field. These relations are first studied in these ideas rigorously but economically, with complete generality for the finite discrete setting, then minimal prerequisites and plenty of geometric Forthcoming partly generalized to specific examples in infinite and intuition.Although this second edition has the J. Lee, University of Michigan, Ann Arbor, MI, USA; S. Leyffer, continuous spaces. same basic structure as the first edition, it has been Argonne National Laboratory, Argonne, IL, USA (Eds.) More on www.springer.com/978-3-642-21215-4 extensively revised and clarified; not a single page has Usually dispatched within 3 to 5 business days been left untouched. The major changes include a new introduction to CW complexes (replacing most Mixed Integer Nonlinear 2011. VIII, 124 p. 9 illus. (École d'Été de Probabilités de Saint- of the material on simplicial complexes in Chapter Programming Flour, Vol. 2026) Softcover 5); expanded treatments of manifolds with boundary, 978-3-642-21215-4 local compactness, group actions, and proper Many engineering, operations, and scientific ▶$49.95 maps; and a new section on paracompactness.This applications include a mixture of discrete and text is designed to be used for an introductory continuous decision variables and nonlinear graduate course on the geometry and topology of relationships involving the decision variables that M. Ledoux, University of Strasbourg, France; M. Talagrand, manifolds. It should be accessible to any student have a pronounced effect on the set of feasible University of Paris VI, France who has completed a solid undergraduate degree in and optimal solutions. Mixed-integer nonlinear mathematics. The author’s book Introduction to programming (MINLP) problems combine the Probability in Banach Spaces Smooth Manifolds is meant to act as a sequel to this numerical difficulties of handling nonlinear functions Isoperimetry and Processes book. with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is Isoperimetric, measure concentration and random More on www.springer.com/978-1-4419-7939-1 one of the most flexible modeling paradigms available process techniques appear at the basis of the modern Usually dispatched within 3 to 5 business days for optimization; but because its scope is so broad, understanding of Probability in Banach spaces. Based in the most general cases it is hopelessly intractable. on these tools, the book presents a complete treatment 2011. XVII, 433 p. 131 illus. (Graduate Texts in Nonetheless, an expanding body of researchers of the main aspects of Probability in Banach spaces Mathematics, Vol. 202) Hardcover and practitioners — including chemical engineers, (integrability and limit theorems for vector valued 978-1-4419-7939-1 operations researchers, industrial engineers, random variables, boundedness and continuity of ▶$74.95 mechanical engineers, economists, statisticians, random processes) and of some of their links to computer scientists, operations managers, and Geometry of Banach spaces (via the type and cotype mathematical programmers — are interested in properties). Its purpose is to present some of the J.M. Lee, University of Washington, Seattle, WA, USA solving large-scale MINLP instances. main aspects of this theory, from the foundations More on www.springer.com/978-1-4614-1926-6 to the most important achievements. The main Introduction to Smooth Manifolds features of the investigation are the systematic use Usually dispatched within 3 to 5 business days December 31, 2011 of isoperimetry and concentration of measure and This book is an introductory graduate-level textbook abstract random process techniques (entropy and on the theory of smooth manifolds. Its goal is to 2012. XVII, 690 p. 82 illus. (The IMA Volumes in Mathematics majorizing measures). Examples of these probabilistic familiarize students with the tools they will need in and its Applications, Vol. 154) Hardcover 978-1-4614-1926-6 tools and ideas to classical Banach space theory are order to use manifolds in mathematical or scientific further developed. research--- smooth structures, tangent vectors and ▶$179.00 covectors, vector bundles, immersed and embedded More on www.springer.com/978-3-642-20211-7 submanifolds, tensors, differential forms, de Rham Usually dispatched within 3 to 5 business days cohomology, vector fields, flows, foliations, Lie 1991. XII, 480 p. 1 illus. (Classics in Mathematics, Vol.) derivatives, Lie groups, Lie algebras, and more. The Softcover approach is as concrete as possible, with pictures 978-3-642-20211-7 and intuitive discussions of how one should think ▶$74.95 geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. Along the way, the book introduces students to some of the most important examples of geometric structures that manifolds 58 springer.com

T. Lery, European Science Foundation, Strasbourg, France; M. Primicerio, Universita degli Studi di Firenze, Italy; M.J. H.-X. Li, City University of Hong Kong, Hong Kong, China; C. S. Liao, Shanghai Jiao Tong University, China Esteban, Université Paris-Dauphine, France; M. Fontes, Qi, Shanghai Jiao Tong University, Shanghai, China Centre for Mathematical Sciences, Lund, Sweden; Y. Maday, Homotopy Analysis Method in Université Pierre et Marie Curie, Paris, France; V. Mehrmann, Spatio-Temporal Modeling of TU Berlin, Germany; G. Quadros, Critical Software SA, Nonlinear Differential Equations Coimbra, Portugal; W. Schilders, TU Eindhoven, Netherlands; Nonlinear Distributed Parameter A. Schuppert, Bayer Technology Service GmbH, Leverkusen, "Homotopy Analysis Method in Nonlinear Germany; H. Tewkesbury, KNT for Industrial Mathematics, Systems Differential Equations" presents the latest Guildford, UK (Eds.) A Time/Space Separation Based Approach developments and applications of the analytic approximation method for highly nonlinear European Success Stories in The purpose of this volume is to provide a brief problems, namely the homotopy analysis method review of the previous work on model reduction Industrial Mathematics (HAM). Unlike perturbation methods, the HAM has and identifi cation of distributed parameter systems nothing to do with small/large physical parameters. (DPS), and develop new spatio-temporal models This unique book presents real world success stories In addition, it provides great freedom to choose and their relevant identifi cation approaches.In of collaboration between mathematicians and the equation-type of linear sub-problems and the this book, a systematic overview and classifi cation industrial partners, showcasing first-hand case base functions of a solution. Above all, it provides on the modeling of DPS is presented fi rst, which studies, and lessons learned from the experiences, a convenient way to guarantee the convergence of includes model reduction, parameter estimation and technologies, and business challenges that led to the a solution. This book consists of three parts. Part I system identifi cation. Next, a class of block-oriented successful development of industrial solutions based provides its basic ideas and theoretical development. nonlinear systems in traditional lumped parameter on mathematics.These success stories show the crucial Part II presents the HAM-based Mathematica package systems (LPS) is extended to DPS, which results contribution of mathematics to innovation and to BVPh 1.0 for nonlinear boundary-value problems in the spatio-temporal Wiener and Hammerstein the industrial creation of value, and the key position and its applications. Part III shows the validity of the systems and their identifi cation methods. Then, of mathematics in the handling of complex systems, HAM for nonlinear PDEs, such as the American put the traditional Volterra model is extended to DPS, amplifying innovation.Each story describes the option and resonance criterion of nonlinear travelling which results in the spatio-temporal Volterra challenge that led to the industrial cooperation, how waves. New solutions to a number of nonlinear model and its identification algorithm. All these the challenge was approached and how the solutions problems are presented, illustrating the originality methods are based on linear time/space separation. were achieved and implemented. When brought of the HAM. Mathematica codes are freely available Sometimes, the nonlinear time/space separation together, they illustrate the versatile European online to make it easy for readers to understand and can play a better role in modeling of very complex landscape of projects in almost all areas of applied use the HAM. This book is suitable for researchers processes.Thus, a nonlinear time/space separation mathematics and across all business sectors.This book and postgraduates in applied mathematics, physics, based neural modeling is also presented for a class of success stories has its origin in the Forward Look nonlinear mechanics, finance and engineering.Dr. of DPS with more complicated dynamics. Finally, about Mathematics and Industry that was funded Shijun Liao, a distinguished professor of Shanghai all these modeling approaches are successfully by the European Science Foundation (ESF) and Jiaotong University, is a pioneer of the HAM. applied to industrial thermal processes, including coordinated by the Applied Mathematics Committee a catalytic rod, a packed-bed reactor and a snap More on www.springer.com/978-3-642-25131-3 of the European Mathematical Society (EMS).In curing oven. The work is presented giving a unifi Due: February 28, 2012 each of these success stories, researchers, students, ed view from time/space separation. The book also entrepreneurs, policy makers and business leaders in 2012. X, 400 p. 50 illus. Hardcover illustrates applications to thermal processes in the a range of disciplines will find valuable material and 978-3-642-25131-3 electronics packaging and chemical industry. This important lessons that can be applied in their own ▶$124.00 volume assumes a basic knowledge about distributed fields. parameter systems, system modeling and identifi More on www.springer.com/978-3-642-23847-5 cation. It is intended for researchers, graduate Online orders shipping within 2-3 days students and engineers interested in distributed 2011. XII, 136 p. 200 illus., 185 in color. 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M. Lifshits, St.Petersburg State University, Russia Lectures on Gaussian Processes Gaussian processes can be viewed as a far-reaching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful springer.com 59 range of tools for probabilistic modelling in various Forthcoming dealing with biological cellular control systems. In academic and technical domains such as Statistics, particular, the book shows how to use the law of L. Linsen, Jacobs University Bremen, Germany; H. Hagen, Forecasting, Finance, Information Transmission, mass balance and the law of mass action to derive Technical University of Kaiserslautern, Germany; B. Hamann, Machine Learning - to mention just a few. The University of California, Davis, CA, USA; H.-C. Hege, Zuse an enzyme kinetic model - the Michaelis-Menten objective of these Briefs is to present a quick and Institute Berlin (ZIB), Germany (Eds.) function or the Hill function, how to use a current- condensed treatment of the core theory that a voltage relation, Nernst potential equilibrium reader must understand in order to make his own Visualization in Medicine and Life equation, and Hodgkin and Huxley's models to independent contributions. The primary intended model an ionic channel or pump, and how to use readership are PhD/Masters students and researchers Sciences II the law of mass balance to integrate these enzyme working in pure or applied mathematics.The Progress and New Challenges or channel models into a complete feedback control first chapters introduce essentials of the classical system. The book also illustrates how to use data to For some time, medicine has been an important theory of Gaussian processes and measures with estimate parameters in a model, how to use MATLAB driver for the development of data processing and the core notions of reproducing kernel, integral to solve a model numerically, how to do computer visualization techniques. Improved technology offers representation, isoperimetric property, large deviation simulations, and how to provide model predictions. the capacity to generate larger and more complex data principle. The brevity being a priority for teaching Furthermore, the book demonstrates how to conduct sets related to imaging and simulation. This, in turn, and learning purposes, certain technical details a stability and sensitivity analysis on a model. creates the need for more effective visualization tools and proofs are omitted. The later chapters touch for medical practitioners to interpret and utilize data More on www.springer.com/978-88-470-2489-2 important recent issues not sufficiently reflected in in meaningful ways. The first edition of Visualization Due: January 13, 2012 the literature, such as small deviations, expansions, in Medicine and Life Sciences (VMLS) emerged and quantization of processes. In university teaching, from a workshop convened to explore the significant 2012. X, 290 p. 61 illus. (MS&A, 0) Hardcover one can build a one-semester advanced course upon data visualization challenges created by emerging 978-88-470-2489-2 these Briefs. technologies in the life sciences. The workshop and ▶$69.95 More on www.springer.com/978-3-642-24938-9 the book addressed questions of whether medical Due: January 31, 2012 data visualization approaches can be devised or 2012. X, 121 p. (SpringerBriefs in Mathematics) Softcover improved to meet these challenges, with the promise 978-3-642-24938-9 of ultimately being adopted by medical experts. ▶$49.95 Visualization in Medicine and Life Sciences II follows the second international VMLS workshop, held in Bremerhaven, Germany, in July 2009. Internationally renowned experts from the visualization and driving application areas came together for this second workshop. The book presents peer-reviewed research and survey papers which document and discuss the progress made, explore new approaches to data visualization, and assess new challenges and research directions. The assembled papers span the frontiers of VMLS, examining these topics: * Feature Extraction J.D. Logan, University of Nebraska-Lincoln, Lincoln, NE, USA * Classification * Volumes and Shapes * Tensor Visualization * Visualizing Genes, Proteins, and A First Course in Differential Molecules Equations More on www.springer.com/978-3-642-21607-7 Z. Lin, Zhejiang University, Hangzhou, China; Z. Bai, National Due: January 28, 2012 This concise and up-to-date textbook is designed for the standard sophomore course in differential University of Singapore, Singapore 2012. VIII, 287 p. 132 illus., 116 in color. (Mathematics and equations. It treats the basic ideas, models, and Visualization) Hardcover solution methods in a user friendly format that Probability Inequalities 978-3-642-21607-7 is accessible to engineers, scientists, economists, $124.00 Inequality has become an essential tool in many areas ▶ and mathematics majors. It emphasizes analytical, of mathematical research, for example in probability graphical, and numerical techniques, and it and statistics where it is frequently used in the proofs. provides the tools needed by students to continue "Probability Inequalities" covers inequalities related to the next level in applying the methods to more with events, distribution functions, characteristic advanced problems. There is a strong connection functions, moments and random variables (elements) to applications with motivations in mechanics and and their sum. The book shall serve as a useful heat transfer, circuits, biology, economics, chemical tool and reference for scientists in the areas of reactors, and other areas. Exceeding the first edition probability and statistics, and applied mathematics. by over one hundred pages, this new edition has a Prof. Zhengyan Lin is a fellow of the Institute of large increase in the number of worked examples Mathematical Statistics and currently a professor and practice exercises, and it continues to provide at Zhejiang University, Hangzhou, China. He is the templates for MATLAB and Maple commands and prize winner of National Natural Science Award of codes that are useful in differential equations. Sample China in 1997. Prof. Zhidong Bai is a fellow of TWAS examination questions are included for students and and the Institute of Mathematical Statistics; he is a instructors. Solutions of many of the exercises are professor at the National University of Singapore and contained in an appendix. Moreover, the text contains W. Liu, University of Central Arkansas, Conway, AR, USA Northeast Normal University, Changchun, China. a new, elementary chapter on systems of differential More on www.springer.com/978-3-642-05260-6 Introduction to Modeling equations, both linear and nonlinear, that introduces key ideas without matrix analysis. Two subsequent Online orders shipping within 2-3 days Biological Cellular Control chapters treat systems in a more formal way. Briefly, 2011. 180 p. Hardcover the topics include: * First-order equations: separable, 978-3-642-05260-6 Systems linear, autonomous, and bifurcation phenomena; ▶$109.00 This textbook contains the essential knowledge in * Second-order linear homogeneous and non- modeling, simulation, analysis, and applications in homogeneous equations; * Laplace transforms; and 60 springer.com

* Linear and nonlinear systems, and phase plane the last thirty years with growing applications in and researchers in applied mathematics, physics, properties. math, computer science, and other applied areas. mechanics, and control. Dr. Albert C.J. Luo is an More on www.springer.com/978-1-4419-7591-1 Topological combinatorics is concerned with internationally respected professor in nonlinear solutions to combinatorial problems by applying dynamics and mechanics, and he works at Southern Usually dispatched within 3 to 5 business days topological tools. In most cases these solutions Illinois University Edwardsville, USA. are very elegant and the connection between 2011. XVIII, 386 p. 82 illus. (Undergraduate Texts in More on www.springer.com/978-3-642-22460-7 combinatorics and topology often arises as an Mathematics) Hardcover unexpected surprise. The textbook covers topics such Due: February 28, 2012 978-1-4419-7591-1 as fair division, graph coloring problems, evasiveness 2012. XI, 697 p. 228 illus., 5 in color. Hardcover $74.95 ▶ of graph properties, and embedding problems from 978-3-642-22460-7 discrete geometry. It is written in plain language and ▶$129.00 many figures support the understanding of concepts and proofs. In many cases several alternative proofs for the same result are given and each chapter ends Forthcoming with a series of exercises. The extensive appendix makes the book completely self–contained. The A. Machi, Università di Roma La Sapienza, Italy textbook is well suited for every undergraduate math major with some basic mathematical experience. Algebra for Symbolic Previous knowledge in topology or graph theory is Computation certainly helpful but not necessary. The text may be used as a basis for a one– or two–semester course Introduction to Computational Algebra as well as a supplementary text for a topology or This book provides basic material for a course in combinatorics class. computer algebra. It revises basic algebra concepts A. Logg, Simula Research Laboratory, Lysaker, Norway; K.- in a form suited for implementation on a computer A. Mardal, Simula Research Laboratory, Lysaker, Norway; G. More on www.springer.com/978-1-4419-7909-4 using one of the available computer algebra systems. Wells, University of Cambridge, U.K. (Eds.) Due: December 2011 More on www.springer.com/978-88-470-2396-3 Automated Solution of 2012. 240 p. 151 illus., 2 in color. Hardcover Due: March 9, 2012 Differential Equations by the 978-1-4419-7909-4 ▶approx. $59.95 2012. 190 p. 11 illus. (La Matematica per il 3+2, 0) Finite Element Method Softcover The FEniCS Book 978-88-470-2396-3 ▶approx. $59.95 This book is written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a tutorial for readers who are new to the topic. Following the tutorial, chapters in Part I address fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in A.C.J. Luo, Southern Illinois University Edwardsville, IL, USA Part II address the design and implementation of the FEnicS software. Chapters in Part III present Discontinuous Dynamical Systems the application of FEniCS to a wide range of A. Machì, Università La Sapienza, Roma, Italia applications, including fluid flow, solid mechanics, “Discontinuous Dynamical Systems” presents electromagnetics and geophysics. a theory of dynamics and flow switchability in Groups More on www.springer.com/978-3-642-23098-1 discontinuous dynamical systems, which can be as the mathematical foundation for a new dynamics An Introduction to Ideas and Methods of the Due: January 3, 2012 of dynamical system networks. The book includes a Theory of Groups theory for flow barriers and passability to boundaries 2012. VI, 718 p. 358 illus., 311 in color. (Lecture Groups are a means of classification, via the group in discontinuous dynamical systems that will Notes in Computational Science and Engineering, Vol. 84) action on a set, but also the object of a classification. Hardcover completely change traditional concepts and ideas How many groups of a given type are there, and 978-3-642-23098-1 in the field of dynamical systems. Edge dynamics how can they be described? Hölder’s program for ▶$89.95 and switching complexity of flows in discontinuous attacking this problem in the case of finite groups dynamical systems are explored in the book and is a sort of leitmotiv throughout the text. Infinite provide the mathematical basis for developing the groups are also considered, with particular attention attractive network channels in dynamical systems. to logical and decision problems. Abelian, nilpotent M. de Longueville, Institut für Mathematik, Technische The theory of bouncing flows to boundaries, Universität Berlin 10623 Germany and solvable groups are studied both in the finite and edges and vertexes in discontinuous dynamical infinite case. Permutation groups and are treated in A Course in Topological systems with multi-valued vector fields is described detail; their relationship with Galois theory is often in the book as a “billiard” theory of dynamical taken into account. The last two chapters deal with Combinatorics system networks. The theory of dynamical system the representation theory of finite group and the interactions in discontinued dynamical systems cohomology theory of groups; the latter with special A Course in Topological Combinatorics is the first can be used as a general principle in dynamical emphasis on the extension problem. The sections are undergraduate textbook on the field of topological system networks, which is applied to dynamical combinatorics, a subject that has become an active system synchronization. The book represents a and innovative research area in mathematics over valuable reference work for university professors springer.com 61 followed by exercises; hints to the solution are given, Y. Matsumoto, Gakushuin University, Tokyo, Japan; J.M. and for most of them a complete solution is provided. Montesinos-Amilibia, Universidad Complutense de Madrid, Spain More on www.springer.com/978-88-470-2420-5 Due: January 20, 2012 Pseudo-periodic Maps and

