Algebra Springer.Com Algebra

Algebra springer.com Algebra

Quadratic Diophantine Equations

T. Andreescu, University of Texas at Dallas; D. Andrica, quadratic fields. It also discusses Pell’s equation and University Cluj-Napoca, Romania its generalizations, and presents some important quadratic diophantine equations and applications. This text treats the classical theory of quadratic The inclusion of examples makes this book useful diophantine equations and guides the reader for both research and classroom settings. through the last two decades of computational techniques and progress in the area. The presen- 2008. Approx. 250 p. 20 illus. (Springer Monographs in tation features two basic methods to investigate Mathematics) Softcover and motivate the study of quadratic diophantine ISBN 978-0-387-35156-8 equations: the theories of continued fractions and

Linear Algebra Done Right

S. Axler, San Francisco State University, CA, USA 7 A didactic masterpiece. 7 Zentralblatt MATH

From the reviews 7 The most original linear algebra 2nd ed. 1997. Corr. 7th printing 2004. XV, 251 p. (Under- book to appear in years, it certainly belongs in every graduate Texts in Mathematics) Softcover undergraduate library. 7 CHOICE ISBN 978-0-387-98258-8

The Riemann Hypothesis A Resource for the Afficionado and Virtuoso The appendices include a selection of original Alike papers. This collection is not very large and encom- P. Borwein, S. Choi, B. Rooney, Simon Fraser University, passes only the most important milestones in the Burnaby, BC, Canada; A. Weirathmueller, University of evolution of theory connected to the Riemann Western Ontario, London, ON, Canada Hypothesis. The appendices also include some authoritative expository papers. These are the This book presents the Riemann Hypothesis, “expert witnesses” whose insight into this field is connected problems, and a taste of the body of both invaluable and irreplaceable. theory developed towards its solution. It is targeted at the educated non-expert. Almost all the material 2007. Approx. 510 p. (CMS Books in Mathematics) is accessible to any senior mathematics student, and Hardcover much is accessible to anyone with some university ISBN 978-0-387-72125-5 mathematics.

Binary Quadratic Forms An Algorithmic Approach theory of quadratic forms, geometry of numbers J. Buchmann, U. Vollmer, Technical University, Darm- and algebraic number theory. The book explains stadt, Germany applications to cryptography and requires only basic mathematical knowledge. The author is a world The book deals with algorithmic problems related leader in number theory. to binary quadratic forms. It uniquely focuses on the algorithmic aspects of the theory. The book 2007. XIV, 318 p. 17 illus. (Algorithms and Computation introduces the reader to important areas of number in Mathematics, Volume 20) Hardcover theory such as diophantine equations, reduction ISBN 978-3-540-46367-2 springer.com Algebra

The Local Langlands Conjecture for GL(2)

C. J. Bushnell, King’s College, London, UK; G. Henniart, related fields. It presupposes no special knowledge Université de Paris Sud, Orsay, France beyond the beginnings of the representation theory of finite groups and the structure theory of local This book contributes an unprecedented text to the fields. so-called “Langlands theory”. It is an ambitious research program of already 40 2006. XI, 351 p. (Grundlehren der mathematischen years and gives a complete and self-contained proof Wissenschaften, Volume 335) Hardcover of the Langlands conjecture in the case n=2. It is ISBN 978-3-540-31486-8 aimed at graduate students and at researchers in

Number Theory Volume I: Tools and Diophantine Equations The book contains more than 350 exercises and the H. Cohen, University of Bordeaux, France text is largely self-contained. Much more sophisticated techniques have been brought to bear on The central theme of this book is the solution of the subject of Diophantine equations, and for this Diophantine equations, i.e., equations or systems reason, the author has included five appendices on of polynomial equations which must be solved in these techniques. integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is 2007. XII, 550 p. (Graduate Texts in Mathematics, the central motivation for the modern theory of Volume 239) Hardcover arithmetic algebraic geometry. In this text, this is ISBN 978-0-387-49922-2 considered through three of its most basic aspects. Algebra springer.com

Number Theory

Volume II: Analytic and Modern Tools theory of arithmetic algebraic geometry. In this text, H. Cohen, University of Bordeaux, France this is considered through three of its most basic aspects. The local aspect, global aspect, and the third This book deals with several aspects of what is now aspect is the theory of zeta and L-functions. This last called “explicit number theory.” The central theme aspect can be considered as a unifying theme for the is the solution of Diophantine equations, i.e., equa- whole subject. tions or systems of polynomial equations which must be solved in integers, rational numbers or 2007. XII, 500 p. (Graduate Texts in Mathematics, more generally in algebraic numbers. This theme, in Volume 240) Hardcover particular, is the central motivation for the modern ISBN 978-0-387-49893-5