2012. XIV, 372 p. 1 illus. (La Matematica per il 3+2) Degeneration of Riemann Softcover Surfaces 978-88-470-2420-5 ▶$59.95 The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms R. Martí, University of Valencia, Spain; G. Reinelt, University was originally introduced by J. Nielsen in 1944 as of Heidelberg, Germany an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic The Linear Ordering Problem mapping classes are completely classified, and Exact and Heuristic Methods in Combinatorial Nielsen’s incomplete classification is corrected. The second part applies the results of the first part to Optimization the topology of degeneration of Riemann surfaces. Complex optimization problems abound in the real It is shown that the set of topological types of all world. In the face of these challenges, established the singular fibers appearing in one-parameter methods often fall short of providing solutions. holomorphic families of Riemann surfaces is in a However, ‘exact’ and ‘heuristic’ techniques are bijective correspondence with the set of conjugacy dramatically enhancing our ability to solve significant classes of the pseudo-periodic maps of negative practical problems in the world of optimization. twists. The correspondence is given by the topological P. Mangani, Università di Firenze, Italy (Ed.) They are changing the landscape in the field, monodromy. Model Theory and Applications broadening the frontiers of the possible, and allowing More on www.springer.com/978-3-642-22533-8 us to engage effectively with a whole new range of Usually dispatched within 3 to 5 business days Lectures given at a Summer School of the Centro challenges. This monograph sets out state-of-the-art Internazionale Matematico Estivo (C.I.M.E.) held optimization methods for tackling the ‘linear ordering 2011. XVI, 238 p. 55 illus. (Lecture Notes in Mathematics, Vol. in Bressanone (Bolzano), Italy, June 20-28, 1975 problem’ (LOP). Whereas important applications 2030) Softcover in business, engineering and economics lie beyond 978-3-642-22533-8 Lectures: G.E. Sacks: Model theory and applications.- ▶$59.95 H.J. Keisler: Constructions in model theory.- the reach of methodologies that have been the focus Seminars: M. Servi: SH formulas and generalized of academic research for three decades, the fresh exponential.- J.A. Makowski: Topological model approaches set out in this volume provide practical theory. solutions to the LOP. The focus on the LOP does V. Mayer, Université Lille 1, Villeneuve d'Ascq, France; B. not limit the monograph’s scope and applicability, Skorulski, Universidad Catolica del Norte, Antofagasta, Chile; More on www.springer.com/978-3-642-11119-8 however. The exact and heuristic techniques outlined M. Urbanski, University of North Texas, Denton, TX, USA Due: February 28, 2012 in these pages can be put to use in any number 2011. 150 p. (C.I.M.E. Summer Schools, Vol. 69) Softcover of combinatorial optimization problems. While Distance Expanding Random 978-3-642-11119-8 the authors employ the LOP to illustrate cutting- Mappings, Thermodynamical ▶$29.95 edge optimization technologies, the book is also a tutorial on how to design effective and successful Formalism, Gibbs Measures and implementations of exact and heuristic procedures alike. The information in these pages provides readers Fractal Geometry with a toolkit that can be employed in a variety of The theory of random dynamical systems originated settings. As a result, the book will be of great interest from stochasticdifferential equations. It is intended to researchers and practitioners in a number of to provide a framework andtechniques to describe fields, including computer science, mathematics, and analyze the evolution of dynamicalsystems operations research, management science, industrial when the input and output data are known only engineering, and economics. It is also suitable for use approximately, according to some probability as a textbook on issues of practical optimization in a distribution. The development of this field, in masters course, or as a reference book for engineering both the theory and applications, has gone in optimization algorithms. The authors have sought to many directions. In this manuscript we introduce make the book accessible to as wide an audience as measurable expanding random dynamical systems, possible by providing the reader with basic definitions develop the thermodynamical formalism and and concepts in optimization. In addition, the establish, in particular, the exponential decay of C. Marchioro, Fondazione CIME, Milano, Italy (Ed.) numerous tutorials aid speedy assimilation, while correlations and analyticity of the expected pressure the coverage given to the next generation of Flash although the spectral gap property does not hold. This Dynamical Systems software prepares readers for future developments. theory is then used to investigate fractal properties Lectures given at a Summer School of the Centro More on www.springer.com/978-3-642-16728-7 of conformal random systems. We prove a Bowen’s Internazionale Matematico Estivo (C.I.M.E.) held Usually dispatched within 3 to 5 business days formula and develop the multifractal formalism in Bressanone (Bolzano), Italy, June 19-27, 1978 of the Gibbs states. Depending on the behavior 2011. XII, 171 p. 38 illus., 12 in color. (Applied Mathematical of the Birkhoff sums of the pressure function we none Sciences, Vol. 175) Hardcover arrive at a natural classification of the systems into 978-3-642-16728-7 More on www.springer.com/978-3-642-13928-4 two classes: quasi-deterministic systems, which $99.00 Due: February 28, 2012 ▶ share manyproperties of deterministic ones; and essentially random systems, which are rather generic 2011. 312 p. (C.I.M.E. Summer Schools, Vol. 78) Softcover 978-3-642-13928-4 and never bi-Lipschitz equivalent to deterministic systems. We show that in the essentially random ▶$49.95 case the Hausdorff measure vanishes, which refutes 62 springer.com a conjecture by Bogenschutz and Ochs. Lastly, we 99 cents? You'll be surprised." Dwight Lee, University present applications of our results to various specific of Georgia conformal random systems and positively answer a More on www.springer.com/978-0-387-76999-8 question posed by Bruck and Buger concerning the Hausdorff dimension of quadratic random Julia sets. Usually dispatched within 3 to 5 business days 2008. XVI, 328 p. 3 illus. Hardcover More on www.springer.com/978-3-642-23649-5 978-0-387-76999-8 Usually dispatched within 3 to 5 business days ▶$27.99 2011. X, 112 p. 3 illus. in color. (Lecture Notes in Mathematics, Vol. 2036) Softcover 978-3-642-23649-5 ▶$49.95 R.B. McKenzie, University of California, Irvine, CA, USA Why Popcorn Costs So Much at the Movies And Other Pricing Puzzles Why Popcorn Costs So Much at the Movies, And Other Pricing Puzzles unravels the pricing mysteries we encounter every day. Have you ever wondered why all movies, whether blockbusters or duds, have R.A. 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Complex systems are risks and relative prices of air vs. automobile travel, systems that comprise many interacting parts with the Sobolev spaces play an outstanding role in modern and jacked up both security costs and flight delays. ability to generate a new quality of collective behavior analysis, in particular, in the theory of partial Professor McKenzie also explores the unintended through self-organization, e.g. the spontaneous differential equations and its applications in consequences of well-meaning efforts to spur the formation of temporal, spatial or functional mathematical physics. They form an indispensable use of environmentally friendly fuels: starvation structures. These systems are often characterized tool in approximation theory, spectral theory, among millions of people around the world, and the by extreme sensitivity to initial conditions as well as differential geometry etc. The theory of these spaces destruction of rainforests in Malaysia and Indonesia. emergent behavior that are not readily predictable is of interest in itself being a beautiful domain of How can these things be? If you think you know or even completely deterministic. The more than mathematics. The present volume includes basics the answers, think again. 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Each chapter features a combination of classical and re¬cent results, well beyond the traditional domain of algebraic logic: among others, a comprehensive account is given of many effective procedures that have been re¬cently developed for the algebraic and geometric objects represented by formulas in Łukasiewicz logic. The book embodies the viewpoint that modern Łukasiewicz logic and MV-algebras provide a benchmark for the study of several deep mathematical prob¬lems, such as Rényi conditionals of continuously valued events, the many-valued generalization of Carathéodory algebraic probability M. Morishita, Kyushu University, Nishi-ku, Fukuoka, Japan theory, morphisms and invari¬ant measures of J.D. Murray, University of Washington, Seattle, WA, USA Knots and Primes rational polyhedra, bases and Schauder bases as jointly refinable partitions of unity, and first-order Mathematical Biology II An Introduction to Arithmetic Topology logic with [0,1]-valued identity on Hilbert space. Complete versions are given of a compact body Spatial Models and Biomedical Applications This is a foundation for arithmetic topology - a of recent results and techniques, proving virtually new branch of mathematics which is focused upon In the ten years since the first edition of this book everything that is used throughout, so that the book the analogy between knot theory and number appeared the field of mathematical biology has can be used both for individual study and as a source theory. Starting with an informative introduction grown at an astonishing rate and has established of reference for the more advanced reader. to its origins, namely Gauss, this text provides a itself as a distinct discipline. Mathematical modelling background on knots, three manifolds and number More on www.springer.com/978-94-007-0839-6 is now being applied in every major discipline fields. Common aspects of both knot theory and Usually dispatched within 3 to 5 business days in the biomedical sciences. Though the field has become increasingly large and specialized, this number theory, for instance knots in three manifolds 2011. XVIII, 256 p. 16 illus. (Trends in Logic, Vol. 35) versus primes in a number field, are compared book remains important as a text that introduces Hardcover some of the exciting problems that arise in biology throughout the book. These comparisons begin at 978-94-007-0839-6 and gives some indication of the wide spectrum of an elementary level, slowly building up to advanced ▶$139.00 theories in later chapters. Definitions are carefully questions that modelling can address. Due to this formulated and proofs are largely self-contained. tremendous development in recent years, for this new When necessary, background information is provided edition Murray is covering certain items in depth, and theory is accompanied with a number of useful Forthcoming giving new applications such as modelling marital interaction, growth of cancer tumours, temperature examples and illustrations, making this a useful text D. Mundici, University of Firenze, Italy for both undergraduates and graduates in the field of sex determination, wolf territoriality, wolf-deer knot theory, number theory and geometry. survival etc. In other areas he discusses basic Logic: a Brief Course modelling concepts and provides further references More on www.springer.com/978-1-4471-2157-2 This short book, geared towards undergraduate as needed. He also provides even closer links between Usually dispatched within 3 to 5 business days December students of computer science and mathematics, is models and experimental data throughout the text. 31, 2011 specifically designed for a first course in mathematical The book continues to present a broad view of the logic. A proof of Gödel's completeness theorem and field of theoretical and mathematical biology and 2012. XI, 191 p. 42 illus. (Universitext) Softcover its main consequences is given using Robinson's gives us an excellent background from which to begin 978-1-4471-2157-2 completeness theorem and Gödel's compactness genuine interdisciplinary research in the biomedical $59.95 ▶ theorem for propositional logic. The reader will sciences. familiarize himself with many basic ideas and artifacts More on www.springer.com/978-0-387-95228-4 of mathematical logic: a non-ambiguous syntax, Usually dispatched within 3 to 5 business days logical equivalence and consequence relation, the Davis-Putnam procedure, Tarski semantics, Herbrand 2003. XXV, 811 p. 296 illus. (Interdisciplinary Applied models, the axioms of identity, Skolem normal forms, Mathematics, Vol. 18) Hardcover nonstandard models and, interestingly enough, 978-0-387-95228-4 proofs and refutations viewed as graphic objects. ▶$99.00 The mathematical prerequisites are minimal: the book is accessible to anybody having some familiarity with proofs by induction. Many exercises on the relationship between natural language and formal proofs make the book also interesting to a wide range of students of philosophy and linguistics. More on www.springer.com/978-88-470-2360-4 D. Mundici, Department of Mathematics "Ulisse Dini", Due: February 3, 2012 University of Florence, Italy 2012. X, 130 p. (La Matematica per il 3+2) Softcover Advanced Łukasiewicz calculus 978-88-470-2360-4 and MV-algebras ▶approx. $59.95 In recent years, the discovery of the relationships between formulas in Łukasiewicz logic and rational polyhedra, Chang MV-algebras and lattice-ordered abelian roups, MV-algebraic states and coherent de Finetti’s assessments of continuous events, has changed the study and practice of many-valued logic. This book is intended as an up-to-date monograph on infinite-valued Łukasiewicz logic and MV-algebras. springer.com 65

the book is, really, a pleasure.” (Dutch Mathematical fundamental physical examples are discussed at Society, 1993) great length in a reader friendly fashion. No detail More on www.springer.com/978-1-4419-7837-0 is left to the reader’s imagination or interpretation. I am not aware of another source where these Usually dispatched within 3 to 5 business days December very important examples and ideas are presented 31, 2011 at a level accessible to beginners.” (Mathematical 2012. XVI, 324 p. 67 illus. (Applied Mathematical Reviews) Sciences, Vol. 92) Hardcover More on www.springer.com/978-1-4419-7894-3 978-1-4419-7837-0 Usually dispatched within 3 to 5 business days ▶approx. $59.95 2011. XII, 419 p. (Applied Mathematical Sciences, Vol. G.L. Naber, Drexel University, Department of Mathematics, 141) Hardcover Philadelphia, PA 978-1-4419-7894-3 ▶$79.95 The Geometry of Minkowski Spacetime An Introduction to the Mathematics of the Forthcoming Special Theory of Relativity W.E. Nagel, Technische Universität Dresden, Germany; D.B. Kröner, Universität Freiburg, Germany; M.M. Resch, This book offers a presentation of the special theory Universität Stuttgart, Germany (Eds.) of relativity that is mathematically rigorous and yet spells out in considerable detail the physical High Performance Computing in significance of the mathematics. It treats, in addition to the usual menu of topics one is accustomed to Science and Engineering '11 G.L. Naber, Drexel University, Philadelphia, PA, USA finding in introductions to special relativity, a wide Transactions of the High Performance variety of results of more contemporary origin. Topology, Geometry and Gauge Computing Center, Stuttgart (HLRS) 2011 These include Zeeman’s characterization of the causal automorphisms of Minkowski spacetime, fields This book presents the state-of-the-art in simulation on supercomputers. Leading researchers present the Penrose theorem on the apparent shape of a Interactions relativistically moving sphere, a detailed introduction results achieved on systems of the High Performance to the theory of spinors, a Petrov-type classification This volume is intended to carry on the program, Computing Center Stuttgart (HLRS) for the year of electromagnetic fields in both tensor and spinor initiated in Topology, Geometry, and Gauge Fields: 2011. The reports cover all fields of computational form, a topology for Minkowski spacetime whose Foundations (Springer, 2010), of exploring the science and engineering, ranging from CFD to homeomorphism group is essentially the Lorentz interrelations between particle physics and topology computational physics and chemistry, to computer group, and a careful discussion of Dirac’s famous that arise from their shared notion of a gauge field. science, with a special emphasis on industrially Scissors Problem and its relation to the notion of The text begins with a synopsis of the geometrical relevant applications. Presenting results for both a two-valued representation of the Lorentz group. background assumed of the reader (manifolds, Lie vector systems and microprocessor-based systems, This second edition includes a new chapter on the groups, bundles, connections, etc.). There follows the book allows readers to compare the performance de Sitter universe which is intended to serve two a lengthy, and somewhat informal discussion of levels and usability of various architectures. As purposes. The first is to provide a gentle prologue a number of the most basic of the classical gauge HLRS operates not only a large cluster system but to the steps one must take to move beyond special theories arising in physics, including classical also one of the largest NEC vector systems in the relativity and adapt to the presence of gravitational electromagnetic theory and Dirac monopoles, the world, this book also offers excellent insights into the fields that cannot be considered negligible. The Klein-Gordon and Dirac equations and SU(2) Yang- potential of vector systems. The book covers the main second is to understand some of the basic features Mills-Higgs theory. The real purpose here is to methods used in high-performance computing. Its of a model of the empty universe that differs witness such things as spacetime manifolds, spinor outstanding results in achieving highest performance markedly from Minkowski spacetime, but may be structures, de Rham cohomology, and Chern classes for production codes are of particular interest for recommended by recent astronomical observations arise of their own accord in meaningful physics. All of scientists and engineers alike. The book comes with a suggesting that the expansion of our own universe is these are then developed rigorously in the remaining wealth of color illustrations and tables of results. accelerating rather than slowing down. The treatment chapters. With the precise definitions in hand, one More on www.springer.com/978-3-642-23868-0 can, for example, fully identify magnetic charge and presumes only a knowledge of linear algebra in Due: January 28, 2012 the first three chapters, a bit of real analysis in the instanton number with the Chern numbers of the 2012. XI, 649 p. 334 illus., 256 in color. Hardcover fourth and, in two appendices, some elementary bundles on which the charge and instanton live, and 978-3-642-23868-0 point-set topology. The first edition of the book uncover the obstruction to the existence of a spinor $179.00 received the 1993 CHOICE award for Outstanding structure in the form of the second Stiefel-Whitney ▶ Academic Title. Reviews of first edition: “… a class. This second edition of the book includes, in valuable contribution to the pedagogical literature an Appendix, a much expanded sketch of Seiberg- which will be enjoyed by all who delight in precise Witten gauge theory, including a brief discussion of mathematics and physics.” (American Mathematical its origins in physics and its implications for topology. Society, 1993) “Where many physics texts explain To provide the reader with the opportunity to pause physical phenomena by means of mathematical en route and join in the fun, there are 228 exercises, models, here a rigorous and detailed mathematical each an integral part of the development and each development is accompanied by precise physical located at precisely the point at which it can be solved interpretations.” (CHOICE, 1993) “… his talent in with optimal benefit. Reviews of first edition: “Naber’s choosing the most significant results and ordering goal is not to teach a sterile course on geometry them within the book can’t be denied. The reading of and topology, but rather to enable us to see the subject in action, through gauge theory.” (SIAM Review) “The presentation … is enriched by detailed discussions about the physical interpretations of connections, their curvatures and characteristic classes. I particularly enjoyed Chapter 2 where many 66 springer.com

refereed and edited selection of papers.Along with the many plenary speakers, the contributors to this proceedings provided inspiring talks and set a high standard of exposition in their descriptions of new directions for research. Many relevant topics in approximation theory are included in this book, such as abstract approximation, approximation with constraints, interpolation and smoothing, wavelets and frames, shearlets, orthogonal polynomials, univariate and multivariate splines, and complex approximation. Marian Neamtu is Professor of Mathematics at Vanderbilt University, Nashville, W. Narkiewicz, Institute of Mathematics, Wrocław University, J. Naudts, Physics Department, University of Antwerp, TN. Larry L. Schumaker is Stevenson Professor of Plac Grunwaldzki 2-4, PL-50-384 Wroclaw, Poland Antwerp, Belgium Mathematics at Vanderbilt University, Nashville, TN. Rational Number Theory in the Generalised Thermostatistics More on www.springer.com/978-1-4614-0771-3 Usually dispatched within 3 to 5 business days 20th Century The domain of non-extensive thermostatistics has been subject to intensive research over the past twenty 2012. XVII, 415 p. 38 illus., 11 in color. (Springer Proceedings From PNT to FLT in Mathematics, Vol. 13) Hardcover years and has matured significantly. Generalised 978-1-4614-0771-3 The last one hundred years have seen many important Thermostatistics cuts through the traditionalism $149.00 achievements in the classical part of number theory. of many statistical physics texts by offering a fresh ▶ After the proof of the Prime Number Theorem perspective and seeking to remove elements of in 1896, a quick development of analytical tools doubt and confusion surrounding the area.The led to the invention of various new methods, like book is divided into two parts - the first covering Brun's sieve method and the circle method of Hardy, topics from conventional statistical physics, whilst Littlewood and Ramanujan. These methods were adopting the perspective that statistical physics is the driving force behind new advances in prime and statistics applied to physics. The second developing additive number theory. At the same time, Hecke’s the formalism of non-extensive thermostatistics, resuscitation of modular forms started a whole new of which the central role is played by the notion body of research which culminated in the solution of a deformed exponential family of probability of Fermat’s problem.Rational Number Theory in the distributions.Presented in a clear, consistent, and 20th Century: From PNT to FLT offers a short survey deductive manner, the book focuses on theory, part of 20th century developments in classical number of which is developed by the author himself, but also theory, documenting between the proof of the Prime provides a number of references towards application- Number Theorem and the proof of Fermat's Last based texts.Written by a leading contributor in the Theorem. The focus lays upon the part of number field, this book will provide a useful tool for learning J. Necas, Charles University, Prague, Czech Republic theory that deals with properties of integers and about recent developments in generalized versions rational numbers. Chapters are divided into five time of statistical mechanics and thermodynamics, Direct Methods in the Theory of periods, which are then further divided into subject especially with respect to self-study. Written for Elliptic Equations areas. With the introduction of each new topic, researchers in theoretical physics, mathematics developments are followed through to the present and statistical mechanics, as well as graduates of Nečas’ book Direct Methods in the Theory of Elliptic day. This book will appeal to graduate researchers and physics, mathematics or engineering. A prerequisite Equations, published 1967 in French, has become a students in number theory, however the presentation knowledge of elementary notions of statistical physics standard reference for the mathematical theory of of main results without technicalities and proofs will and a substantial mathematical background are linear elliptic equations and systems. This English make this accessible to anyone with an interest in the required. edition presents Nečas’ work essentially in the form area. Detailed references and a vast bibliography offer it was published in 1967. It gives a timeless and in More on www.springer.com/978-0-85729-354-1 an excellent starting point for readers who wish to some sense definitive treatment of a number issues delve into specific topics. Usually dispatched within 3 to 5 business days in variational methods for elliptic systems and higher More on www.springer.com/978-0-85729-531-6 2011. X, 201 p. 28 illus. Hardcover order equations. The text is recommended to graduate 978-0-85729-354-1 Usually dispatched within 3 to 5 business days students of partial differential equations, postdoctoral ▶$99.00 associates in Analysis, and scientists working with 2012. XIV, 654 p. (Springer Monographs in Mathematics) linear elliptic systems. In fact, any researcher using Hardcover the theory of elliptic systems will benefit from 978-0-85729-531-6 having the book in his library.The volume gives a ▶$129.00 M. Neamtu, Vanderbilt University, Nashville, TN, USA; L. Schumaker, Vanderbilt University, Nashville, TN, USA (Eds.) self-contained presentation of the elliptic theory based on the "direct method", also known as the Approximation Theory XIII: San variational method. Due to its universality and close connections to numerical approximations, Antonio 2010 the variational method has become one of the most These proceedings were prepared in connection important approaches to the elliptic theory. The with the international conference Approximation method does not rely on the maximum principle Theory XIII, which was held March 7–10, 2010 in San or other special properties of the scalar second Antonio, Texas. The conference was the thirteenth order elliptic equations, and it is ideally suited for in a series of meetings in Approximation Theory handling systems of equations of arbitrary order. held at various locations in the United States, and The prototypical examples of equations covered by was attended by 144 participants.The book will the theory are, in addition to the standard Laplace be of interest to mathematicians, engineers, and equation, Lame’s system of linear elasticity and the computer scientists working in approximation theory, biharmonic equation (both with variable coefficients, computer-aided geometric design, numerical analysis, of course). General ellipticity conditions are discussed and related application areas. It contains a carefully and most of the natural boundary condition is springer.com 67 covered. The necessary foundations of the function recent theoretical and experimental works related to space theory are explained along the way, in an interfacial convection in multilayer systems and is a arguably optimal manner. The standard boundary valuable contribution.” (Mathematical Reviews, 2007) regularity requirement on the domains is the More on www.springer.com/978-0-387-87713-6 Lipschitz continuity of the boundary, which "when going beyond the scalar equations of second order" Due: February 29, 2012 turns out to be a very natural class. These choices 2012. 400 p. (Applied Mathematical Sciences, Vol. 179) reflect the author's opinion that the Lame system Hardcover and the biharmonic equations are just as important 978-0-387-87713-6 as the Laplace equation, and that the class of the ▶$99.00 domains with the Lipschitz continuous boundary (as opposed to smooth domains) is the most natural J. Nocedal, Northwestern University, Evanston, IL, USA; S. class of domains to consider in connection with these Wright, University of Wisconsin, WI, USA equations and their applications. Numerical Optimization More on www.springer.com/978-3-642-10454-1 Usually dispatched within 3 to 5 business days Numerical Optimization presents a comprehensive and up-to-date description of the most effective 2012. XVI, 372 p. 11 illus. (Springer Monographs in methods in continuous optimization. It responds to Mathematics) Hardcover the growing interest in optimization in engineering, 978-3-642-10454-1 science, and business by focusing on the methods $129.00 ▶ that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for J.W. Neuberger, Department of Mathematics, University of optimization, both of which are used widely in North Texas, Denton, TX, USA practice and the focus of much current research. Because of the emphasis on practical methods, as well A Sequence of Problems on as the extensive illustrations and exercises, the book Semigroups is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, A Sequence of Problems on Semigroups consists of mathematics, computer science, and business. It also an arrangement of problems which are designed to serves as a handbook for researchers and practitioners develop a variety of aspects to understanding the area in the field. The authors have strived to produce a of one-parameter semigroups of operators. Written text that is pleasant to read, informative, and rigorous in the Socratic/Moore method, this is a problem book - one that reveals both the beautiful nature of the A. Nepomnyashchy, Technion - Israel Institute of with neither the proofs nor the answers presented. discipline and its practical side. There is a selected Technology, Haifa, Israel; I. Simanovskii, Technion - Israel To get the most out of the content requires high solutions manual for instructors for the new edition. Institute of Technology, Haifa, Israel; J.C. Legros, Universite motivation to work out the exercises. However, the More on www.springer.com/978-0-387-30303-1 Libre de Bruxelles, Belgium reader is given the opportunity to discover important developments of the subject and to quickly arrive Usually dispatched within 3 to 5 business days Interfacial Convection in at the point of independent research. Many of the Multilayer Systems problems are not found easily in other books and 2006. XXII, 664 p. 85 illus. (Springer Series in they vary in level of difficulty. A few open research Operations Research and Financial Engineering) Hardcover The interfacial convection is a widespread questions are also presented. The compactness of 978-0-387-30303-1 phenomenon which has numerous applications. the volume and the reputation of the author lends ▶$79.95 This book describes the basic models of interfacial this concise set of problems to be a 'classic' in the convection used on different spatial scales. It presents making. This text is highly recommended for use a variety of physical mechanisms and types of as supplementary material for three graduate level instability characteristic for liquid systems with courses. interfaces. The book summarizes results obtained in More on www.springer.com/978-1-4614-0429-3 the field of interfacial convection during a number of decades, including recent developments in Usually dispatched within 3 to 5 business days exploration of microfluidic convective flows. The book will appeal to researchers and graduate students 2011. VI, 146 p. (Problem Books in Mathematics) working in the field of fluid dynamics. It will help Hardcover 978-1-4614-0429-3 readers to master the mathematical approaches which are used for studying convective flows and ▶$49.95 understand the underlying physical phenomena. This new edition has been updated throughout and contains the significant progress achieved in I. Nåsell, Royal Institute of Technology, Stockholm, Sweden studying phenomena in ultra-thin films, in systems with phase transitions, multicomponent systems, Extinction and Quasi-Stationarity and nanosuspensions. Reviews of first edition: “In summary, the bulk of this book is excellent…If in the Stochastic Logistic SIS the authors could expand the content of chapters Model six and seven to give the same level of coverage as the first five chapters, this would be an even more This volume presents explicit approximations of the valuable resource for mathematicians, physicists and quasi-stationary distribution and of the expected engineers working on the stability of thermocapillary time to extinction from the state one and from quasi- flows.” (Journal of Fluid Mechanics, 2007) “This stationarity for the stochastic logistic SIS model. monograph pulls together the large amount of very The approximations are derived separately in three 68 springer.com different parameter regions, and then combined into data are prescribed on only part of the boundary) a uniform approximation across all three regions. and closed boundary conditions (in which data Subsequently, the results are used to derive thresholds are prescribed on the entire boundary) are both as functions of the population size N. considered. Emphasis is placed on the formulation More on www.springer.com/978-3-642-20529-3 of boundary conditions for which solutions can be shown to exist in an appropriate function space, and Usually dispatched within 3 to 5 business days specific applications to plasma physics, optics, and 2011. XI, 199 p. 10 illus. in color. (Mathematical Biosciences analysis on projective spaces are discussed. Subseries, Vol. 2022) Softcover 978-3-642-20529-3 More on www.springer.com/978-3-642-24414-8 ▶$59.95 Due: January 31, 2012 2012. IX, 216 p. 26 illus., 11 in color. (Lecture Notes in A. Olivieri, Università di Parma, Italy; E. Pitacco, Università di Mathematics, Vol. 2043) Softcover 978-3-642-24414-8 Forthcoming Trieste, Italy ▶$59.95 A. Némethi, Rényi Institute of Mathematics, Budapest, Introduction to Insurance Hungary; Á. Szilárd, Rényi Institute of Mathematics, Budapest, Hungary Mathematics Technical and Financial Features of Risk Milnor Fiber Boundary of a Non- Transfers isolated Surface Singularity The book aims at presenting technical and financial features of life insurance, non-life insurance, pension In the study of algebraic/analytic varieties a key plans. The book has been planned assuming non- aspect is the description of the invariants of their actuarial readers as its “natural” target, namely - singularities. This book targets the challenging advanced undergraduate and graduate students in non-isolated case. Let f be a complex analytic Economics, Business and Finance; - professionals hypersurface germ in three variables whose zero set and technicians operating in Insurance and pension has a 1-dimensional singular locus. We develop an areas, whose job may regard investments, risk explicit procedure and algorithm that describe the analysis, financial reporting, etc, and hence implies boundary M of the Milnor fiber of f as an oriented a communication with actuarial professionals and S. Ovchinnikov, San Francisco State University, CA, USA plumbed 3-manifold. This method also provides managers. Given the assumed target, the book focuses the characteristic polynomial of the algebraic on technical and financial aspects of insurance, Graphs and Cubes monodromy. We then determine the multiplicity however avoiding the use of complex mathematical system of the open book decomposition of M cut This introductory text in graph theory focuses on tools. In this sense, the book can be placed at some out by the argument of g for any complex analytic partial cubes, which are graphs that are isometrically “midpoint” of the existing literature, part of which germ g such that the pair (f,g) is an ICIS. Moreover, embeddable into hypercubes of an arbitrary adopts more formal approaches to insurance the horizontal and vertical monodromies of the dimension, as well as bipartite graphs, and cubical problems implying the use of non-elementary transversal type singularities associated with the graphs. This branch of graph theory has developed mathematics, whereas another part addresses practical singular locus of f and of the ICIS (f,g) are also rapidly during the past three decades, producing questions totally avoiding even simple mathematical described. The theory is supported by a substantial exciting results and establishing links to other tools (which, in our opinion, can conversely provide amount of examples, including homogeneous branches of mathematics. Currently, Graphs and effective tools for presenting technical and financial and composed singularities and suspensions. The Cubes is the only book available on the market that features of the insurance business). properties peculiar to M are also emphasized presents a comprehensive coverage of cubical graph More on www.springer.com/978-3-642-16028-8 and partial cube theories. Many exercises, along More on www.springer.com/978-3-642-23646-4 Usually dispatched within 3 to 5 business days with historical notes, are included at the end of every Due: February 29, 2012 chapter, and readers are encouraged to explore the 2012. XII, 240 p. (Lecture Notes in Mathematics, Vol. 2037) 2011. XV, 475 p. 180 illus. Softcover exercises fully, and use them as a basis for research Softcover 978-3-642-16028-8 projects. The prerequisites for this text include 978-3-642-23646-4 ▶$74.95 familiarity with basic mathematical concepts and ▶$59.95 methods on the level of undergraduate courses in discrete mathematics, linear algebra, group theory, and topology of Euclidean spaces. While the book Forthcoming is intended for lower-division graduate students in Th.H. Otway, Yeshiva University, New York, NY, USA mathematics, it will be of interest to a much wider audience; because of their rich structural properties, The Dirichlet Problem for Elliptic- partial cubes appear in theoretical computer science, coding theory, genetics, and even the political and Hyperbolic Equations of Keldysh social sciences. Type More on www.springer.com/978-1-4614-0796-6 Partial differential equations of mixed elliptic- Usually dispatched within 3 to 5 business days hyperbolic type arise in diverse areas of physics and geometry, including fluid and plasma dynamics, 2011. XIII, 287 p. 172 illus. (Universitext) Softcover optics, cosmology, traffic engineering, projective 978-1-4614-0796-6 geometry, geometric variational theory, and the ▶$74.95 theory of isometric embeddings. And yet even the linear theory of these equations is at a very early stage. This text examines various Dirichlet problems that can be formulated for Keldysh-type equations, one of the two main classes of linear elliptic-hyperbolic equations. Open boundary conditions (in which springer.com 69

Forthcoming students, scientists and scholars wishing to keep interested in the interdisciplinary application of abreast of this important area of research. data mining techniques. Biomarker discovery is J. Pach, Faculté de Sciences de Base, École Polytechnique an important area of biomedical research that can Fédérale de Lausanne, Lausanne, CH-1015, Switzerland (Ed.) More on www.springer.com/978-94-91216-16-9 lead to significant breakthroughs in disease analysis Usually dispatched within 3 to 5 business days Thirty Essays on Geometric Graph and targeted therapy. Moreover, the discovery and 2011. XV, 285 p. (Atlantis Studies in Mathematics for management of new biomarkers is a challenging and Theory Engineering and Science, Vol. 9) Hardcover attractive problem in the emerging field of biomedical 978-94-91216-16-9 informatics. This volume is a collection of state- The field of geometric graph theory is a fairly ▶$99.00 of-the-art research from select participants of the new discipline that began to burgeon in the past “International Conference on Biomedical Data and couple decades after many critical mathematical Knowledge Mining: Towards Biomarker Discovery,” developments were made in graph theory. It was held July 7-9, 2010 in Chania, Greece. Contributions developed to solve problems in combinatorial and M. Padula, University of Ferrara, Ferrara, Italy focus on biomarker data integration, information computational geometry, and has quickly become retrieval methods, and statistical machine learning a useful tool for both discrete mathematicians and Asymptotic Stability of Steady techniques, all presented with new results, models, computer scientists.This contributed volume contains Compressible Fluids and algorithms. twenty-five original survey and research papers on important recent developments in geometric This volume introduces a systematic approach to the More on www.springer.com/978-1-4614-2106-1 graph theory. These contributions were thoroughly solution of some mathematical problems that arise Due: February 29, 2012 in the study of the hyperbolic-parabolic systems of reviewed and written by active researchers in this 2012. XXIII, 283 p. 89 illus., 58 in color. (Springer equations that govern the motions of thermodynamic field. Optimization and Its Applications, Vol. 65) Hardcover fluids. It is intended for a wide audience of theoretical 978-1-4614-2106-1 More on www.springer.com/978-1-4614-0109-4 and applied mathematicians with an interest in $124.00 Due: February 23, 2012 compressible flow, capillarity theory, and control ▶ 2012. XX, 430 p. 190 illus., 15 in color. (Algorithms and theory.The focus is particularly on recent results Combinatorics, Tentative volume 29) Hardcover concerning nonlinear asymptotic stability, which are 978-1-4614-0109-4 independent of assumptions about the smallness of Forthcoming the initial data. Of particular interest is the loss of ▶approx. $149.00 C. Pechstein control that sometimes results when steady flows of compressible fluids are upset by large disturbances. Finite and Boundary Element The main ideas are illustrated in the context of three different physical problems:(i) A barotropic Tearing and Interconnecting viscous gas in a fixed domain with compact boundary. Solvers for Multiscale Problems The domain may be either an exterior domain or a bounded domain, and the boundary may be either Tearing and interconnecting methods, such as impermeable or porous.(ii) An isothermal viscous FETI, FETI-DP, BETI, etc., are among the most gas in a domain with free boundaries.(iii) A heat- successful domain decomposition solvers for partial conducting, viscous polytropic gas. differential equations. The purpose of this book is More on www.springer.com/978-3-642-21136-2 to give a detailed and self-contained presentation of these methods, including the corresponding Usually dispatched within 3 to 5 business days algorithms as well as a rigorous convergence 2011. XIV, 235 p. (Lecture Notes in Mathematics, Vol. 2024) theory. In particular, two issues are addressed Softcover that have not been covered in any monograph B.G. Pachpatte, Marathwada University, Aurangabad, India 978-3-642-21136-2 yet: the coupling of finite and boundary elements ▶$59.95 within the tearing and interconnecting framework Multidimensional Integral including exterior problems, and the case of highly Equations and Inequalities varying (multiscale) coefficients not resolved by the subdomain partitioning. In this context, the book Since from more than a century, the study of various offers a detailed view to an active and up-to-date area types of integral equations and inequalities has of research. been focus of great attention by many researchers, More on www.springer.com/978-3-642-23587-0 interested both in theory and its applications. In particular, there exists a very rich literature related Due: April 11, 2012 to the integral equations and inequalities and 2012. 300 p. (Lecture Notes in Computational Science and their applications. The present monograph is an Engineering, Vol. 87) Hardcover attempt to organize recent progress related to the 978-3-642-23587-0 Multidimensional integral equations and inequalities, ▶approx. $109.00 which we hope will widen the scope of their new applications. The field to be covered is extremely wide and it is nearly impossible to treat all of them P.M. Pardalos, University of Florida, Gainesville, FL, USA; P. here. The material included in the monograph is Xanthopoulos, University of Florida, Gainesville, FL, USA; M. recent and hard to find in other books. It is accessible Zervakis, Technical University of Crete, Chania, Greece (Eds.) to any reader with reasonable background in real analysis and acquaintance with its related areas. All Data Mining for Biomarker results are presented in an elementary way and the Discovery book could also serve as a textbook for an advanced graduate course. The book deserves a warm welcome Data Mining for Biomarker Discovery is designed to those who wish to learn the subject and it will also to motivate collaboration and discussion among be most valuable as a source of reference in the field. various disciplines and will be of interest to students It will be an invaluable reading for mathematicians, and researchers in engineering, computer science, physicists and engineers and also for graduate applied mathematics, medicine, and anyone 70 springer.com

students and researchers in mathematics and other fields to develop them further. More on www.springer.com/978-3-642-14787-6 Usually dispatched within 3 to 5 business days 2011. XXX, 736 p. 182 illus., 120 in color. (Springer Proceedings in Mathematics, Vol. 2) Hardcover 978-3-642-14787-6 ▶$219.00

3rd Edition R. Peikert, ETH Zürich, Switzerland; H. Hauser, University of M.M. Peixoto, IMPA, Rio de Janeiro, RJ, Brasil; A.A. Pinto, Bergen, Norway; H. Carr, University of Leeds, UK; R. Fuchs, University of Porto, Portugal; D.A. Rand, University of L. Perko, Northern Arizona University, Flagstaff, AZ, USA ETH Zürich, Switzerland (Eds.) Warwick, Coventry, UK (Eds.) Differential Equations and Topological Methods in Data Dynamics, Games and Science I Dynamical Systems Analysis and Visualization II DYNA 2008, in Honor of Maurício Peixoto Theory, Algorithms, and Applications and David Rand, University of Minho, Braga, This textbook presents a systematic study of the Portugal, September 8-12, 2008 qualitative and geometric theory of nonlinear When scientists analyze datasets in a search for differential equations and dynamical systems. underlying phenomena, patterns or causal factors, Dynamics, Games and Science I and II are a Although the main topic of the book is the local their first step is often an automatic or semi- selection of surveys and research articles written and global behavior of nonlinear systems and their automatic search for structures in the data. Of these by leading researchers in mathematics. The bifurcations, a thorough treatment of linear systems feature-extraction methods, topological ones stand majority of the contributions are on dynamical is given at the beginning of the text. All the material out due to their solid mathematical foundation. systems and game theory, focusing either on necessary for a clear understanding of the qualitative Topologically defined structures—as found in scalar, fundamental and theoretical developments or on behavior of dynamical systems is contained in this vector and tensor fields—have proven their merit applications to modeling in biology, ecomonics, textbook, including an outline of the proof and in a wide range of scientific domains, and scientists engineering, finances and psychology. The papers examples illustrating the proof of the Hartman- have found them to be revealing in subjects such as are based on talks given at the International Grobman theorem, the use of the Poincaré map in physics, engineering, and medicine. Full of state-of- Conference DYNA 2008, held in honor of the theory of limit cycles, the theory of rotated vector the-art research and contemporary hot topics in the Mauricio Peixoto and David Rand at the fields and its use in the study of limit cycles and subject, this volume is a selection of peer-reviewed University of Braga, Portugal, on September 8-12, homoclinic loops, and a description of the behavior papers originally presented at the fourth Workshop 2008. The aim of these volumes is to present cutting- and termination of one-parameter families of limit on Topology-Based Methods in Data Analysis and edge research in these areas to encourage graduate cycles. In addition to minor corrections and updates Visualization, TopoInVis 2011, held in Zurich, students and researchers in mathematics and other throughout, this new edition includes materials on Switzerland. The workshop brought together many of fields to develop them further. higher order Melnikov theory and the bifurcation the leading lights in the field for a mixture of formal More on www.springer.com/978-3-642-11455-7 of limit cycles for planar systems of differential presentations and discussion. One topic currently Usually dispatched within 3 to 5 business days equations, including new sections on Francoise's generating a great deal of interest, and explored in algorithm for higher order Melnikov functions and on 2011. XXXI, 809 p. (Springer Proceedings in Mathematics, several chapters here, is the search for topological the finite codimension bifurcations that occur in the Vol. 1) Hardcover structures in time-dependent flows, and their class of bounded quadratic systems. 978-3-642-11455-7 relationship with Lagrangian coherent structures. $219.00 More on www.springer.com/978-0-387-95116-4 Contributors also focus on discrete topologies of ▶ scalar and vector fields, and on persistence-based Usually dispatched within 3 to 5 business days simplification, among other issues of note. The new research results included in this volume relate to all M.M. Peixoto, IMPA, Rio de Janeiro, RJ, Brazil; A.A. Pinto, 2001. XIV, 553 p. 229 illus. (Texts in Applied Mathematics, Vol. 7) Hardcover three key areas in data analysis—theory, algorithms University of Porto, Portugal; D.A. Rand, University of 978-0-387-95116-4 and applications. Warwick, Coventry, UK (Eds.) ▶$95.00 More on www.springer.com/978-3-642-23174-2 Dynamics, Games and Science II Due: February 28, 2012 DYNA 2008, in Honor of Maurício Peixoto 2012. XI, 296 p. (Mathematics and Visualization) Hardcover and David Rand, University of Minho, Braga, 978-3-642-23174-2 Portugal, September 8-12, 2008 ▶$124.00 Dynamics, Games and Science I and II are a selection of surveys and research articles written by leading researchers in mathematics. The majority of the contributions are on dynamical systems and game theory, focusing either on fundamental and theoretical developments or on applications to modeling in biology, ecomonics, engineering, finances and psychology.The papers are based on talks given at the International Conference DYNA 2008, held in honor of Mauricio Peixoto and David Rand at the University of Braga, Portugal, on September 8-12, 2008.The aim of these volumes is to present cutting- edge research in these areas to encourage graduate springer.com 71

capital of the federal state of Brandenburg (Germany) X. Jia, The University of New South Wales, Canberra, ACT, chose the Graßmann Conference as the first-time Australia (Eds.) winner of the Potsdam Conference-Award in the category "Innovative and/or exceptional events". 2011 International Symposium More on www.springer.com/978-3-0346-0404-8 on Computational Models for Life Usually dispatched within 3 to 5 business days Sciences (CMLS-11) 2011. XX, 580 p. 73 illus., 10 in color. Hardcover 978-3-0346-0404-8 . ▶$149.00 More on www.springer.com/978-0-7354-0931-6 Online orders shipping within 2-3 days

C. Perna, University of Salerno, Italy; M. Sibillo, University of 2011. 356 p. (Mathematical and Statistical Physics, Vol. Salerno, Italy (Eds.) 1371) Softcover 978-0-7354-0931-6 Mathematical and Statistical ▶$163.00 Methods for Actuarial Sciences and Finance The book develops the capabilities arising from the cooperation between mathematicians and statisticians working in insurance and finance fields. It gathers some of the papers presented at the conference MAF2010, held in Ravello (Amalfi coast), and successively, after a reviewing process, worked out to F. Pham, Université de Nice, France this aim. Singularities of integrals More on www.springer.com/978-88-470-2341-3 Homology, hyperfunctions and microlocal Due: October 25, 2011 analysis 2012. XII, 408 p. 99 illus., 1 in color. Hardcover M. Pietikäinen, Machine Vision Group, Department of 978-88-470-2341-3 Bringing together two fundamental texts from Computer Science and Engineering, University of Oulu, ▶$149.00 Frédéric Pham’s research on singular integrals, the Oulu, Finland; A. Hadid, Machine Vision Group, Department first part of this book focuses on topological and of Computer Science and Engineering, University of Oulu, geometrical aspects while the second explains the Oulu, Finland; G. Zhao, Machine Vision Group, Department analytic approach. Using notions developed by J. H.-J. Petsche, Potsdam, Germany; A.C. Lewis, The of Computer Science and Engineering, University of Oulu, Leray in the calculus of residues in several variables Educational Advancement Foundation, Austin, Texas, USA; Oulu, Finland; T. Ahonen, Visual Computing and Ubiquitous J. Liesen, Technische Universität Berlin, Germany; S. Russ, and R. Thom’s isotopy theorems, Frédéric Pham’s Imaging Research Team, Nokia Research Center, Palo Alto, University of Warwick, Coventry, UK (Eds.) foundational study of the singularities of integrals CA, USA lies at the interface between analysis and algebraic From Past to Future: Graßmann's geometry, culminating in the Picard-Lefschetz Computer Vision Using Local formulae. These mathematical structures, enriched Work in Context by the work of Nilsson, are then approached using Binary Patterns Graßmann Bicentennial Conference, September methods from the theory of differential equations and The recent emergence of Local Binary Patterns (LBP) 2009 generalized from the point of view of hyperfunction has led to significant progress in applying texture theory and microlocal analysis.Providing a ‘must- methods to various computer vision problems and On the occasion of the 200th anniversary of the have’ introduction to the singularities of integrals, applications. The focus of this research has broadened birth of Hermann Graßmann (1809-1877), an a number of supplementary references also offer from 2D textures to 3D textures and spatiotemporal interdisciplinary conference was held in Potsdam, a convenient guide to the subjects covered.This (dynamic) textures. Also, where texture was once Germany, and in Graßmann's hometown Szczecin, book will appeal to both mathematicians and utilized for applications such as remote sensing, Poland. The idea of the conference was to present a physicists with an interest in the area of singularities industrial inspection and biomedical image analysis, multi-faceted picture of Graßmann, and to uncover of integrals.Frédéric Pham, now retired, was Professor the introduction of LBP-based approaches have the complexity of the factors that were responsible for at the University of Nice. He has published several provided outstanding results in problems relating his creativity. The conference demonstrated not only educational and research texts. His recent work to face and activity analysis, with future scope for the very influential reception of his work at the turn of concerns semi-classical analysis and resurgent face and facial expression recognition, biometrics, the 20th century, but also the unexpected modernity functions. visual surveillance and video analysis. Computer of his ideas, and their continuing development in the Vision Using Local Binary Patterns provides a 21st century. This book contains 37 papers presented More on www.springer.com/978-0-85729-602-3 detailed description of the LBP methods and their at the conference. They investigate the significance Usually dispatched within 3 to 5 business days variants both in spatial and spatiotemporal domains. of Graßmann's work for philosophical as well as This comprehensive reference also provides an for scientific and methodological questions, for 2011. XI, 217 p. 62 illus. (Universitext) Softcover excellent overview as to how texture methods can comparative philology in general and for Indology 978-0-85729-602-3 be utilized for solving different kinds of computer in particular, for psychology, physiology, religious ▶$59.95 vision and image analysis problems. Source codes studies, musicology, didactics, and, last but not of the basic LBP algorithms, demonstrations, some least, mathematics. In addition, the book contains databases and a comprehensive LBP bibliography numerous illustrations and English translations of T.D. Pham, The University of New South Wales, Canberra, can be found from an accompanying web site.Topics original sources, which are published here for the ACT, Australia; X. Zhou, Cornell University, Houston, TX, USA; include: - Local binary patterns and their variants first time. These include life histories of Graßmann H. Tanaka, Tokyo Medical and Dental University, Japan; M. in spatial and spatiotemporal domains- Texture (written by his son Justus) and of his brother Robert Oyama-Higa, Osaka University, Japan; X. Jiang, University classification and segmentation, description of (written by Robert himself), as well as the paper "On of Münster, Germany; C. Sun, CSIRO, North Ryde, NSW, interest regions- Applications in image retrieval the concept and extent of pure theory of number'' by Australia; J. Kowalski, Emory University, Atlanta, GA, USA; and 3D recognition- Recognition and segmentation Justus Graßmann (the father).In November 2010 the 72 springer.com of dynamic textures- Background subtraction, of important theoretical models in the scheduling recognition of actions- Face analysis using still images literature as well as significant scheduling problems and image sequences, visual speech recognition- LBP that occur in the real world. It again includes in various applications Written by pioneers of LBP, supplementary material in the form of slide- this book is an essential resource for researchers, shows from industry and movies that professional engineers and graduate students show implementations of scheduling systems. in computer vision, image analysis and pattern The main structure of the book as per previous recognition. The book will also be of interest to all edition consists of three parts. The first part those who work with specific applications of machine focuses on deterministic scheduling and the vision. related combinatorial problems. The second More on www.springer.com/978-0-85729-747-1 part covers probabilistic scheduling models; in this part it is assumed that processing times and Usually dispatched within 3 to 5 business days M.L. Pinedo, New York University, New York, NY, USA other problem data are random and not known 2011. XV, 207 p. 87 illus., 56 in color. (Computational in advance. The third part deals with scheduling Imaging and Vision, Vol. 40) Hardcover Scheduling in practice; it covers heuristics that are popular 978-0-85729-747-1 with practitioners and discusses system design and ▶$99.00 Theory, Algorithms, and Systems implementation issues. All three parts of this new This book on scheduling covers theoretical models edition have been revamped and streamlined. The as well as scheduling problems in the real world. references have been made completely up-to-date. Author Michael Pinedo also includes a CD that Theoreticians and practitioners alike will find this contains slide-shows from industry and movies book of interest. Graduate students in operations dealing with implementations of scheduling systems. management, operations research, industrial The book consists of three parts. The first part focuses engineering, and computer science will find the book on deterministic scheduling with the associated an accessible and invaluable resource. Scheduling combinatorial problems. The second part covers - Theory, Algorithms, and Systems will serve as probabilistic scheduling models. In this part it is an essential reference for professionals working on assumed that processing times and other problem scheduling problems in manufacturing, services, and data are not known in advance. The third part deals other environments. Michael L. Pinedo is the Julius with scheduling in practice. It covers heuristics Schlesinger Professor of Operations Management in that are popular with practitioners and discusses the Stern School of Business at New York University. system design and development issues. Each chapter Reviews of third edition:This well-established text A. Pignedoli, Università di Firenze, Italy (Ed.) contains a series of computational and theoretical covers both the theory and practice of scheduling. exercises. This book is of interest to theoreticians and he book begins with motivating examples and the Some Aspects of Diffusion Theory practitioners alike. Graduate students in operations penultimate chapterReviews of third edition:This well-established text covers both the theory and Lectures given at a Summer School of the Centro management, operations research, industrial practice of scheduling. The book begins with Internazionale Matematico Estivo (C.I.M.E.) held engineering and computer science will find the book to be an accessible and invaluable resource. motivating examples and the penultimate chapter in Varenna (Como), Italy, September 9-27,1966 Scheduling will serve as an essential reference for discusses some commercial scheduling systems and V.C.A. Ferraro: Diffusion of ions in a plasma with professionals working on scheduling problems examples of their implementations." (Mathematical applications to the ionosphere.- P.C. Kendall: On in manufacturing and computing environments. Reviews, 2009) the diffusion in the atmosphere and ionosphere.-F. Michael Pinedo is the Julius Schlesinger Professor of More on www.springer.com/978-1-4614-1986-0 Operations Management at New York University. Henin: Kinetic equations and Brownian motion.- T. Due: February 29, 2012 Kahan:Théorie des réacteurs nucléaires: méthodes More on www.springer.com/978-0-387-78934-7 de résolution perturbationnelles, interactives et Usually dispatched within 3 to 5 business days 2012. DCXC, 14 p. 123 illus., 10 in color. Hardcover variationnelles.- C. Cattaneo: Sulla conduzione 978-1-4614-1986-0 del calore.- C. Agostinelli: Formule di Green 2008. XVIII, 678p. With online files/update. Hardcover ▶$84.95 per la diffusione del campo magnetico in un 978-0-387-78934-7 fluido elettricamente conduttore.- A. Pignedoli: $99.00 Transformational methods applied to some one- ▶ dimensional problems concerning the equations of the neutron transport theory.- A. Pignedoli: On the rigorous analysis of the problem of neutron transport in a slab geometry and on some other results.- G. Sestini: Principi di massimo per le soluzioni di equazioni paraboliche. More on www.springer.com/978-3-642-11050-4 Usually dispatched within 3 to 5 business days 2011. 550 p. (C.I.M.E. Summer Schools, Vol. 42) Softcover 978-3-642-11050-4 ▶$69.95 F. Poloni, Technische Universität Berlin, Germany M.L. Pinedo, New York University, New York, NY, USA Algorithms for Quadratic Matrix Scheduling and Vector Equations Theory, Algorithms, and Systems This book is devoted to studying algorithms for the This new edition of the well established solution of a class of quadratic matrix and vector text Scheduling - Theory, Algorithms, and equations. These equations appear, in different forms, Systems provides an up-to-date coverage in several practical applications, especially in applied springer.com 73 probability and control theory. The equations are via www.springer.com Praise for the first edition: first presented using a novel unifying approach; "The text is nicely illustrated, the definitions are then, specific numerical methods are presented well-motivated and the proofs are particularly well- for the cases most relevant for applications, and written and student-friendly…this book would make new algorithms and theoretical results developed an excellent text for an undergraduate course, but by the author are presented. The book focuses on could also well be used for a reading course, or simply “matrix multiplication-rich” iterations such as cyclic read for pleasure." Australian Mathematical Society reduction and the structured doubling algorithm Gazette "Excellent figures supplement a good account, (SDA) and contains a variety of new research results sprinkled with illustrative examples." Times Higher which, as of today, are only available in articles or Education Supplement preprints. More on www.springer.com/978-1-84882-890-2 More on www.springer.com/978-88-7642-383-3 Usually dispatched within 3 to 5 business days F. Preparata, Università di Pisa, Italy (Ed.) Due: January 28, 2012 2011. 250 p. (Theses (Scuola Normale Superiore), Vol. 16) Theoretical Computer Sciences 2012. XI, 395 p. 150 illus. (Springer Undergraduate Mathematics Series) Softcover Softcover Lectures given at a Summer School of the Centro 978-88-7642-383-3 978-1-84882-890-2 Internazionale Matematico Estivo (C.I.M.E.) held ▶$24.95 ▶$49.95 in Bressanone (Bolzano), Italy, June 9-17, 1975 R.E. Miller: Parallel program schemata.- D.E. Muller: Forthcoming Theory of automata.- R. Karp: Computational complexity of combinatorial and graph-theoretic O. Post, Durham University, United Kingdom problems. Spectral Analysis on Graph-like More on www.springer.com/978-3-642-11118-1 Spaces Usually dispatched within 3 to 5 business days 2011. 184 p. (C.I.M.E. Summer Schools, Vol. 68) Softcover Small-radius tubular structures have attracted 978-3-642-11118-1 considerable attention in the last few years, and ▶$29.95 are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis. In this monograph, we analyse Laplace- like operators on thin tubular structures ("graph-like A. Prestel, Universität Konstanz, Germany; C.N. Delzell, spaces''), and their natural limits on metric graphs. In Louisiana State University, Baton Rouge, LA, USA particular, we explore norm resolvent convergence, convergence of the spectra and resonances. Since the Mathematical Logic and Model underlying spaces in the thin radius limit change, and become singular in the limit, we develop new Theory tools such as -norm convergence of operators acting A Brief Introduction in different Hilbert spaces, - an extension of the Mathematical Logic and Model Theory: A Brief concept of boundary triples to partial differential Introduction offers a streamlined yet easy-to-read operators, and -an abstract definition of resonances introduction to mathematical logic and basic model via boundary triples. These tools are formulated in A.N. Pressley, King's College, London, UK theory. It presents, in a self-contained manner, an abstract framework, independent of the original the essential aspects of model theory needed to problem of graph-like spaces, so that they can be Elementary Differential Geometry understand model theoretic algebra.As a profound applied in many other situations where the spaces are application of model theory in algebra, the last perturbed. Curves and surfaces are objects that everyone can see, part of this book develops a complete proof of Ax More on www.springer.com/978-3-642-23839-0 and many of the questions that can be asked about and Kochen's work on Artin's conjecture about them are natural and easily understood. Differential Due: December 31, 2011 Diophantine properties of p-adic number fields. geometry is concerned with the precise mathematical The character of model theoretic constructions and 2012. XV, 431 p. 28 illus. (Lecture Notes in Mathematics, Vol. formulation of some of these questions. It is a results differs significantly from that commonly 2039) Softcover subject that contains some of the most beautiful and found in algebra, by the treatment of formulae as 978-3-642-23839-0 profound results in mathematics yet many of these are mathematical objects. It is therefore indispensable to $89.95 ▶ accessible to higher-level undergraduates. Elementary first become familiar with the problems and methods Differential Geometry presents the main results in the of mathematical logic. Therefore, the text is divided differential geometry of curves and surfaces suitable into three parts: an introduction into mathematical for a first course on the subject. Prerequisites are logic (Chapter 1), model theory (Chapters 2 and 3), kept to an absolute minimum – nothing beyond first and the model theoretic treatment of several algebraic courses in linear algebra and multivariable calculus theories (Chapter 4).This book will be of interest to – and the most direct and straightforward approach both advanced undergraduate and graduate students is used throughout. New features of this revised studying model theory and its applications to algebra. and expanded second edition include: a chapter on It may also be used for self-study. non-Euclidean geometry, a subject that is of great More on www.springer.com/978-1-4471-2175-6 importance in the history of mathematics and crucial in many modern developments. The main results Usually dispatched within 3 to 5 business days can be reached easily and quickly by making use of the results and techniques developed earlier in the 2011. X, 194 p. (Universitext, 0) Softcover book. 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P. Quintela, Universidade de Santiago de Compostela, Spain; K. Ramasubramanian, IIT Bombay, Mumbai, India; M.S. S.T. Rassia, University of Cambridge, UK; P.M. Pardalos, T. Sánchez, Fundación CESGA, Santiago de Compostela, Sriram, University of Madras, Chennai, India University of Florida, Gainesville, FL, USA (Eds.) Spain; G. Parente, Fundación CESGA, Santiago de Compostela, Spain; A. Martínez, Fundación CESGA, Santiago Tantrasangraha of Nilakantha Sustainable Environmental de Compostela, Spain; A.B. Fernández, Universidade de Santiago de Compostela, Spain (Eds.) Somayaji Design in Architecture Tantrasaṅgraha, composed by the renowned Kerala Impacts on Health TransMath astronomer Nīlakaṅtha Somayaji (c. 1444–1545 The chapters in this book, written by international Innovative Solutions from Mathematical CE) ranks along with Āryabhatīya of Āryabhata experts from different fields of architecture and Technology and Siddhāntaśiromani of Bhāskarācārya as one engineering, are devoted to recent interdisciplinary of the major works that significantly influenced The book "TransMath. Innovative Solutions from works in a variety of subjects related to sustainable further work on astronomy in India. One of the Mathematical Technology" has been conceived architecture and engineering, environmental distinguishing features of this text is the introduction as a scientific knowledge spread instrument. This modeling, behavioral science and public health. of a major revision of the traditional planetary publication is addressed to those companies with The invited contributions focus on new ideas, models which includes a unified theory of planetary innovation needs that could be covered by using concepts and research work with multidisciplinary latitudes and a better formulation of the equation of mathematical technology. The book is a map that applications. Special features of this volume include centre for the interior planets (Mercury and Venus) shows the (existing and possible) interactions indoor and urban design impacts on human comfort, than was previously available. Several important and connections for the Spanish mathematical modeling and assessment of multi-scale design innovations in mathematical technique are also to research with the technology transfer to industrial dynamics, as well as new results from diverse areas of be found in Tantrasaṅgraha, especially related to and business sectors. The entrepreneurs may research spanning from architecture and engineering the computation of accurate sine tables, the use of determine the level of implementation and demand to neuroscience and public health. Sustainable series for evaluating the sine and cosine functions, for this technology in other companies in their Environmental Design in Architecture is intended and a systematic treatment of the problems related sector, to known the benefits of using mathematical for graduate students and researchers of architecture, to the diurnal motion of the celestial objects. The techniques for other companies and industry engineering, neuroscience, public health, social and spherical trigonometry relations presented in the innovations carried out using this technology.The computational sciences, architectural modeling and text—applied to a variety of problems such as the information is classified into eleven sectors of related fields. computation eclipses, elevation of the moon’s economy activity: Public Administration; Food; More on www.springer.com/978-1-4419-0744-8 cusps and so forth—are also exact. In preparing the Energy, Chemistry and Environment; Metal and translation and explanatory notes, the authors have Usually dispatched within 3 to 5 business days Machinery; Construction; Transport and Storage; used authentic Sanskrit editions of Tantrasaṅgraha 2012. XVIII, 336 p. 120 illus., 69 in color. (Springer Information and Communication Technology; by Suranad Kunjan Pillai and K V Sarma. The text Optimization and Its Applications, Vol. 56) Hardcover Finance; Health; Management Services; Technical consists of eight chapters—mean londitudes, true 978-1-4419-0744-8 Services. longitues, gnomonic shadow, lunar eclipse, solar ▶$149.00 More on www.springer.com/978-88-470-2405-2 eclipse, vyatīpāta, reduction to observation and Due: March 31, 2012 elevation of the moon’s cusps—and 432 verses. All the verses have been translated into English 2012. X, 150 p. (SxI - Springer for Innovation / SxI - and are supplemented with detailed explanations Springer per l'Innovazione, 1) Softcover including all mathematical relations, figures and 978-88-470-2405-2 tables using modern mathematical notation. This ▶approx. $59.95 edition of Tantrasaṅgraha will appeal to historians of astronomy as well as those who are keen to know about the actual computational procedures employed in Indian astronomy. It is a self-contained text with several appendices included, enabling the reader to comprehend the subject matter without the need for further research. More on www.springer.com/978-0-85729-035-9 T.M. Rassias, National Technical University of Athens, Online orders shipping within 2-3 days Department of Mathematics, Athens, Greece; J. Brzdek, 2011. XXX, 598 p. 173 illus., 167 in color. (Sources and Pedagogical University, Department of Mathematics, Studies in the History of Mathematics and Physical Sciences) Krakow, Poland (Eds.) Hardcover 978-0-85729-035-9 Functional Equations in ▶$179.00 Mathematical Analysis Functional Equations in Mathematical Analysis, dedicated to S.M. Ulam in honor of his 100th birthday, focuses on various important areas of research in mathematical analysis and related springer.com 75 subjects, providing an insight into the study of numerous nonlinear problems. Among other topics, it supplies the most recent results on the solutions to the Ulam stability problem. The original stability problem was posed by S.M. Ulam in 1940 and concerned approximate homomorphisms. The pursuit of solutions to this problem, but also to its generalizations and/or modifications for various classes of equations and inequalities, is an expanding area of research, and has led to the development of what is now called the Hyers–Ulam J. Richter-Gebert, Technische Universität, München, stability theory. Comprised of contributions from Germany; U.H. Kortenkamp, Pädagogische Hochschule, eminent scientists and experts from the international A. Reventós Tarrida, Department of Mathematics, Karlsruhe, Germany mathematical community, the volume presents Universitat Autònoma de Barcelona, Bellaterra, Barcelona, several important types of functional equations and Spain The Cinderella.2 Manual inequalities and their applications in mathematical analysis, geometry, physics, and applied mathematics. Affine Maps, Euclidean Motions Working with The Interactive Geometry It is intended for researchers and students in and Quadrics Software mathematics, physics, and other computational and Cinderella.2, the new version of the well-known Affine geometry and quadrics are fascinating subjects applied sciences. interactive geometry software, has become an alone, but they are also important applications of More on www.springer.com/978-1-4614-0054-7 even more versatile tool than its predecessor. linear algebra. 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Affinities, Euclidean Motions comprehensive documentation from start to finish. Tohoku University, Sendai, Japan; S. Roller, German and Quadrics takes rudimentary, and often taken- Research School for Simulation Sciences, Aachen, Germany for-granted, knowledge and presents it in a new, More on www.springer.com/978-3-540-34924-2 (Eds.) comprehensive form. Standard and non-standard Due: February 28, 2012 examples are demonstrated throughout and an High Performance Computing on appendix provides the reader with a summary of 2012. CDLVIII, 14 p. 575 illus. in color. Hardcover Vector Systems 2011 advanced linear algebra facts for quick reference to 978-3-540-34924-2 the text. All factors combined, this is a self-contained ▶$49.95 The book presents the state of the art in high book ideal for self-study that is not only foundational performance computing and simulation on modern but unique in its approach.’This text will be of use supercomputer architectures. It covers trends in to lecturers in linear algebra and its applications to hardware and software development in general geometry as well as advanced undergraduate and and specifically the future of vector-based systems beginning graduate students. and heterogeneous architectures. The application contributions cover computational fluid dynamics, More on www.springer.com/978-0-85729-709-9 material science, medical applications and climate Usually dispatched within 3 to 5 business days research. Innovative fields like coupled multi-physics or multi-scale simulations are presented. All papers 2011. XVIII, 458 p. 49 illus. (Springer Undergraduate were chosen from presentations given at the 13th Mathematics Series, 0) Softcover Teraflop Workshop held in October 2010 at Tohoku 978-0-85729-709-9 University, Japan. ▶$49.95 More on www.springer.com/978-3-642-22243-6 Due: January 28, 2012 J. Richter-Gebert, TU München, Germany 2012. VIII, 184 p. 89 illus., 68 in color. Hardcover 978-3-642-22243-6 Perspectives on Projective ▶$124.00 Geometry A Guided Tour Through Real and Complex Geometry Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction 76 springer.com to this fascinating field and its applications. In standard calculus topics. Optional sections invite particular, it explains how metric concepts may students to study such topics as metric spaces and be best understood in projective terms. One of the Riemann-Stieltjes integrals. major themes that appears throughout this book More on www.springer.com/978-0-387-90459-7 is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially Usually dispatched within 3 to 5 business days be used as a guide that explains how geometric objects 1980. X, 368 p. 34 illus. (Undergraduate Texts in and operations may be most elegantly expressed in Mathematics) Hardcover algebraic terms, making it a valuable resource for 978-0-387-90459-7 mathematicians, as well as for computer scientists $54.95 and physicists. The book is based on the author’s ▶ experience in implementing geometric software and includes hundreds of high-quality illustrations. R. Rosen More on www.springer.com/978-3-642-17285-4 Anticipatory Systems Online orders shipping within 2-3 days Philosophical, Mathematical, and Methodological Foundations 2011. XXII, 571 p. 380 illus., 250 in color. Hardcover 978-3-642-17285-4 Robert Rosen was not only a biologist, he was also ▶$84.95 a brilliant mathematician whose extraordinary contributions to theoretical biology were tremendous. Founding, with this book, the area of Anticipatory Systems Theory is a remarkable outcome of his work in theoretical biology.This second edition of his book Anticipatory Systems, has been carefully revised and edited, and includes an Introduction J.J. Rotman, University of Illinois at Urbana-Champaign, by Judith Rosen. It has also been expanded with a Urbana, IL, USA set of Prolegomena by Dr. Mihai Nadin, who offers an historical survey of this fast growing field since An Introduction to Homological the original work was published. There is also some exciting new work, in the form of an additional Algebra chapter on the Ontology of Anticipation, by Dr. John With a wealth of examples as well as abundant Kineman. An addendum-- with autobiographical applications to Algebra, this is a must-read work: a reminiscences by Robert Rosen, himself, and a clearly written, easy-to-follow guide to Homological L. Robbiano, Università di Genova, Italia short story by Judith Rosen about her father-- adds Algebra. The author provides a treatment of a personal touch. This work, now available again, Homological Algebra which approaches the subject Linear Algebra for Everyone serves as the guiding foundations for the growing in terms of its origins in algebraic topology. In this field of Anticipatory Systems and, indeed, any area of brand new edition the text has been fully updated This book provides students with the rudiments of science that deals with living organisms in some way, and revised throughout and new material on sheaves Linear Algebra, a fundamental subject for students including the study of Life and Mind. It will also be and abelian categories has been added. Applications in all areas of science and technology. The book of interest to graduate students and researchers in the include the following: * to rings -- Lazard's theorem would also be good for statistics students studying field of Systems Science. that flat modules are direct limits of free modules, linear algebra.It is the translation of a successful More on www.springer.com/978-1-4614-1268-7 Hilbert's Syzygy Theorem, Quillen-Suslin's solution textbook currently being used in Italy. The author is Due: January 31, 2012 of Serre's problem about projectives over polynomial a mathematician sensitive to the needs of a general rings, Serre-Auslander-Buchsbaum characterization 2012. LX, 470 p. 60 illus. (IFSR International Series on audience. In addition to introducing fundamental of regular local rings (and a sketch of unique ideas in Linear Algebra through a wide variety Systems Science and Engineering, Vol. 1) Hardcover 978-1-4614-1268-7 factorization); * to groups -- Schur-Zassenhaus, of interesting examples, the book also discusses Gaschutz's theorem on outer automorphisms of finite ▶$124.00 topics not usually covered in an elementary text p-groups, Schur multiplier, cotorsion groups; * to (e.g. the "cost" of operations, generalized inverses, sheaves -- sheaf cohomology, Cech cohomology, approximate solutions). The challenge is to show discussion of Riemann-Roch Theorem over compact why the "everyone" in the title can find Linear Algebra K.A. Ross, University of Oregon, Eugene, OR, USA Riemann surfaces. Learning Homological Algebra is useful and easy to learn.The translation has been a two-stage affair. Firstly, one must learn the language prepared by a native English speaking mathematician, Elementary Analysis of Ext and Tor, and what this describes. Secondly, Professor Anthony V. Geramita. The Theory of Calculus one must be able to compute these things using a More on www.springer.com/978-88-470-1838-9 separate language: that of spectral sequences. The Designed for students having no previous experience basic properties of spectral sequences are developed Online orders shipping within 2-3 days with rigorous proofs, this text on analysis can be used using exact couples. All is done in the context of immediately following standard calculus courses. It bicomplexes, for almost all applications of spectral 2011. XV, 235 p. Softcover is highly recommended for anyone planning to study 978-88-470-1838-9 sequences involve indices. Applications include advanced analysis, e.g., complex variables, differential Grothendieck spectral sequences, change of rings, ▶$59.95 equations, Fourier analysis, numerical analysis, Lyndon-Hochschild-Serre sequence, and theorems several variable calculus, and statistics. It is also of Leray and Cartan computing sheaf cohomology. recommended for future secondary school teachers. A Joseph Rotman is Professor Emeritus of Mathematics limited number of concepts involving the real line and at the University of Illinois at Urbana-Champaign. functions on the real line are studied. Many abstract He is the author of numerous successful textbooks, ideas, such as metric spaces and ordered systems, are including Advanced Modern Algebra (Prentice- avoided. The least upper bound property is taken Hall 2002), Galois Theory, 2nd Edition (Springer as an axiom and the order properties of the real line 1998) A First Course in Abstract Algebra (Prentice- are exploited throughout. 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4th Edition (Springer 1995), and Introduction to ▶$49.95 (Malgrange, Hormander, Kawai, Quinto, Kuchment) Algebraic Topology (Springer 1988). were his collaborators. More on www.springer.com/978-0-387-24527-0 More on www.springer.com/978-88-470-1946-1 Usually dispatched within 3 to 5 business days Due: April 27, 2012 2012. X, 290 p. 11 illus. In 1 volumes, not available 2009. XIV, 710 p. 11 illus. (Universitext) Softcover separately. Hardcover 978-0-387-24527-0 978-88-470-1946-1 ▶$49.95 ▶approx. $129.00

N.S.N. Sastry, Indian Statistical Institute, Bangalore, India (Ed.) Buildings, Finite Geometries and R.Z. Ríos-Mercado, Universidad Autónoma de Nuevo Groups León, San Nicolas de los Garza, NL, Mexico; Y.A. Ríos-Solís, Universidad Autónoma de Nuevo León, San Nicolas de los Proceedings of a Satellite Conference, Garza, NL, Mexico (Eds.) International Congress of Mathematicians, Hyderabad, India, 2010 Just-in-Time Systems This volume collects articles inspired by the Whether different types of costs are to be reduced, Proceedings of the ICM 2010 Satellite Conference on V. Rovenski, University of Haifa, Department of benefits to be maximized or scarce resources to be “Buildings, Finite Geometries and Groups” organized Mathematics, 31905 Haifa, Israel; P. Walczak, University of managed, scheduling theory provides intelligent at the Indian Statistical Institute, Bangalore, from Lodz, Department of Mathematics, 90238, Lodz, Poland methods for practitioners and scientists. The just-in- August 29 – 31, 2010. These contributors include time (JIT) production philosophy has enriched the some of the most active researchers in areas related Topics in Extrinsic Geometry of classical scheduling theory with models that consider to finite simple groups, Chevalley groups and their characteristics such as inventory costs, set-up times, generalizations: theory of buildings, finite incidence Codimension-One Foliations lot sizing, or maintenance.This edited volume geometries, modular representations, Lie theory, Extrinsic geometry describes properties of foliations considers the specifics of just-in-time systems. It and more. Contributions reflect the current major on Riemannian manifolds which can be expressed provides knowledge and insights on recent advances trends in research in the geometric and combinatorial in terms of the second fundamental form of the in scheduling theory where just-in-time aspects aspects of the study of these groups. The unique leaves. The authors of Topics in Extrinsic Geometry are considered. Contributions on models, theory, perspective that the authors bring to their articles of Codimension-One Foliations achieve a technical algorithms, and applications, that bring the theory on current developments and major problems in tour de force, which will lead to important geometric up-to-date on the state-of-the-art of JIT systems are their area is expected to be very useful to research results. The Integral Formulae, introduced in chapter presented.Professionals, researchers and graduate mathematicians, graduate students and potential new 1, is a useful for problems such as: prescribing higher students will find this book useful. entrants to these fields. mean curvatures of foliations, minimizing volume More on www.springer.com/978-1-4614-1122-2 More on www.springer.com/978-1-4614-0708-9 and energy defined for vector or plane fields on Usually dispatched within 3 to 5 business days Usually dispatched within 3 to 5 business days manifolds, and existence of foliations whose leaves 2012. XII, 341 p. 1 illus. (Springer Proceedings in enjoy given geometric properties. The Integral 2012. XV, 304 p. 79 illus., 21 in color. (Springer Optimization and Its Applications, Vol. 60) Hardcover Mathematics, Vol. 10) Hardcover Formulae steams from a Reeb formula, for foliations 978-1-4614-1122-2 978-1-4614-0708-9 on space forms which generalize the classical ones. $149.00 For a special auxiliary functions the formulae involve ▶$149.00 ▶ the Newton transformations of the Weingarten operator. The central topic of this book is Extrinsic Geometric Flow (EGF) on foliated manifolds, which Forthcoming may be a tool for prescribing extrinsic geometric I. Sabadini, D.C. Struppa (Eds.) properties of foliations. To develop EGF, one needs Variational Formulae, revealed in chapter 2, which expresses a change in different extrinsic geometric The Mathematical Legacy of Leon quantities of a fixed foliation under leaf-wise variation Ehrenpreis of the Riemannian Structure of the ambient manifold. Chapter 3 defines a general notion of EGF and Leon Ehrenpreis has been one of the leading studies the evolution of Riemannian metrics along mathematicians in the twentieth century. His the trajectories of this flow(e.g., describes the short- contributions to the theory of partial differential time existence and uniqueness theory and estimate equations were part of the golden era of PDEs, the maximal existence time).Some special solutions and led him to what is maybe his most important (called Extrinsic Geometric Solutions) of EGF are contribution, the Fundamental Principle, which he O. Scherzer, University of Innsbruck, Austria (Ed.) presented and are of great interest, since they provide announced in 1960, and fully demonstrated in 1970. Riemannian Structures with very particular geometry His most recent work, on the other hand, focused Handbook of Mathematical of the leaves. This work is aimed at those who have an on a novel and far reaching understanding of the Methods in Imaging interest in the differential geometry of submanifolds Radon transform, and offered new insights in integral and foliations of Riemannian manifolds. geometry. Leon Ehrenpreis died in 2010, and this The Handbook of Mathematical Methods in volume collects writings in his honor by a cadre Imaging provides a comprehensive treatment More on www.springer.com/978-1-4419-9907-8 of distinguished mathematicians, many of which of the mathematical techniques used in imaging Usually dispatched within 3 to 5 business days science. The material is grouped into two central 2011. XV, 114 p. 6 illus. (SpringerBriefs in Mathematics) themes, namely, Inverse Problems (Algorithmic Softcover Reconstruction) and Signal and Image Processing. 978-1-4419-9907-8 Each section within the themes covers applications 78 springer.com

(modeling), mathematics, numerical methods (using as mixed combinatorial optimization problems are a case example) and open questions. Written by considered. Numerical examples based on facility experts in the area, the presentation is mathematically location problems support the theory. Applications rigorous. The entries are cross-referenced for easy of geometric branch-and-bound methods, namely navigation through connected topics. Available the circle detection problem in image processing, in both print and electronic forms, the handbook the integrated scheduling and location makespan is enhanced by more than 150 illustrations and problem, and the median line location problem in an extended bibliography. It will benefit students, the three-dimensional space are also presented.The scientists and researchers in applied mathematics. book is intended for both researchers and students Engineers and computer scientists working in in the areas of mathematics, operations research, imaging will also find this handbook useful. engineering, and computer science.

More on www.springer.com/978-0-387-92921-7 P. Schneider, University of Münster, Germany More on www.springer.com/978-1-4614-1950-1 Title available online only, not as print version. Usually dispatched within 3 to 5 business days 2011. XVIII, 1607 p. 150 illus. Print + eReference. p-Adic Lie Groups 2012. XIV, 142 p. 26 illus. (Nonconvex Optimization and Its 978-0-387-92921-7 Applications, Vol. 63) Hardcover Manifolds over complete nonarchimedean fields $849.00 978-1-4614-1950-1 ▶ together with notions like tangent spaces and vector ▶$99.00 fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with a self-contained and detailed introduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets up the analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The second part of the book contains, for the first time in a textbook, a detailed exposition of Lazard's algebraic approach to compact p-adic Lie groups, via his notion of a p-valuation, together with its application to the D. Schleicher, Jacobs University Bremen, Germany; M. structure of completed group rings. Lackmann, Jacobs University Bremen, Germany (Eds.) R. Schoof, Università di Roma, Italia More on www.springer.com/978-3-642-21146-1 An Invitation to Mathematics Usually dispatched within 3 to 5 business days Catalan's Conjecture 2011. XI, 254 p. (Grundlehren der mathematischen From Competitions to Research Eugène Charles Catalan made his famous conjecture Wissenschaften, Vol. 344) Hardcover This Invitation to Mathematics consists of 14 978-3-642-21146-1 – that 8 and 9 are the only two consecutive perfect powers of natural numbers – in 1844 in a letter to the contributions, many from the world's leading ▶$99.00 mathematicians, that introduce the readers to editor of Crelle’s mathematical journal. One hundred exciting aspects of current mathematical research. and fifty-eight years later, Preda Mihailescu proved The contributions are as varied as the personalities it. Catalan’s Conjecture presents this spectacular of active mathematicians, but together they show result in a way that is accessible to the advanced mathematics as a rich and lively field of research. The undergraduate. The first few sections of the book contributions are written for interested students at the require little more than a basic mathematical age of transition between high school and university background and some knowledge of elementary who know high school mathematics and perhaps number theory, while later sections involve Galois competition mathematics and who want to find out theory, algebraic number theory and a small amount what current research mathematics is about. We of commutative algebra. The prerequisites, such as the hope that it will also be of interest to teachers or more basic facts from the arithmetic of cyclotomic fields, advanced mathematicians who would like to learn are all discussed within the text. The author dissects about exciting aspects of mathematics outside of their both Mihailescu’s proof and the earlier work it made own work or specialization. Together with a team of use of, taking great care to select streamlined and young ``test readers'', editors and authors have taken transparent versions of the arguments and to keep D. Scholz, Georg-August-University Göttingen, Germany great care, through a substantial ``active editing'' the text self-contained. Only in the proof of Thaine’s process, to make the contributions understandable by theorem is a little class field theory used; it is hoped the intended readership. Deterministic Global Optimization that this application will motivate the interested Geometric Branch-and-bound Methods and reader to study the theory further. Beautifully More on www.springer.com/978-3-642-19532-7 their Applications clear and concise, this book will appeal not only to Usually dispatched within 3 to 5 business days specialists in number theory but to anyone interested This monograph deals with a general class of solution 2011. XIV, 220 p. 56 illus., 31 in color. Softcover in seeing the application of the ideas of algebraic approaches in deterministic global optimization, 978-3-642-19532-7 number theory to a famous mathematical problem. namely the geometric branch-and-bound methods $34.95 ▶ which are popular algorithms, for instance, in More on www.springer.com/978-1-84800-184-8 Lipschitzian optimization, d.c. programming, and Usually dispatched within 3 to 5 business days interval analysis.It also introduces a new concept for the rate of convergence and analyzes several bounding 2009. IX, 124 p. 10 illus. (Universitext) Softcover operations reported in the literature, from the 978-1-84800-184-8 theoretical as well as from the empirical point of view. ▶$49.95 Furthermore, extensions of the prototype algorithm for multicriteria global optimization problems as well springer.com 79

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Schuss, Tel Aviv University, Israel physics. The part on integrability and vector fields is devoted to the study of multicomponent nonlinear Nonlinear Filtering and Optimal Schrodinger (MNLS) equations which play important Phase Tracking role for understanding hydro-dynamical processes, the phenomena of Bose-Einstein condensates, etc. This book offers an analytical rather than measure- The symmetries of these MNLS equations are also theoretical approach to the derivation of the partial studied, as well as their reductions and Lie algebraic differential equations of nonlinear filtering theory. properties. The third part of these proceedings The basis for this approach is the discrete numerical treats problems of contemporary mechanics and scheme used in Monte-Carlo simulations of stochastic mathematical physics. The methods of differential differential equations and Wiener's associated path geometry quite unexpectedly provide important tool integral representation of the transition probability for modeling and studying microinjections in cell density. Furthermore, it presents analytical methods membranes, the equilibrium. for constructing asymptotic approximations to their D. Serre, Unité de Mathématiques Pures et Appliquées, École More on www.springer.com/978-0-7354-0895-1 solution and for synthesizing asymptotically optimal Normale Supérieure de Lyon, 69364 Lyon Cedex 07, France filters. It also offers a new approach to the phase Online orders shipping within 2-3 days tracking problem, based on optimizing the mean 2011. 254 p. (Mathematical and Statistical Physics, Vol. Matrices time to loss of lock. The book is based on lecture 1340) Softcover Theory and Applications notes from a one-semester special topics course 978-0-7354-0895-1 In this book, Denis Serre begins by providing a on stochastic processes and their applications that ▶$132.00 clean and concise introduction to the basic theory of the author taught many times to graduate students matrices. He then goes on to give many interesting of mathematics, applied mathematics, physics, applications of matrices to different aspects of chemistry, computer science, electrical engineering, mathematics and also other areas of science and and other disciplines. The book contains exercises engineering. With forty percent new material, this and worked-out examples aimed at illustrating the second edition is significantly different from the methods of mathematical modeling and performance first edition. 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Gerdjikov, advanced undergraduate and graduate students with Representing Finite Groups either applied or theoretical goals. This book is based Bulgarian Academy of Sciences, Sofia, Bulgaria; Y. A Semisimple Introduction Matsushita, University of Shiga Prefecture, Hikone, Japan; on a course given by the author at the École Normale I.M. Mladenov, Bulgarian Academy of Sciences, Sofia, This graduate textbook presents the basics of Supérieure de Lyon. Bulgaria (Eds.) representation theory for finite groups from the More on www.springer.com/978-1-4419-7682-6 point of view of semisimple algebras and modules Usually dispatched within 3 to 5 business days International Workshop on over them. The presentation interweaves insights Complex Structures, Integrability from specific examples with development of 2010. XIV, 289 p. 2 illus. (Graduate Texts in general and powerful tools based on the notion of Mathematics, 216) Hardcover and Vector Fields semisimplicity. 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It will be interesting also and some advanced undergraduate courses in to a much broader audience of scholars and scientists mathematics. Prerequisites include acquaintance working or interested in classical and quantum with elementary group theory and some familiarity mechanics, in cell membranes, integrability and with rings and modules. A final chapter presents 80 springer.com s Republic of China; L.-L. Wang, Nanyang Technological optimization theory, nonsmooth analysis, algebraic can learn a wide variety of techniques and solve University, Republic of Singapore topology and singularity theory. numerous nonlinear PDEs included and many other More on www.springer.com/978-1-4614-1896-2 differential equations, simplifying and transforming Spectral Methods the equations and solutions, arbitrary functions Algorithms, Analysis and Applications Usually dispatched within 3 to 5 business days and parameters, presented in the book). Numerous 2012. XI, 193 p. 29 illus. 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Hardcover a unified framework for designing and analyzing 978-3-7091-0516-0 spectral algorithms for a variety of problems, Beyond ▶$124.00 including in particular high-order differential equations and problems in unbounded domains. The This is an advanced book on modular forms. While book contains a large number of figures which are there are many books published about modular designed to illustrate various concepts stressed in forms, they are written at an elementary level, and S.E. Shreve, Carnegie Mellon University, Pittsburgh, PA, USA the book. A set of basic matlab codes has been made not so interesting from the viewpoint of a reader available online to help the readers to develop their who already knows the basics. This book offers Stochastic Calculus for Finance II own spectral codes for their specific applications. something new, which may satisfy the desire of such a Continuous-Time Models reader. 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Thus the book is presented so that the reader can learn such theories systematically. precise statements of results, plausibility arguments, Ultimately, we concentrate on the following two and even some proofs, but more importantly intuitive themes:(I) The correspondence between the forms explanations developed and refine through classroom of half-integral weight and those of integral weight. experience with this material are provided. The book (II) The arithmeticity of various Dirichlet series includes a self-contained treatment of the probability associated with modular forms of integral or half- theory needed for stochastic calculus, including integral weight.Goro Shimura is currently a professor Brownian motion and its properties. Advanced emeritus of mathematics at Princeton University. topics include foreign exchange models, forward measures, and jump-diffusion processes. This book is More on www.springer.com/978-1-4614-2124-5 being published in two volumes. 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The material progresses systematically Solving Nonlinear Partial and establishes a comprehensive theory for a rather broad class of optimization problems Differential Equations with Maple tailored to their particular type of nonsmoothness. and Mathematica Topological Aspects of Nonsmooth Optimization will benefit researchers and graduate students in The emphasis of this work is on constructing different applied mathematics, especially those working in types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader springer.com 81

counting algorithm, Miller's algorithm to compute Mathematics. All the research areas of Numerical the Tate and Weil pairings, and a description of Analysis and Computational Mathematics(Numerical aspects of elliptic curve cryptography. There is also ODEs, Numerical PDEs (inc. BVPs), Scientific a new section on Szpiro's conjecture and ABC, as Computing and Algorithms, Stochastic Differential well as expanded and updated accounts of recent Equations, Approximation, Numerical Linear developments and numerous new exercises. The Algebra, Numerical Integral Equations, Error book contains three appendices: Elliptic Curves in Analysis and Interval Analysis, Difference Equations Characteristics 2 and 3, Group Cohomology, and a and Recurrence Relations, Numerical problems in third appendix giving an overview of more advanced Dynamical Systems, Applications to the Sciences topics. 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Simos, University of Peloponnese, Tripolis, Greece; of engineering and environmental processes, are drawn from practical problems in quantitative G. Psihoyios, University of Buckingham, UK; C. Tsitouras, manufacturing, and industrial systems, heat transfer, finance Technological Educational Institution of Chalkis, Psahna, Greece (Eds.) fluid mechanics, CFD, and transport phenomena; More on www.springer.com/978-0-387-24968-1 solid mechanics and mechanics of metals; Usually dispatched within 3 to 5 business days ICNAAM 2010 electromagnets and MHD; reliability modeling and system optimization; decision sciences in an industrial International Conference of Numerical Analysis and manufacturing context; civil engineering systems 2004. XVI, 187 p. 33 illus. 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The Sonar Applications, Transient Analysis, Medical importance for the reader is that with this book one Imaging, Multigrid Methods, Frames, Bifurcation and can finds all the new developments in the research on Singularity Theory, Deterministic Chaos and Fractals, Numerical, Industrial and Applied Mathematics. Soliton and Coherent Phenomena, Formation of Pattern, Evolution, Complexity Theory and Neural More on www.springer.com/978-0-7354-0831-9 Networks, Analytical Approaches and Simulations Due: December 31, 2011 for more Accurate Descriptions, Predictions, Experimental Observations and Applications of 2011. CD-ROM. (Mathematical and Statistical Physics, Nonlinear Phenomena in Science and Engineering, Vol. 1281) CDSP J.H. Silverman, Brown University, Providence, RI, USA Theoretical and Applied aspects of Computational 978-0-7354-0831-9 Geometry, Control Theory and Automation, Fuzzy approx. $359.00 The Arithmetic of Elliptic Curves ▶ Sets and Systems and Fuzzy Logic, Applied Algebra, The theory of elliptic curves is distinguished by its Quality Theory of Differential Equations, Neural long history and by the diversity of the methods Networks , etc.) T.E. Simos, University of Peloponnese, Tripolis, Greece; G. that have been used in its study. This book treats More on www.springer.com/978-0-7354-0956-9 the arithmetic theory of elliptic curves in its modern Psihoyios, University of Peloponnese, Tripolis, Greece; C. Tsitouras, Technological Educational Institution of Chalkis, Online orders shipping within 2-3 days formulation, through the use of basic algebraic Psahna, Greece; Z. Anastassi, School of Pedagogical and number theory and algebraic geometry. The book 2011. 2118 p. 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play a significant role in applications and are treated Cut a Triangle?] reads like an adventure story. In fact, here, along with an introduction to monotone systems it is an adventure story, complete with interesting generated by delay equations. The book contains characters, moments of exhilaration, examples of some quite recent results such as the Poincare- serendipity, and unanswered questions. It conveys Bendixson theory for monotone cyclic feedback the spirit of mathematical discovery and it celebrates systems, obtained by Mallet-Paret and Sell. The the event as have mathematicians throughout history. linear chain trick for a special family of infinite delay —Cecil Rousseau The beginner, who is interested equations is treated. The book is distinguished by the in the book, not only comprehends a situation in a wealth of examples that are introduced and treated creative mathematical studio, not only is exposed to in detail. These include the delayed logistic equation, good mathematical taste, but also acquires elements delayed chemostat model of microbial growth, of modern mathematical culture. And (not less inverted pendulum with delayed feedback control, important) the reader imagines the role and place of L.A. Skinner a gene regulatory system, and an HIV transmission intuition and analogy in mathematical investigation; model. An entire chapter is devoted to the interesting he or she fancies the meaning of generalization in Singular Perturbation Theory dynamics exhibited by a chemostat model of modern mathematics and surprising connections bacteriophage parasitism of bacteria. The book has between different parts of this science (that are, as This book is a rigorous presentation of the method a large number of exercises and illustrations. Hal one might think, far from each other) that unite of matched asymptotic expansions, the primary tool Smith is a Professor at the School of Mathematical them. —V.G. Boltyanski SIAM Review Alexander for attacking singular perturbation problems. A and Statistical Sciences at Arizona State University. Soifer is a wonderful problem solver and inspiring knowledge of conventional asymptotic analysis is teacher. His book will tell young mathematicians what assumed. The first chapter introduces the theory More on www.springer.com/978-1-4419-7645-1 mathematics should be like, and remind older ones and is followed by four chapters of applications to Usually dispatched within 3 to 5 business days who may be in danger of forgetting. —John Baylis ordinary differential equation problems of increasing The Mathematical Gazette complexity. Exercises are included as well as several 2011. XII, 177 p. (Texts in Applied Mathematics, Vol. Maple programs for computing the terms of the 57) Hardcover More on www.springer.com/978-0-387-74650-0 various asymptotic expansions that arise in solving 978-1-4419-7645-1 Usually dispatched within 3 to 5 business days the problems. ▶$49.95 More on www.springer.com/978-1-4419-9957-3 2009. XXX, 176 p. 83 illus. Softcover 978-0-387-74650-0 Usually dispatched within 3 to 5 business days ▶$39.95 2011. X, 85 p. Softcover 978-1-4419-9957-3 ▶$49.95

A. Soifer, University of Colorado, Colorado Springs, CO, USA How Does One Cut a Triangle? A. Soifer, University of Colorado, Colorado Springs, CO, USA How Does One Cut a Triangle? is a work of art, and rarely, perhaps never, does one find the talents The Colorado Mathematical of an artist better suited to his intention than we H. Smith, Arizona State University, Tempe, AZ, USA find in Alexander Soifer and this book. —Peter Olympiad and Further D. Johnson, Jr. This delightful book considers and Explorations An Introduction to Delay solves many problems in dividing triangles into Differential Equations with n congruent pieces and also into similar pieces, From the Mountains of Colorado to the Peaks of Mathematics Applications to the Life Sciences as well as many extremal problems about placing points in convex figures. The book is primarily This book presents the 20-year account of the This book is intended to be an introduction to meant for clever high school students and college Colorado Mathematical Olympiad — its dreams Delay Differential Equations for upper level students interested in geometry, but even mature and rewards, hard work and conflict. It features undergraduates or beginning graduate mathematics mathematicians will find a lot of new material in more than just original wonderful problems and students who have a good background in ordinary it. I very warmly recommend the book and hope their ingenious solutions; it tells a compelling story differential equations and would like to learn the readers will have pleasure in thinking about the involving the lives of those who have been part of about the applications. It may also be of interest to unsolved problems and will find new ones. —Paul the Olympiad. The reader will meet Olympians applied mathematicians, computational scientists, Erdös It is impossible to convey the spirit of the book and follow their paths as professionals. In the vast and engineers. It focuses on key tools necessary to by merely listing the problems considered or even field of competition books, this book is unique, understand the applications literature involving delay a number of solutions. The manner of presentation for it builds bridges between Olympiads and “real” equations and to construct and analyze mathematical and the gentle guidance toward a solution and hence mathematics by demonstrating through 20 “Further models. Aside from standard well-posedness to generalizations and new problems takes this Explorations,” the trains of mathematical thought, results for the initial value problem, it focuses on elementary treatise out of the prosaic and into the showing how a solved Olympiad problem gives birth stability of equilibria via linearization and Lyapunov stimulating realm of mathematical creativity. Not to deeper problems and leads to the forefront of functions and on Hopf bifurcation. It contains a brief only young talented people but dedicated secondary mathematical research full of striking results and open introduction to abstract dynamical systems focused teachers and even a few mathematical sophisticates problems.Like Gauss, Alexander Soifer would not on those generated by delay equations, introducing will find this reading both pleasant and profitable. — hesitate to inject Eureka! at the right moment. Like limit sets and their properties. Differential inequalities L.M. Kelly Mathematical Reviews [How Does One van der Waerden, he can transform a dispassionate springer.com 83 exercise in logic into a compelling account of sudden (we can hope) have a great and salutary influence on insights and ultimate triumph. — Cecil Rousseau all writing on mathematics in the future.“ –Peter D. Chair, USA Mathematical Olympiad Committee ... Johnson Jr., Auburn University Just now a postman this book is not so much mathematical literature as came to the door with a copy of the masterpiece it is literature built around mathematics… with the of the century. I thank you and the mathematics Further Explorations sections, anyone so inclined community should thank you for years to come. You could spend a lifetime on the mathematics sprouting have set a standard for writing about mathematics from this volume. —Peter D. Johnson, Jr., Auburn and mathematicians that will be hard to match. – University I finished reading the book in one sitting Harold W. Kuhn, Princeton University The beautiful – I just could not put it down. Professor Soifer has and unique Mathematical coloring book of Alexander indebted us all by first making the effort to organize Soifer is another case of ``good mathematics''… and the Colorado Mathematical Olympiads, and then presenting mathematics as both a science and an making the additional effort to tell us about it in such art… It is difficult to explain how much beautiful and G. Sommaruga, ETH Zurich, Switzerland (Ed.) an engaging and useful way. —Branko Grünbaum, good mathematics is included and how much wisdom University of Washington A delightful feature of the about life is given. –Peter Mihók, Mathematical Foundational Theories of Classical book is that in the second part more related problems Reviews are discussed. Some of them are still unsolved. —Paul More on www.springer.com/978-0-387-74640-1 and Constructive Mathematics Erdős The book is a gold mine of brilliant reasoning Online orders shipping within 2-3 days The book “Foundational Theories of Classical with special emphasis on the power and beauty of and Constructive Mathematics” is a book on the coloring proofs. Strongly recommended to both 2009. XXX, 610 p. 211 illus. Hardcover classical topic of foundations of mathematics. Its serious and recreational mathematicians on all levels 978-0-387-74640-1 originality resides mainly in its treating at the same of expertise. —Martin Gardner ▶$69.95 time foundations of classical and foundations of More on www.springer.com/978-0-387-75471-0 constructive mathematics. This confrontation of Usually dispatched within 3 to 5 business days two kinds of foundations contributes to answering questions such as: Are foundations/foundational 2011. XXXIX, 408 p. 185 illus., 18 in color. Softcover theories of classical mathematics of a different nature 978-0-387-75471-0 compared to those of constructive mathematics? Do ▶$59.95 they play the same role for the resp. mathematics? Are there connections between the two kinds of foundations? Etc. The confrontation and comparison is often implicit and sometimes explicit. Its great advantage is to extend the traditional discussion of foundations of mathematics and to render it at the same time more subtle and more differentiated.Another important aspect of the book is that some of its contributions are of a more S.A.-H. Soliman, Misr University for Science and Technology, philosophical, others of a more technical nature. Sixth of October City, Egypt; A.-A.H. Mantawy, Ain Shams This double face is emphasized, since foundations of University, Cairo, Egypt mathematics is an eminent topic in the philosophy of Modern Optimization Techniques mathematics: hence both sides of this discipline ought to be and are being paid due to. with Applications in Electric More on www.springer.com/978-94-007-0430-5 Power Systems Usually dispatched within 3 to 5 business days A. Soifer, University of Colorado at Colorado Springs, Colorado Springs, CO, USA This book presents the application of some AI 2011. XI, 314 p. (The Western Ontario Series in Philosophy of related modern optimization techniques in the Science, Vol. 76) Hardcover The Mathematical Coloring Book operation and control of electric power systems. 978-94-007-0430-5 $139.00 Mathematics of Coloring and the Colorful Life of With practical applications and examples the use ▶ its Creators of functional analysis, simulated annealing, Tabu- search, Genetic algorithms and fuzzy systems for I have never encountered a book of this kind. The the optimization of power systems is discussed best description of it I can give is that it is a mystery in detail. Preliminary mathematical concepts are novel… I found it hard to stop reading before I presented before moving to more advanced material. finished (in two days) the whole text. Soifer engages Researchers, senior undergraduate and graduate the reader's attention not only mathematically, but students will benefit from this book. Engineers emotionally and esthetically. May you enjoy the book working in utility companies, operations and control, as much as I did! –Branko Grünbaum University and water resource management will also find this of Washington You are doing great service to the book useful. community by taking care of the past, so the things More on www.springer.com/978-1-4614-1751-4 are better understood in the future. –Stanislaw P. Radziszowski, Rochester Institute of Technology Usually dispatched within 3 to 5 business days January 31, 2012 They [Van der Waerden’s sections] meet the highest standards of historical scholarship. –Charles C. 2012. XVII, 412 p. 101 illus., 61 in color. (Energy Systems) A. Sorokin, University of Florida, Gainesville, FL, USA; S. Gillispie, Princeton University You have dug up a Hardcover Rebennack, Colorado School of Mines, Golden, CO, USA; great deal of information – my compliments! –Dirk 978-1-4614-1751-4 P.M. Pardalos, University of Florida, Gainesville, FL, USA; N.A. van Dalen, Utrecht University I have just finished ▶$124.00 reading your (second) article "in search of van der Waerden". It is a masterpiece, I could not stop reading it... Congratulations! –Janos Pach, Courant Institute of Mathematics "Mathematical Coloring Book" will 84 springer.com

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Recent rapid developments in and planning of natural gas systems, pricing, as of marriages between paper-based and electronic the area require analyzing energy systems not as well as optimal location of gas supply units. In documents.Max Mühlhäuser, Technische Universität independent components but rather as connected addition, the second volume covers the topics of DarmstadtEveryone interested in how to design for interdependent networks. The Handbook of interactions between energy networks. Each subject real-world activities would profit from reading this Networks in Power Systems includes the state-of- is identified following the activity on the domain and book.James D. Hollan, University of California, San the-art developments that occurred in the power the recognition of each subject as an area of research. 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Steimle, TU Darmstadt, Germany Groups Pen-and-Paper User Interfaces An Introductory Approach Integrating Printed and Digital Documents Representation Theory of Finite Groups presents Even at the beginning of the 21st century, we are group representation theory at a level accessible to far from becoming paperless. Pen and paper is still advanced undergraduate students and beginning the only truly ubiquitous information processing graduate students. The required background is technology. Pen-and-paper user interfaces bridge the maintained to the level of linear algebra, group theory, gap between paper and the digital world. Rather than and very basic ring theory and avoids prerequisites replacing paper with electronic media, they seamlessly in analysis and topology by dealing exclusively with integrate both worlds in a hybrid user interface. finite groups. Module theory and Wedderburn Classical paper documents become interactive. This theory, as well as tensor products, are deliberately opens up a huge field of novel computer applications omitted. Instead, an approach based on discrete at our workplaces and in our homes. This book Fourier Analysis is taken, thereby demanding less provides readers with a broad and extensive overview background from the reader.The main topics covered A. Sorokin, University of Florida, Gainesville, FL, USA; S. in this text include character theory, the group algebra Rebennack, Colorado School of Mines, Golden, CO, USA; of the field, so as to provide a full and up-to-date and Fourier analysis, Burnside's pq-theorem and the P.M. Pardalos, University of Florida, Gainesville, FL, USA; N.A. picture of pen-and-paper computing. It covers dimension theorem, permutation representations, Iliadis, EnerCoRD, Athens, Greece; M.V.F. Pereira, PSR, Rio de the underlying technologies, reviews the variety Janeiro, Brazil (Eds.) of modern interface concepts and discusses future induced representations and Mackey's theorem, and directions of pen-and-paper computing. Based the representation theory of the symmetric group. For Handbook of Networks in Power on the author’s award-winning dissertation, the those students who have an elementary knowledge book also provides the first theoretical interaction of probability and statistics, a chapter on random Systems II model of pen-and-paper user interfaces and an walks on finite groups serves as an illustration to link finite stochastics and representation theory. Energy has been an inevitable component of human integrated set of interaction techniques for knowledge Applications to the spectral theory of graphs are lives for decades. Recent rapid developments in workers. 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They integrate well-established engage a broad readership due to the significance fuels, freight networks, as well as their interactions. paper-based practices with concepts derived from of representation theory in diverse branches of The book is separated into two volumes with three hypertext and social media.Researchers, practitioners springer.com 85 mathematics, engineering, and physics, to name a few. topology, this essential concept and its analogies have Its primary intended use is as a one semester textbook found numerous applications in mathematics that are for a third or fourth year undergraduate course or an still being investigated today, and which are explored introductory graduate course on group representation in this volume, the result of a meeting at Heidelberg theory. The content can also be of use as a reference to University that brought together mathematicians researchers in all areas of mathematics, statistics, and who use or study fundamental groups in their work several mathematical sciences. with an eye towards applications in arithmetic.The More on www.springer.com/978-1-4614-0775-1 book acknowledges the varied incarnations of the fundamental group: pro-finite, ℓ-adic, p-adic, pro- Usually dispatched within 3 to 5 business days algebraic and motivic. It explores a wealth of topics that range from anabelian geometry (in particular 2012. XIII, 157 p. 4 illus. (Universitext) Softcover the section conjecture), the ℓ-adic polylogarithm, 978-1-4614-0775-1 J. Stillwell, Department of Mathematics, University of San gonality questions of modular curves, vector bundles ▶$49.95 Francisco, San Francisco, CA 94117-1080 USA in connection with monodromy, and relative pro- algebraic completions, to a motivic version of Mathematics and Its History Minhyong Kim's non-abelian Chabauty method and From the reviews of the second edition:"This book p-adic integration after Coleman. The editor has covers many interesting topics not usually covered also included the abstracts of all the talks given at the in a present day undergraduate course, as well as Heidelberg meeting, as well as the notes on Coleman certain basic topics such as the development of the integration and on Grothendieck's fundamental group calculus and the solution of polynomial equations. with a view towards anabelian geometry taken from a The fact that the topics are introduced in their series of introductory lectures given by Amnon Besser historical contexts will enable students to better and Tamás Szamuely, respectively. appreciate and understand the mathematical ideas More on www.springer.com/978-3-642-23904-5 involved...If one constructs a list of topics central to Due: January 28, 2012 a history course, then they would closely resemble those chosen here."(David Parrott, Australian 2012. XII, 380 p. 66 illus. (Contributions in Mathematical and Computational Sciences, Vol. 2) Hardcover J. Stillwell, University of San Francisco, CA, USA Mathematical Society)"The book...is presented in 978-3-642-23904-5 a lively style without unnecessary detail. It is very $149.00 Naive Lie Theory stimulating and will be appreciated not only by ▶ students. Much attention is paid to problems and to In this new textbook, acclaimed author John Stillwell the development of mathematics before the end of presents a lucid introduction to Lie theory suitable the nineteenth century... This book brings to the non- for junior and senior level undergraduates. In order specialist interested in mathematics many interesting to achieve this, he focuses on the so-called "classical results. It can be recommended for seminars groups'' that capture the symmetries of real, complex, and will be enjoyed by the broad mathematical and quaternion spaces. These symmetry groups may community." (European Mathematical Society)"Since be represented by matrices, which allows them to be Stillwell treats many topics, most mathematicians studied by elementary methods from calculus and will learn a lot from this book as well as they will linear algebra. This naive approach to Lie theory find pleasant and rather clear expositions of custom is originally due to von Neumann, and it is now materials. The book is accessible to students that possible to streamline it by using standard results have already experienced calculus, algebra and of undergraduate mathematics. To compensate for geometry and will give them a good account of how the limitations of the naive approach, end of chapter the different branches of mathematics interact."(Denis discussions introduce important results beyond those Bonheure, Bulletin of the Belgian Society)This third S. Stojanovic, University of Cincinnati, OH, USA proved in the book, as part of an informal sketch of edition includes new chapters on simple groups and Lie theory and its history. John Stillwell is Professor combinatorics, and new sections on several topics, Neutral and Indifference Portfolio of Mathematics at the University of San Francisco. including the Poincare conjecture. The book has also He is the author of several highly regarded books Pricing, Hedging and Investing been enriched by added exercises. published by Springer, including The Four Pillars With applications in Equity and FX of Geometry (2005), Elements of Number Theory More on www.springer.com/978-1-4419-6052-8 This book is written for quantitative finance (2003), Mathematics and Its History (Second Edition, Usually dispatched within 3 to 5 business days professionals, students, educators, and 2002), Numbers and Geometry (1998) and Elements mathematically inclined individual investors. It is of Algebra (1994). 2010. XXII, 660 p. 222 illus. (Undergraduate Texts in about some of the latest developments in pricing, Mathematics) Hardcover More on www.springer.com/978-0-387-78214-0 978-1-4419-6052-8 hedging, and investing in incomplete markets. With regard to pricing, two frameworks are fully Usually dispatched within 3 to 5 business days $69.95 ▶ elaborated: neutral and indifference pricing. With 2008. XIII, 218 p. (Undergraduate Texts in regard to hedging, the most conservative and relaxed Mathematics) Hardcover hedging formulas are derived. With regard to 978-0-387-78214-0 Forthcoming investing, the neutral pricing methodology is also ▶$54.95 J. Stix, University of Heidelberg, Germany (Ed.) considered as a tool for connecting market asset prices with optimal positions in such assets.While The Arithmetic of Fundamental there are many books on the financial mathematics of incomplete markets based on probability, and Groups equivalent martingale measure approach to pricing, PIA 2010 this book is based solely on the analytical aspects of stochastic control, or more precisely, portfolio In the more than 100 years since the fundamental optimization. Namely, relying solely on portfolio group was first introduced by Henri Poincaré it has optimization, neutral and indifference pricing as evolved to play an important role in different areas of well as hedging methodologies were fully developed mathematics. Originally conceived as part of algebraic 86 springer.com in the context of arbitrary diffusive Markovian in two volumes (this is the 2nd volume). In the market models and portfolios of contracts. That was eighties, a group of theoretical physicists introduced made possible by some recent discoveries, the most several models for certain disordered systems, specific one being a recently found matrix inverse called "spin glasses". These models are simple and – the fundamental matrix of derivatives pricing rather canonical random structures, of considerable and hedging. This approach, while very general, interest for several branches of science (statistical is very feasible for practical implementations. So, physics, neural networks and computer science). The many examples are fully derived. The reader will get physicists studied them by non-rigorous methods the full understanding of the relationship between and predicted spectacular behaviors. This book neutral and indifference pricing, how to implement introduces in a rigorous manner this exciting new either one of these pricing methodologies, how to area to the mathematically minded reader. It requires implement hedging methodologies, and how to apply no knowledge whatsoever of any physics. The present all these in equity portfolio valuations and foreign D.W. Stroock, Massachusetts Institute of Technology, Volume II contains a considerable amount of new exchange.Srdjan D. Stojanovic is Professor in the Cambridge, MA, USA material, in particular all the fundamental low- Department of Mathematical Sciences at University temperature results obtained after the publication of of Cincinnati (USA) and Professor in the Center for Essentials of Integration Theory the first edition. Financial Engineering at Suzhou University (China). for Analysis More on www.springer.com/978-3-642-22252-8 More on www.springer.com/978-0-387-71417-2 Essentials of Integration Theory for Analysis is a Usually dispatched within 3 to 5 business days Usually dispatched within 3 to 5 business days substantial revision of the best-selling Birkhäuser 2011. XII, 629 p. (Ergebnisse der Mathematik und ihrer title by the same author, A Concise Introduction Grenzgebiete. 3. Folge A Series of Modern Surveys in 2012. XIV, 263 p. 6 illus. Hardcover to the Theory of Integration. Highlights of this new Mathematics, Vol. 55) Hardcover 978-0-387-71417-2 textbook for the GTM series include revisions to 978-3-642-22252-8 ▶$59.95 Chapter 1 which add a section about the rate of ▶$189.00 convergence of Riemann sums and introduces a discussion of the Euler–MacLauren formula. In Chapter 2, where Lebesque’s theory is introduced, Forthcoming a construction of the countably additive measure is done with sufficient generality to cover both Lebesque E. Tanfani, University of Genova, Italy; A. Testi, University of and Bernoulli measures. Chapter 3 includes a proof Genova, Italy (Eds.) of Lebesque’s differential theorem for all monotone functions and the concluding chapter has been Advanced Decision Making expanded to include a proof of Carathéory’s method Methods Applied to Health Care for constructing measures and his result is applied to the construction of the Hausdorff measures. The most difficult part of making decisions in the This new gem is appropriate as a text for a one- health care field on all levels (national, regional, semester graduate course in integration theory and institutional, patient) is linked to the very complexity is complimented by the addition of several problems of the system itself, to the intrinsic uncertainty B. Straughan, Durham University, Durham, United Kingdom related to the new material. The text is also highly involved and its dynamic nature. This requires useful for self-study. A complete solutions manual is not only the ability to analyze and interpret a large Heat Waves available for instructors who adopt the text for their amount of information but also arrange it so that it courses.Additional publications by Daniel W. Stroock: becomes a cognitive base for appropriate decision- This book surveys significant modern contributions An Introduction to Markov Processes, ©2005 making. Moreover, decisions in the health care field to the mathematical theories of generalized heat Springer (GTM 230), ISBN: 978-3-540-23499-9; A are subjected to many challenges and constraints: fast wave equations. The first three chapters form a Concise Introduction to the Theory of Integration, © change and uncertain outcomes, aging population, comprehensive survey of most modern contributions 1998 Birkhäuser Boston, ISBN: 978-0-8176-4073-6; increasing citizen expectations, equity considerations also describing in detail the mathematical properties (with S.R.S. Varadhan) Multidimensional Diffusion and limited resources. Operations research, statistical of each model. Acceleration waves and shock waves Processes, © 1979 Springer (Classics in Mathematics), and economic-related quantitative methods supply are the focus in the next two chapters. Numerical ISBN: 978-3-540-28998-2. these decisions making tools and methodology. The techniques, continuous data dependence, and contributed book presents a collection of applications More on www.springer.com/978-1-4614-1134-5 spatial stability of the solution in a cylinder, feature to concrete situations detailing the problem area, prominently among other topics treated in the Usually dispatched within 3 to 5 business days the methodology employed, the implementation following two chapters. The final two chapters are and results. Each topic addressed in the book will devoted to a description of selected applications 2011. XI, 243 p. (Graduate Texts in Mathematics, Vol. be structured in such a way that an interdisciplinary 262) Hardcover and the corresponding formation of mathematical and wide audience will be able to use the materials 978-1-4614-1134-5 models. Illustrations are taken from a broad range presented. As an example the book chapters will $59.95 that includes nanofluids, porous media, thin films, ▶ address health policies issues, planning health nuclear reactors, traffic flow, biology, and medicine, services, epidemiology and disease modelling, home- all of contemporary active technological importance care modelling, logistics in health care, capacity and interest. This book will be of value to applied 2nd Edition planning, quality and appropriateness. mathematicians, theoretical engineers and other practitioners who wish to know both the theory and M. Talagrand, Université Paris 6, Paris, France More on www.springer.com/978-88-470-2320-8 its relevance to diverse applications. Due: January 28, 2012 Mean Field Models for Spin More on www.springer.com/978-1-4614-0492-7 2012. 15 illus. Softcover 978-88-470-2320-8 Usually dispatched within 3 to 5 business days Glasses ▶approx. $129.00 2011. XII, 318 p. 6 illus. (Applied Mathematical Sciences, Vol. Volume II: Advanced Replica-Symmetry and Low 177) Hardcover Temperature 978-1-4614-0492-7 This is a new, completely revised, updated and $124.00 ▶ enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians" springer.com 87

K. Tapp, Saint Joseph's University, Philadelphia, PA, USA D.S. Tartakoff, University of Illinois, Chicago, IL, USA A. Taylor, Union College, Schenectady, NY, USA; A.M. Pacelli, Symmetry Nonelliptic Partial Differential Williams College, Williamstown, MA, USA A Mathematical Exploration Equations Mathematics and Politics This textbook is perfect for a math course for Analytic Hypoellipticity and the Courage to Strategy, Voting, Power, and Proof non-math majors, with the goal of encouraging Localize High Powers of T Mathematics and Politics requires no prerequisites effective analytical thinking and exposing students to This book fills a real gap in the analytical literature. in either subject. The underlying philosophy involves elegant mathematical ideas. It includes many topics After many years and many results of analytic minimizing algebraic computations while focusing on commonly found in sampler courses, like Platonic regularity for partial differential equations, the the conceptual aspects of mathematics in the context solids, Euler’s formula, irrational numbers, countable only access to the technique known as $(T^p)_\phi of real-world questions in political science. This new sets, permutations, and a proof of the Pythagorean $ has remained embedded in the research papers addition has an added co-author, Allison Pacelli, and Theorem. All of these topics serve a single compelling themselves, making it difficult for a graduate student covers six major topics: social choice, yes-no voting goal: understanding the mathematical patterns or a mature mathematician in another discipline systems, political power, game-theoretic models underlying the symmetry that we observe in the to master the technique and use it to advantage. of international conflict, fairness, and escalation. physical world around us.The exposition is engaging, This monograph takes a particularly non-specialist In addition to having two new chapters (treating precise and rigorous. The theorems are visually approach, one might even say gentle, to smoothly apportionment and conflict resolution), the text has motivated with intuitive proofs appropriate for the bring the reader into the heart of the technique been extensively reorganized and the number of intended audience. Students from all majors will and its power, and ultimately to show many of the exercises increased to over 300. EXCERPTS FROM enjoy the many beautiful topics herein, and will come results it has been instrumental in proving. Another REVIEWS OF THE FIRST EDITION "Taylor has to better appreciate the powerful cumulative nature technique developed simultaneously by F. Treves is done a remarkable job of showing the power of of mathematics as these topics are woven together developed and compared and contrasted to ours. The deductive reasoning in … the strategic choices actors into a single fascinating story about the ways in which techniques developed here are tailored to proving real make in conflict situations … a penetrating analysis objects can be symmetric.Kristopher Tapp is currently analytic regularity to solutions of sums of squares of of both real-life and hypothetical situations." -- a mathematics professor at Saint Joseph's University. vector fields with symplectic characteristic variety Steven Brams, New York University Alan Taylor’s He is the author of 17 research papers and one well- and others, real and complex. The motivation came book is carefully crafted. He is ever aware of his reviewed undergraduate textbook, Matrix Groups for from the field of several complex variables and the audience, but relentlessly presses the beginning Undergraduates. He has been awarded two National seminal work of J. J. Kohn. It has found application student to understand more and more." -- Samuel Science Foundation research grants and several in non-degenerate (strictly pseudo-convex) and Merrill III, American Mathematical Monthly This teaching awards. degenerate situations alike, linear and non-linear, book is a unique and valuable source … Coverage More on www.springer.com/978-1-4614-0298-5 partial and pseudo-differential equations, real and is thorough and extensive; ideas are explained Due: December 31, 2011 complex analysis. The technique is utterly elementary, clearly and at an appropriate mathematical level." involving powers of vector fields and carefully chosen -- Ed Packel, Lake Forest College "… Mathematics 2012. XIV, 215 p. 159 illus., 152 in color. Hardcover localizing functions. No knowledge of advanced and Politics is a nearly perfect solution, either for 978-1-4614-0298-5 techniques, such as the FBI transform or the theory classes or for the serious professional who wants ▶$49.95 of hyperfunctions is required. In fact analyticity is to retool. … The writing is crisp, and the sense of proved using only $C^\infty$ techniques. The book is excitement about learning mathematics is seductive." intended for mathematicians from graduate students -- Michael Munger, Chance " I like this book. It’s up, whether in analysis or not, who are curious which nice mathematics with serious applications." -- non-elliptic partial differential operators have the John Ewing, Indiana University "Now we have, in property that all solutions must be real analytic. Alan Taylor’s book, an introduction to these ideas Enough background is provided to prepare the reader that is delightfully lucid and requires almost no with it for a clear understanding of the text, although mathematical prerequisites." -- Phillip D. Straffin, this is not, and does not need to be, very extensive. College Mathematics Journal "[The book] breaks In fact, it is very nearly true that if the reader is new ground and could stand as the definitive willing to accept the fact that pointwise bounds on the undergraduate textbook in this area for quite some derivatives of a function are equivalent to bounds on time." -- Stan Wagon, Macalester College the $L^2$ norms of its derivatives locally, the book More on www.springer.com/978-0-387-77643-9 should read easily. Usually dispatched within 3 to 5 business days More on www.springer.com/978-1-4419-9812-5 Usually dispatched within 3 to 5 business days 2009. XVI, 364 p. Hardcover 2011. VIII, 203 p. 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world networks, a theme that is becoming pervasive in many disciplines ranging from mathematics and computer science to the social and biological sciences. Optimization of complex networks with real-world applications requires a deep understanding of the interplay between the dynamics of the physical network and the information dynamics within the network. The Handbook of Optimization in Complex Networks: Theory and Applications provides the basic theory of these networks with several new mathematical approaches and optimization techniques to design and analyze dynamic complex O. Teschke, Zentralblatt MATH, Berlin, Germany; B. Wegner, M.T. Thai, University of Florida, Gainesville,FL, USA networks. The volume features a wide range of Technische Universität Berlin, Germany; D. Werner, Freie applications and optimization problems derived Universität Berlin, Germany (Eds.) Group Testing Theory in Network from research areas such as computer science, Security operations research, cellular and molecular chemistry, 80 Years of Zentralblatt MATH brain physiology, epidemiology, and ecology. This 80 Footprints of Distinguished Mathematicians An Advanced Solution volume, as well as its companion (The Handbook of in Zentralblatt Group Testing Theory in Network Security explores Optimization in Complex Networks: Communication a new branch of group testing theory with an and Social Networks ISBN: 978-1-4614-0856-7) is an Founded in 1931 by Otto Neugebauer as the printed application which enhances research results in excellent resource for graduate students, researchers, documentation service "Zentralblatt für Mathematik network security. This brief presents new solutions and practitioners who wish to learn about the most und ihre Grenzgebiete"', Zentralblatt celebrates its on several advanced network security problems and up to date theory and applications on optimization of 80th anniversary in 2011 as the most comprehensive mathematical frameworks based on the group testing complex real-world networks. reference database worldwide, now under the new theory, specifically denial-of-service and jamming name ZBMATH.Several prominent mathematicians More on www.springer.com/978-1-4614-0753-9 attacks. A new application of group testing, illustrated have been involved in this service as reviewers or Usually dispatched within 3 to 5 business days December in this text, requires additional theories, such as size editors. Zentralblatt has covered their work as a part 31, 2011 constraint group testing and connected group testing. of its general documentation activities, dealing with Included in this text is a chapter devoted to discussing 2012. XIV, 544 p. 219 illus., 140 in color. (Springer all mathematicians worldwide. All mathematicians Optimization and Its Applications, Vol. 57) Hardcover open problems and suggesting new solutions for have left their footprints in Zentralblatt, in a long list 978-1-4614-0753-9 various network security problems. This text also of entries describing all of their research publications $179.00 exemplifies the connection between mathematical ▶ in mathematics.This book provides one review approaches and practical applications to group testing from each of the 80 years of Zentralblatt, most often theory in network security. This work will appeal connected with a prominent mathematician related to to a multidisciplinary audience with interests in Zentralblatt as a member of the editorial board or as computer communication networks, optimization, a reviewer. Names like Courant, Kolmogorov, Hardy, and engineering. Hirzebruch, Faltings and many others can be found here. In addition to the original reviews, the book More on www.springer.com/978-1-4614-0127-8 offers the authors' profiles indicating their co-authors, Usually dispatched within 3 to 5 business days their favourite journals and the time span of their 2012. XI, 86 p. 24 illus., 17 in color. (SpringerBriefs in publication activities.In addition to this, a generously Optimization) Softcover illustrated essay by Silke Göbel describes the history of 978-1-4614-0127-8 Zentralblatt. ▶$49.95 More on www.springer.com/978-3-642-21171-3 Usually dispatched within 3 to 5 business days M.T. Thai, University of Florida, Gainesville, FL, USA; P.M. 2011. V, 194 p. 122 illus. Softcover Pardalos, University of Florida, Gainesville, FL, USA (Eds.) 978-3-642-21171-3 ▶$29.95 Handbook of Optimization in Complex Networks Communication and Social Networks This second volume of the "Handbook Optimization in Complex Networks" presents the most recent research and developments in the application of optimization techniques to the study of complex communication and social networks. This book M.T. Thai, University of Florida, Gainesville, FL, USA; P.M. present several optimization models and their Pardalos, University of Florida, Gainesville, FL, USA (Eds.) application to a variety of network settings including: online social networks, wireless communication Handbook of Optimization in networks, as well as models that describe virus and social media propagation. This book can serve as a Complex Networks useful resource to any student or researcher interested Theory and Applications Complex Networks is a newly emerging field with applications in a variety of domains, such as communication networks, engineering networks, social networks, and biological networks. There has been an explosive growth of research on complex real- springer.com 89 in the application of optimization techniques to of mathematics: topological algebra, functional review facts from real analysis and linear algebra. communication and or social networks. analysis, and general topology. Cp-theory has an Hints and solutions are provided to many of the More on www.springer.com/978-1-4614-0856-7 important role in the classification and unification exercises and problems. Requiring only minimal of heterogeneous results from each of these areas undergraduate prerequisites, "An Introduction to Usually dispatched within 3 to 5 business days of research. Through over 500 carefully selected Manifolds" is also an excellent foundation for the 2012. X, 541 p. 191 illus., 126 in color. (Springer problems and exercises, this volume provides a self- author's publication with Raoul Bott, "Differential Optimization and Its Applications, Vol. 58) Hardcover contained introduction to Cp-theory and general Forms in Algebraic Topology." 978-1-4614-0856-7 topology. By systematically introducing each of the More on www.springer.com/978-1-4419-7399-3 ▶$179.00 major topics in Cp-theory, this volume is designed to bring a dedicated reader from basic topological Usually dispatched within 3 to 5 business days principles to the frontiers of modern research. 2011. XVIII, 410 p. 124 illus., 1 in color. (Universitext) Key features include: - A unique problem-based D.A. Timashev, Moscow State University, Russia Softcover introduction to the theory of function spaces. - 978-1-4419-7399-3 Detailed solutions to each of the presented problems Homogeneous Spaces and $59.95 and exercises. - A comprehensive bibliography ▶ Equivariant Embeddings reflecting the state-of-the-art in modern Cp-theory. - Homogeneous spaces of linear algebraic groups Numerous open problems and directions for further lie at the crossroads of algebraic geometry, theory research. This volume can be used as a textbook for of algebraic groups, classical projective and courses in both Cp-theory and general topology as enumerative geometry, harmonic analysis, and well as a reference guide for specialists studying Cp- representation theory. By standard reasons of theory and related topics. This book also provides algebraic geometry, in order to solve various problems numerous topics for PhD specialization as well as a on a homogeneous space, it is natural and helpful large variety of material suitable for graduate research. to compactify it while keeping track of the group More on www.springer.com/978-1-4419-7441-9 action, i.e., to consider equivariant completions Usually dispatched within 3 to 5 business days or, more generally, open embeddings of a given homogeneous space. Such equivariant embeddings 2011. XV, 485 p. (Problem Books in Mathematics) are the subject of this book. We focus on the Hardcover classification of equivariant embeddings in terms 978-1-4419-7441-9 J. Ueberberg, Universität Gießen, Deutschland of certain data of "combinatorial" nature (the Luna- ▶$84.95 Vust theory) and description of various geometric Foundations of Incidence and representation-theoretic properties of these varieties based on these data. The class of spherical Geometry varieties, intensively studied during the last three Projective and Polar Spaces decades, is of special interest in the scope of this book. Spherical varieties include many classical examples, Incidence geometry is a central part of modern such as Grassmannians, flag varieties, and varieties mathematics that has an impressive tradition. The of quadrics, as well as well-known toric varieties. We main topics of incidence geometry are projective have attempted to cover most of the important issues, and affine geometry and, in more recent times, the including the recent substantial progress obtained in theory of buildings and polar spaces.Embedded into and around the theory of spherical varieties. the modern view of diagram geometry, projective and affine geometry including the fundamental More on www.springer.com/978-3-642-18398-0 theorems, polar geometry including the Theorem of Usually dispatched within 3 to 5 business days Buekenhout-Shult and the classification of quadratic 2011. XXI, 253 p. 16 illus. (Encyclopaedia of Mathematical sets are presented in this volume. Incidence geometry Sciences, Vol. 138) Hardcover L.W. Tu, Tufts University, Medford, MA, USA is developed along the lines of the fascinating work 978-3-642-18398-0 of Jacques Tits and Francis Buekenhout.The book ▶$124.00 An Introduction to Manifolds is a clear and comprehensible introduction into a wonderful piece of mathematics. More than 200 Manifolds, the higher-dimensional analogues of figures make even complicated proofs accessible to smooth curves and surfaces, are fundamental objects the reader. in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also More on www.springer.com/978-3-642-20971-0 been applied to classical mechanics, general relativity, Usually dispatched within 3 to 5 business days and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is 2011. XII, 248 p. 277 illus. (Springer Monographs in presented with the aim of helping the reader achieve Mathematics) Hardcover a rapid mastery of the essential topics. By the end of 978-3-642-20971-0 the book the reader should be able to compute, at least ▶$99.00 for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and V.V. Tkachuk, Universidad Autónoma Metropolitana, topology. The second edition contains fifty pages of Iztapalapa, Mexico new material. Many passages have been rewritten, proofs simplified, and new examples and exercises A Cp-Theory Problem Book added. This work may be used as a textbook for a Topological and Function Spaces one-semester graduate or advanced undergraduate The theory of function spaces endowed with the course, as well as by students engaged in self-study. topology of pointwise convergence, or Cp-theory, The requisite point-set topology is included in an exists at the intersection of three important areas appendix of twenty-five pages; other appendices 90 springer.com

physics to computer science. This text is unique in author, whose mathematical education evolved making this engaging subject accessible to advanced out of his interactions with Mackey and Harish- graduate and beginning graduate students and Chandra, concludes this volume with brief portraits focuses on applications of Hopf algebras to algebraic of their work, embedded in the context of personal number theory and Galois module theory, providing reminiscences. a smooth transition from modern algebra to Hopf More on www.springer.com/978-1-4419-0666-3 algebras.After providing an introduction to the spectrum of a ring and the Zariski topology, the text Usually dispatched within 3 to 5 business days treats presheaves, sheaves, and representable group 2011. X, 231 p. Hardcover functors. In this way the student transitions smoothly 978-1-4419-0666-3 from basic algebraic geometry to Hopf algebras. ▶$99.00 The importance of Hopf orders is underscored M. Ullah, University of Rostock, Rostock, Germany; O. with applications to algebraic number theory, Galois Wolkenhauer, University of Rostock, Rostock, Germany module theory and the theory of formal groups. K. Veselić, Fernuniversität Hagen, Hagen, Germany By the end of the book, readers will be familiar Stochastic Approaches for with established results in the field and ready to Damped Oscillations of Linear Systems Biology pose research questions of their own.An exercise set is included in each of twelve chapters with Systems This textbook focuses on stochastic modelling and questions ranging in difficulty. Open problems and A Mathematical Introduction its applications in systems biology. In addition to a research questions are presented in the last chapter. The theory of linear damped oscillations was review of probability theory, the authors introduce Prerequisites include an understanding of the originally developed more than hundred years ago key concepts, including those of stochastic process, material on groups, rings, and fields normally covered and is still of vital research interest to engineers, Markov property, and transition probability, side by in a basic course in modern algebra. side with notions of biochemical reaction networks. mathematicians and physicists alike. This theory More on www.springer.com/978-0-387-72765-3 This leads to an intuitive presentation guided by plays a central role in explaining the stability of a series of biological examples that are revisited Usually dispatched within 3 to 5 business days mechanical structures in civil engineering, but throughout the text. The text shows how the notion it also has applications in other fields such as of propensity, the chemical master equation and the 2011. XIV, 273 p. 3 illus. Hardcover electrical network systems and quantum mechanics. stochastic simulation algorithm arise as consequences 978-0-387-72765-3 This volume gives an introduction to linear finite of the Markov property. The nontrivial relationships ▶$74.95 dimensional damped systems as they are viewed by an between various stochastic approaches are derived applied mathematician. After a short overview of the and illustrated. The text contains many illustrations, physical principles leading to the linear system model, examples and exercises to communicate methods and a largely self-contained mathematical theory for analyses. Matlab code to simulate cellular systems is this model is presented. This includes the geometry also provided where appropriate and the reader is of the underlying indefinite metric space, spectral encouraged to experiment with the examples and case theory of J-symmetric matrices and the associated studies provided. Senior undergraduate and graduate quadratic eigenvalue problem. Particular attention students in applied mathematics, the engineering is paid to the sensitivity issues which influence and physical sciences as well as researchers working numerical computations. Finally, several recent in the areas of systems biology, theoretical and research developments are included, e.g. Lyapunov computational biology will find this text useful. stability and the perturbation of the time evolution. More on www.springer.com/978-1-4614-0477-4 More on www.springer.com/978-3-642-21334-2 Usually dispatched within 3 to 5 business days Usually dispatched within 3 to 5 business days 2011. XV, 200 p. 8 illus. (Lecture Notes in Mathematics, Vol. V.S. Varadarajan, University of California, Los Angeles, CA, 2023) Softcover 2011. XXXII, 290 p. 73 illus. Hardcover USA 978-1-4614-0477-4 978-3-642-21334-2 ▶$74.95 Reflections on Quanta, ▶$49.95 Symmetries, and Supersymmetries Unitary representation theory has great intrinsic beauty which enters other parts of mathematics at a very deep level. In quantum physics it is the preferred language for describing symmetries and supersymmetries. Two of the greatest figures in its history are Mackey and Harish-Chandra. Their work (to use the words of Weyl) affords shade to large parts of present day mathematics and high energy physics. It is to their memory that this volume is lovingly dedicated.Mackey and Harish-Chandra. R.G. Underwood, Department of Mathematics, Auburn Their work (to use the words of Weyl) affords University, Montgomery, AL 36124 USA shade to large parts of present day mathematics and high energy physics. It is to their memory that An Introduction to Hopf Algebras this volume is lovingly dedicated.The essays in this volume are like a stroll through a garden of The study of Hopf algebras spans many fields in ideas of this rich subject: quantum algebras, super mathematics including topology, algebraic geometry, geometry, unitary supersymmetries, differential algebraic number theory, Galois module theory, equations, non-archimedean physics, are a few cohomology of groups, and formal groups and has of the topics encountered along the way. The wide-ranging connections to fields from theoretical springer.com 91

shows how Mathematica can be used to discover new subspace method and Lie group method; and the things. Striking examples include the design of a road practical applications, such as the reconstruction on which a square wheel bike can ride, the design of a problem for inverse scattering, molecular spectra data drill that can drill square holes, an illustration of the processing, quantitative remote sensing inversion, Banach—Tarski Paradox via hyperbolic geometry, seismic inversion using the Lie group method, and the new and surprising formulas for p, the discovery gravitational lensing problem. Scientists, researchers of shadow orbits for chaotic systems, and the use and engineers, as well as graduate students engaged of powerful new capabilities for three-dimensional in applied mathematics, engineering, geophysics, graphics. Visualization is emphasized throughout, medical science, image processing, remote sensing with finely crafted graphics in each chapter.Wagon and atmospheric science will benefit from this book. is the author of eleven books on mathematics, Dr. Yanfei Wang is a Professor at the Institute of including A Course in Computational Number Geology and Geophysics, Chinese Academy of E. Vesentini, Università di Pisa, Italy (Ed.) Theory, named one of the ten best math books of Sciences, China. Dr. Sc. Anatoly G. Yagola is a 2000 by the American Library Association. He has Professor and Assistant Dean of the Physical Faculty, Geometry of Homogeneous written extensively on the educational applications Lomonosov Moscow State University, Russia. Dr. of Mathematica, including the books VisualDSolve: Changchun Yang is a Professor and Vice Director Bounded Domains Visualizing Differential Equations with Mathematica, of the Institute of Geology and Geophysics, Chinese Lectures given at a Summer School of the Centro and Animating Calculus: Mathematica Notebooks for Academy of Sciences, China. Internazionale Matematico Estivo (C.I.M.E.) held the Laboratory.From reviews of the second edition:"In More on www.springer.com/978-3-642-13741-9 in Urbino (Pesaro), Italy, July 3-13, 1967 a dazzling range of examples Stan Wagon shows how such features as animation, 3-dimensional Online orders shipping within 2-3 days S.G. Gindikin, I.I. Pjateckii-Sapiro, E.B. Vinberg: graphics and high-precision integer arithmetic can 2011. 400 p. 36 illus. Hardcover Homogeneous Kähler manifolds.- S.G. Greenfield: contribute to our understanding and enjoyment of 978-3-642-13741-9 Extendibility properties of real submanifolds of mathematics."—Richard Walker, The Mathematical ▶$129.00 Cn.- W. Kaup: Holomorphische Abbildungen in Gazette"The bottom line is that Mathematica in Hyperbolische Räume.- A. Koranyi: Holomorphic Action is an outstanding book containing many and harmonic functions on bounded symmetric examples of real uses of Mathematica for the novice, domains.- J.L. Koszul: Formes harmoniques intermediate, and expert user."—Mark McClure, vectorielles sur les espaces localement symétriques.- S. Mathematica in Education and Research Murakami: Plongements holomorphes de domaines symétriques.- E.M. Stein: The analogues of Fatous’s More on www.springer.com/978-0-387-75366-9 theorem and estimates for maximal functions. Usually dispatched within 3 to 5 business days More on www.springer.com/978-3-642-11059-7 2010. XVIII, 574 p. 531 illus., 216 in color. With online Usually dispatched within 3 to 5 business days files/update. Softcover 2011. 307 p. (C.I.M.E. Summer Schools, Vol. 45) Softcover 978-0-387-75366-9 978-3-642-11059-7 ▶$84.95 ▶$49.95

A.-M. Wazwaz, Saint Xavier University, Chicago, IL, USA Linear and Nonlinear Integral Equations Methods and Applications Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and S. Wagon, Macalester College, St. Paul, MN, USA Y. Wang, Chinese Academy of Sciences, Beijing, China; A.G. complement the existing procedures for solving Mathematica® in Action Yagola, Moscow State University, Russia; C. Yang, Chinese linear integral equations. The Volterra integral and Academy of Sciences, Beijing, China (Eds.) integro-differential equations, the Fredholm integral Problem Solving Through Visualization and and integro-differential equations, the Volterra- Computation Optimization and Regularization Fredholm integral equations, singular and weakly singular integral equations, and systems of these In this third edition of Mathematica® in Action, for Computational Inverse equations, are handled in this part by using many award-winning author Stan Wagon guides beginner different computational schemes. Selected worked- and veteran users alike through Mathematica's Problems and Applications through examples and exercises will guide readers powerful tools for mathematical exploration. The "Optimization and Regularization for Computational through the text. Part II provides an extensive transition to Mathematica 7 is made smooth with Inverse Problems and Applications" focuses on exposition on the nonlinear integral equations and plenty of examples and case studies that utilize advances in inversion theory and recent developments their varied applications, presenting in an accessible Mathematica's newest tools, such as dynamic with practical applications, particularly emphasizing manner a systematic treatment of ill-posed Fredholm manipulations and adaptive three-dimensional the combination of optimization and regularization problems, bifurcation points, and singular points. plotting. Mathematica in Action also emphasizes the for solving inverse problems. This book covers both Selected applications are also investigated by using the breadth of Mathematica and the impressive results the methods, including standard regularization powerful Padé approximants. This book is intended of combining techniques from different areas. This theory, Fejer processes for linear and nonlinear for scholars and researchers in the fields of physics, material enables the reader to use Mathematica to problems, the balancing principle, extrapolated applied mathematics and engineering. It can also solve a variety of complex problems.Case studies regularization, nonstandard regularization, nonlinear be used as a text for advanced undergraduate and ranging from elementary to sophisticated are gradient method, the nonmonotone gradient method, graduate students in applied mathematics, science provided throughout. Whenever possible, the book 92 springer.com and engineering, and related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University in Chicago, Illinois, USA. More on www.springer.com/978-3-642-21448-6 Online orders shipping within 2-3 days 2011. XVIII, 639 p. 4 illus. Hardcover 978-3-642-21448-6 ▶$199.00

C. Woodford, University of Newcastle upon Tyne, UK; C. R. Wilson, Queen Mary University of London, UK Phillips, University of Newcastle upon Tyne, UK The Finite Simple Groups Numerical Methods with Worked The finite simple groups are the building blocks from Examples: Matlab Edition which all the finite groups are made and as such they are objects of fundamental importance throughout This book is for students following an introductory mathematics. The classification of the finite course in numerical methods, numerical techniques simple groups was one of the great mathematical or numerical analysis. It introduces MATLAB as achievements of the twentieth century, yet these a computing environment for experimenting with groups remain difficult to study which hinders numerical methods. It approaches the subject from S.H. Weintraub, Lehigh University, Bethlehem, PA, USA applications of the classification. This textbook brings a pragmatic viewpoint; theory is kept at a minimum the finite simple groups to life by giving concrete commensurate with comprehensive coverage of the Galois Theory constructions of most of them, sufficient to illuminate subject and it contains abundant worked examples their structure and permit real calculations both in the which provide easy understanding through a clear The book discusses classical Galois theory groups themselves and in the underlying geometrical and concise theoretical treatment. This edition places in considerable generality, treating fields of or algebraic structures. This is the first time that all even greater emphasis on ‘learning by doing’ than the characteristic zero and of positive characteristic with the finite simple groups have been treated together in previous edition. Fully documented MATLAB code consideration of both separable and inseparable this way and the book points out their connections, for the numerical methods described in the book will extensions, but with a particular emphasis on for example between exceptional behaviour of generic be available as supplementary material to to the book algebraic extensions of the field of rational numbers. groups and the existence of sporadic groups, and on http://extras.springer.com While most of the book is concerned with finite discusses a number of new approaches to some of More on www.springer.com/978-94-007-1365-9 extensions, it discusses algebraic closure and infinite the groups. Many exercises of varying difficulty Galois extensions, and concludes with a new chapter are provided. The Finite Simple Groups is aimed Usually dispatched within 3 to 5 business days on transcendental extensions. Key topics and features at advanced undergraduate and graduate students of this second edition: - Approaches Galois theory in algebra as well as professional mathematicians 2012. X, 256 p. 32 illus. With online files/update. from the linear algebra point of view, following and scientists who use groups and want to apply Hardcover 978-94-007-1365-9 Artin; - Presents a number of applications of Galois the knowledge which the classification has given us. theory, including symmetric functions, finite fields, The main prerequisite is an undergraduate course in ▶$59.95 cyclotomic fields, algebraic number fields, solvability group theory up to the level of Sylow’s theorems. of equations by radicals, and the impossibility of More on www.springer.com/978-1-84800-987-5 solution of the three geometric problems of Greek antiquity. Review from the first edition: "The text Usually dispatched within 3 to 5 business days offers the standard material of classical field theory and Galois theory, though in a remarkably original, 2009. XV, 298 p. (Graduate Texts in Mathematics, Vol. 251) Hardcover unconventional and comprehensive manner … . the 978-1-84800-987-5 book under review must be seen as a highly welcome $59.95 and valuable complement to existing textbook ▶ literature … . It comes with its own features and Special offer valid until December 31, 2011 ▶$39.50 advantages … it surely is a perfect introduction to this evergreen subject. The numerous explaining remarks, hints, examples and applications are particularly commendable … just as the outstanding clarity and fullness of the text." (Zentralblatt MATH, Vol. 1089 Z. Yosibash, Ben-Gurion University, Beer-Sheva, Israel (15), 2006) Steven H. Weintraub is a Professor of Mathematics at Lehigh University and the author Singularities in Elliptic Boundary of seven books. This book grew out of a graduate Value Problems and Elasticity and course he taught at Lehigh. He is also the author of Algebra: An Approach via Module Theory (with W. Their Connection with Failure A. Adkins). Initiation More on www.springer.com/978-0-387-87574-3 This introductory and self-contained book gathers Usually dispatched within 3 to 5 business days as much explicit mathematical results on the linear-elastic and heat-conduction solutions in the 2009. XIV, 212 p. (Universitext) Softcover neighborhood of singular points in two-dimensional 978-0-387-87574-3 domains, and singular edges and vertices in three- $59.95 ▶ dimensional domains. These are presented in an engineering terminology for practical usage. The author treats the mathematical formulations from an springer.com 93 engineering viewpoint and presents high-order finite- fundamental forces which act in the universe: element methods for the computation of singular gravitative, electromagnetic, weak interaction and solutions in isotropic and anisotropic materials, and strong interaction. Volume III concentrates on the multi-material interfaces. The proper interpretation classical aspects of gauge theory, describing the four of the results in engineering practice is advocated, fundamental forces by the curvature of appropriate so that the computed data can be correlated to fiber bundles. This must be supplemented by the experimental observations. The book is divided into crucial, but elusive quantization procedure. The book fourteen chapters, each containing several sections. is arranged in four sections, devoted to realizing the Most of it (the first nine Chapters) addresses two- universal principle force equals curvature: Part I: The dimensional domains, where only singular points Euclidean Manifold as a ParadigmPart II: Ariadne's exist. The solution in a vicinity of these points admits Thread in Gauge TheoryPart III: Einstein's Theory an asymptotic expansion composed of eigenpairs and of Special RelativityPart IV: Ariadne's Thread in associated generalized flux/stress intensity factors M. Zarghami, University of Tabriz, Iran; F. Szidarovszky, Cohomology For students of mathematics the book (GFIFs/GSIFs), which are being computed analytically University of Arizona, Tucson, USA is designed to demonstrate that detailed knowledge when possible or by finite element methods otherwise. of the physical background helps to reveal interesting Singular points associated with weakly coupled Multicriteria Analysis interrelationships among diverse mathematical topics. thermoelasticity in the vicinity of singularities are Applications to Water and Environment Physics students will be exposed to a fairly advanced also addressed and thermal GSIFs are computed. The Management mathematics, beyond the level covered in the typical computed data is important in engineering practice physics curriculum. Quantum Field Theory builds a Multicriteria analysis is one of the most important for predicting failure initiation in brittle materials bridge between mathematicians and physicists, based fields of decision science. This book gives an outline on a daily basis. Several failure laws for two- on challenging questions about the fundamental of the formulation of an appropriate model and dimensional domains with V-notches are presented forces in the universe (macrocosmos), and in the presents a comprehensive summary of the most and their validity is examined by comparison to world of elementary particles (microcosmos). popular methods for solving multicriteria decision experimental observations. A sufficient simple and problems. In addition to the classical approach the More on www.springer.com/978-3-642-22420-1 reliable condition for predicting failure initiation book introduces fuzzy and stochastic methodology, (crack formation) in micron level electronic devices, Usually dispatched within 3 to 5 business days models with uncertainty, social choice and conflict involving singular points, is still a topic of active 2011. XXXII, 1126 p. 154 illus. Hardcover resolution. All methods are illustrated with easy research and interest, and is addressed herein. Explicit 978-3-642-22420-1 to follow simple examples. At the end of each singular solutions in the vicinity of vertices and ▶$139.00 chapter detailed case studies are given in water and edges in three-dimensional domains are provided environment management including inter-basin in the remaining five chapters. New methods for the water transfer, urban water management, water computation of generalized edge flux/stress intensity allocation, groundwater quality management, forest functions along singular edges are presented and treatment, ranking water resources projects, reservoir demonstrated by several example problems from planning, water distribution network design and long- the field of fracture mechanics; including anisotropic term watershed management. The new methodology domains and bimaterial interfaces. Circular edges and the wide variety of case studies are not easily are also presented and the author concludes with accessible elsewhere. some remarks on open questions.This well illustrated book will appeal to both applied mathematicians and More on www.springer.com/978-3-642-17936-5 engineers working in the field of fracture mechanics Usually dispatched within 3 to 5 business days and singularities. More on www.springer.com/978-1-4614-1507-7 2011. XI, 159 p. 40 illus. Hardcover 978-3-642-17936-5 Usually dispatched within 3 to 5 business days December 31, 2011 ▶$119.00 F. Zhang, Nova Southeastern University, Fort Lauderdale, FL, USA 2012. XXI, 459 p. 203 illus., 13 in color. (Interdisciplinary Applied Mathematics, Vol. 37) Hardcover 978-1-4614-1507-7 Matrix Theory ▶$124.00 Basic Results and Techniques The aim of this book is to concisely present fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. The book contains ten chapters covering various topics ranging from similarity and special types of matrices to Schur complements and matrix normality. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems. Major changes in this revised and expanded second edition: E. Zeidler, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany -Expansion of topics such as matrix functions, nonnegative matrices, and (unitarily invariant) Quantum Field Theory III: Gauge matrix norms-The inclusion of more than 1000 exercises-A new chapter, Chapter 4, with updated Theory material on numerical ranges and radii, matrix norms, A Bridge between Mathematicians and and special operations such as the Kronecker and Physicists Hadamard products and compound matrices-A new chapter, Chapter 10, on matrix inequalities, In this third volume of his modern introduction to which presents a variety of inequalities on the quantum field theory, Eberhard Zeidler examines eigenvalues and singular values of matrices and the mathematical and physical aspects of gauge unitarily invariant norms.This book can be used theory as a principle tool for describing the four as a textbook or a supplement for a linear algebra 94 springer.com and matrix theory class or a seminar for senior M. Zili, Preparatory Institute to the Military Academies as interdisciplinary, industrial and international undergraduate or graduate students. Prerequisites (E.P.A.M.), Sousse, Tunisia; D.V. Filatova, Jan Kochanowski cooperation. This book presents new advances include a decent background in elementary linear University in Kielce, Poland (Eds.) in several areas of mathematics and engineering algebra and calculus. The book can also serve as mathematics including applications in modern a reference for instructors and researchers in the Stochastic Differential Equations technology, engineering and life sciences. Thirteen fields of algebra, matrix analysis, operator theory, and Processes high-quality chapters put forward many new methods statistics, computer science, engineering, operations and results, reviews of up to date research and open SAAP, Tunisia, October 7-9, 2010 research, economics, and other fields.Fuzhen Zhang directions and problems for future research. A is a professor of mathematics at Nova Southeastern Selected papers submitted by participants of the special chapter by Gunnar Sparr and Georg Lindgren University, Fort Lauderdale, Florida. He received international Conference “Stochastic Analysis and contains a historical account and important aspects his Ph.D. in Mathematics from the University of Applied Probability 2010” ( www.saap2010.org ) of engineering mathematicsresearch and education, California at Santa Barbara, M.S. from Beijing make up the basis of this volume.The SAAP 2010 and the implementation of the highly successful Normal University, and B.Sc. from Shenyang Normal was held in Tunisia, from 7-9 October, 2010, education programme in Engineering Mathematics University (China). In addition to research papers, he and was organized by the “Applied Mathematics at Lund Institute of Technology, where not only is the author of the book Linear Algebra: Challenging & Mathematical Physics” research unit of the the mathematical sciences have played a role.This Problems for Students and the editor of The Schur preparatory institute to the military academies of book will serve as a source of inspiration for a broad Complement and Its Applications. Sousse (Tunisia), chaired by Mounir Zili.The papers spectrum of researchers and research students. More on www.springer.com/978-1-4614-1098-0 cover theoretical, numerical and applied aspects More on www.springer.com/978-3-642-20235-3 of stochastic processes and stochastic differential Usually dispatched within 3 to 5 business days Due: January 31, 2012 equations. The study of such topic is motivated in part by the need to model, understand, forecast and 2012. XVI, 345 p. 74 illus., 23 in color. (Springer Proceedings 2011. XVII, 399 p. 8 illus., 1 in color. (Universitext) control the behavior of many natural phenomena that in Mathematics, Vol. 6) Hardcover Softcover 978-3-642-20235-3 978-1-4614-1098-0 evolve in time in a random way. Such phenomena appear in the fields of finance, telecommunications, ▶$149.00 $74.95 ▶ economics, biology, geology, demography, physics, chemistry, signal processing and modern control theory, to mention just a few.As this book emphasizes Forthcoming the importance of numerical and theoretical studies of the stochastic differential equations and stochastic K. Zhu, Department of Mathematics and Statistics, State University of New York at Albany, Albany, NY 12222 USA processes, it will be useful for a wide spectrum of researchers in applied probability, stochastic Analysis on Fock Spaces numerical and theoretical analysis and statistics, as well as for graduate students. To make it more Several natural Lp spaces of analytic functions have complete and accessible for graduate students, been widely studied in the past few decades, including practitioners and researchers, the editors Mounir Zili Hardy spaces, Bergman spaces, and Fock spaces. and Daria Filatova have included a survey dedicated The terms “Hardy spaces” and “Bergman spaces” are to the basic concepts of numerical analysis of the by now standard and well established. But the term stochastic differential equations, written by Henri “Fock spaces” is a different story.Numerous excellent Schurz. E. Çinlar, Operations Research and Financial Engineering, books now exist on the subject of Hardy spaces. Princeton University, Princeton, NJ, USA More on www.springer.com/978-3-642-22367-9 Several books about Bergman spaces, including some of the author’s, have also appeared in the past few Usually dispatched within 3 to 5 business days Probability and Stochastics decades. But there has been no book on the market 2012. XII, 261 p. 2 illus. (Springer Proceedings in This text is an introduction to the modern theory concerning the Fock spaces. The purpose of this book Mathematics, Vol. 7) Hardcover and applications of probability and stochastics. The is to fill that vacuum. There seems to be an honest 978-3-642-22367-9 style and coverage is geared towards the theory need for such a book, especially when many results ▶$124.00 of stochastic processes, but with some attention are by now complete. This book presents important to the applications. In many instances the gist of results and techniques summarized in one place, the problem is introduced in practical, everyday so that new comers, especially graduate students, Forthcoming language and then is made precise in mathematical have a convenient reference to the subject.This book form. The first four chapters are on probability contains proofs that are new and simpler than the K. Åström, Centre for Mathematical Sciences, Lund theory: measure and integration, probability spaces, existing ones in the literature. In particular, the book University, Sweden; L.-E. Persson, Luleå University conditional expectations, and the classical limit avoids the use of the Heisenberg group, the Fourier of Technology, Sweden; S.D. Silvestrov, Centre for theorems. There follows chapters on martingales, transform, and the heat equation. This helps to keep Mathematical Sciences, Lund University, Sweden (Eds.) Poisson random measures, Levy Processes, Brownian the prerequites to a minimum. A standard graduate motion, and Markov Processes.Special attention is course in each of real analysis, complex analysis, and Analysis for Science, Engineering paid to Poisson random measures and their roles functional analysis should be sufficient preparation and Beyond in regulating the excursions of Brownian motion for the reader. The Tribute Workshop in Honour of Gunnar and the jumps of Levy and Markov processes. Each More on www.springer.com/978-1-4419-8800-3 Sparr held in Lund, May 8-9, 2008 chapter has a large number of varied examples and Due: March 12, 2012 exercises. The book is based on the author’s lecture This book project was initiated at The Tribute notes in courses offered over the years at Princeton Workshop in Honour of Gunnar Sparr and the 2012. XX, 230 p. Hardcover University. These courses attracted graduate students follow-up workshop Inequalities, Interpolation, Non- 978-1-4419-8800-3 from engineering, economics, physics, computer commutative Analysis, Non-commutative Geometry approx. $59.95 sciences, and mathematics. Erhan Çinlar has received ▶ and Applications, held at the Centre for Mathematical many awards for excellence in teaching, including Sciences, Lund University in May and November of the President’s Award for Distinguished Teaching at 2008. The resulting book is dedicated in celebration Princeton University. His research interests include of Gunnar Sparr's sixty-fifth anniversary and more theories of Markov processes, point processes, than forty years of exceptional service to mathematics stochastic calculus, and stochastic flows. The book is and its applications in engineering and technology, full of insights and observations that only a lifetime mathematics and engineering education, as well springer.com 95 researcher in probability can have, all told in a lucid yet precise style. More on www.springer.com/978-0-387-87858-4 Usually dispatched within 3 to 5 business days

2011. XIII, 557 p. (Graduate Texts in Mathematics, Vol. 261) Hardcover 978-0-387-87858-4 ▶$74.95

Dude, Can You Count? Stories, Challenges and Adventures in Mathematics Imagine algebra class meets The Hitchhiker’s Guide to the Galaxy… Meet JJ, an unusual character with a unique vantage position from which he can measure and monitor humanity’s progress. Armed with a device that compels all around it to tell the truth, JJ offers a satirical evaluation of our attitudes to numeracy and logic, touching upon several aspects B. Øksendal, University of Oslo, Norway of life on Earth along the way, from the criminal justice system and people’s use of language to Stochastic Differential Equations highway driving and modern art. A collection of An Introduction with Applications mathematically-flavored stories and jokes, interlaced This book gives an introduction to the basic theory with puzzles, paradoxes and problems, fuse together of stochastic calculus and its applications. Examples in an entertaining, free-flowing narrative that will are given throughout the text, in order to motivate engage and amuse anyone with an interest in the and illustrate the theory and show its importance issues confronting society today. JJ demonstrates how for many applications in e.g. economics, biology a lack of elementary mathematical knowledge can and physics. The basic idea of the presentation is to taint our work and general thinking and reflects upon start from some basic results (without proofs) of the the importance of what is arguably our most valuable easier cases and develop the theory from there, and weapon against ignorance: a sound mathematical to concentrate on the proofs of the easier case (which education. What is JJ’s prognosis for our future? nevertheless are often sufficiently general for many There’s only one way to find out... "Numbers, purposes) in order to be able to reach quickly the logic, human behavior and aliens: this unique parts of the theory which is most important for the book blends them all into a captivating narrative applications. For the 6th edition the author has added of serious talk and satire, where wit and scholarly further exercises and, for the first time, solutions details are counterpointed by instructive puzzles and to many of the exercises are provided. Apart from mathematical fun. A ‘must read’ for anybody who several minor corrections and improvements, based appreciates humor and culture." Stanislav Potapenko, on useful comments from readers and experts, the Department of Civil and Environmental Engineering, most important change in the corrected 5th printing University of Waterloo, Canada "... a real delight. of the 6th edition is in Theorem 10.1.9, where the Constanda has managed to intertwine stories, puzzles, proof of part b has been corrected and rewritten. logic and some very rich mathematics concepts The corrected 5th printing of the 6th edition is into a very readable, enjoyable novel... I believe this forthcoming and expected in September 2010. book should be in the personal library of every high school mathematics teacher." Tom Becvar, St Louis More on www.springer.com/978-3-540-04758-2 University High School, USA "…a highly readable, Usually dispatched within 3 to 5 business days unique and fascinating combination of humor, mathematics and social commentary that is factual, 2003. XXX, 374 p. 15 illus. (Universitext) Softcover educational and, more importantly, understandable. 978-3-540-04758-2 Given what is taking place in today’s society, J.J. ▶$49.95 Moon brings mathematics back to earth! I’ll never go through the car buying process again without thinking about SCAM 16!" Jerry Hoopert, VP / Chief Administrative Officer, Tulsa Teachers Credit Union, USA More on www.springer.com/978-1-84882-538-3 Online orders shipping within 2-3 days 2010. XIX, 294 p. 25 illus. Dustjacket 978-1-84882-538-3 ▶$27.50 Order Now! Springer Customized Catalog

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copies ISBN $

copies ISBN $

copies ISBN $

copies ISBN $

copies ISBN $

copies ISBN $

copies ISBN $

copies ISBN $

copies ISBN $

copies ISBN $

copies ISBN $

copies ISBN $

copies ISBN $

Methods of Payment Check/Money Order enclosed AmEx MasterCard VISA

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CA, MA, NJ, NY, and PA residents, please add sales tax. Canadian residents, please add 5% GST. Subtotal: Please add $5.00 for shipping one book and $1.00 for each additional book. Outside the US and Canada add $10.00 for first book, $5.00 for each additional book. All orders are processed upon receipt. Sales Tax: If an order cannot be fulfilled within 90 days, payment will be refunded upon request. Prices are payable in US currency or its equivalent. Remember, your 30-day return privilege is always guaranteed. Shipping: Pre-publication pricing: Unless otherwise stated, pre-pub prices are valid through the end of the third month following publication, and therefore are subject to change. TOTAL:

Easy Ways to Order (for the Americas) 7 Write: Springer Order Department, PO Box 2485, Secaucus, NJ 07096-2485, USA 7 Web: springer.com 7 Call: (toll free) 1-800-SPRINGER (8:30 am – 5:30 pm ET) 7 Fax: 1-201-348-4505 7 Email: [email protected] or (for outside the Americas) 7 Write: Springer Customer Service Center GmbH, Haberstrasse 7, 69126 Heidelberg, Germany 7 Call: +49 (0) 6221-345-4301 7 Fax : +49 (0) 6221-345-4229 7 Email: [email protected] 7 Prices are subject to change without notice. All prices are net prices.