The Book of Numbers

J. H. Conway, Princeton University, Princeton, NJ, USA; everything from language to flowers to the imagina- R. Guy, University of Calgary, ON, Canada tion. 7 Science News 7 … The great feature of the book is that anyone can From the reviews 7 This is a really fascinating book read it without excessive head scratching … You’ll either to read or to browse in, or for reference - there find plenty here to keep you occupied, amused, and is a good index, and I can strongly recommend it - it informed. Buy, dip in, wallow. 7 New Scientist should be in every school and college library! 7 The Mathematical Gazette 1st ed. 1996. Corr. 2nd printing 1998. IX, 310 pp. 7 … A delightful look at numbers and their roles in 270 illus., 48 in color. Hardcover ISBN 978-0-387-97993-9

Introduction to Lie Algebras

K. Erdmann, M. J. Wildon, University of Oxford, UK cises are provided to test understanding, along with more demanding problems, several of which have Lie groups and Lie algebras have become essential to solutions. many parts of mathematics and theoretical physics, Introduction to Lie Algebras covers the core with Lie algebras a central object of interest in their material required for almost all other work in Lie own right. theory and provides a self-study guide suitable This book provides an elementary introduction for undergraduate students in their final year and to Lie algebras based on a lecture course given to graduate students and researchers in mathematics fourth-year undergraduates. The only prerequisite and theoretical physics. is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is 2006. X, 251 p. 36 illus. (Springer Undergraduate kept as simple as possible with no attempt at full Mathematics Series) Softcover generality. Numerous worked examples and exer- ISBN 978-1-84628-040-5

Educational Algebra A Theoretical and Empirical Approach treatments. The book gives priority to “meaning in E. Filloy, T. Rojano, Centre for Research and Advanced use” over “formal meaning”. These approaches and Studies, Mexico City, Mexico; L. Puig, University of others of similar nature lead to a focus on compe- Valencia, Spain tence rather than a user’s activity with mathematical language. This book takes a theoretical perspective on the study of school algebra, in which both semiotics and 2007. Approx. 220 p. (Mathematics Education Library, history occur. The Methodological design allows for Volume 43) Hardcover the interpretation of specific phenomena and the ISBN 978-0-387-71253-6 inclusion of evidence not addressed in more general springer.com Algebra

Abstract Algebra

P. A. Grillet, Tulane University, New Orleans, LA, USA a remarkably detailed and strategically skillful elabo- ration of the more sophisticated, abstract theories. From the reviews 7 The text is geared to the needs 7 Zentralblatt of the beginning graduate student, covering with complete, well-written proofs the usual major For the new edition, the author has completely branches of groups, rings, fields, and modules...[n]one rewritten the text, reorganized many of the sections, of the material one expects in a book like this is and even cut or shortened material which is no missing, and the level of detail is appropriate for its longer essential. He has added a chapter on Ext and intended audience. 7 MathSciNet Tor, as well as a bit of topology. 7 This text promotes the conceptual understanding of algebra as a whole, and that with great meth- 2nd ed. 2007. Approx. 678 p. (Graduate Texts in odological mastery. Although the presentation is Mathematics, Volume 242) Hardcover predominantly abstract...it nevertheless features a ISBN 978-0-387-71567-4 careful selection of important examples, together with

Lie Groups, Lie Algebras, and Representations

An Elementary Introduction be genuinely unique in both the organization of the B. Hall, University of Notre Dame, IN, USA material and the care in which it is presented. This is an important addition to the textbook literature … It From the reviews 7 This is an excellent book. It is highly recommended. 7 The Mathematical Gazette deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group 1st ed. 2003. Corr. 2nd printing 2004. XIV, 351 p. 31 illus. theory … . It is clearly written … A reader of this (Graduate Texts in Mathematics, Volume 222) Hardcover book will be rewarded with an excellent under- ISBN 978-0-387-40122-5 standing of Lie groups … . Hall’s book appears to

Algebras, Rings and Modules Volume 2 This updated and revised edition of Algebras, Rings M. Hazewinkel, CWI, Amsterdam, The Netherlands; and Modules provides the classical aspects of the N. Gubareni, Technical University of Czestochowa, Poland; theory of groups and their representations, as well V. Kirichenko, Kiev Taras Shevchenko University, Ukraine as a general introduction to the modern theory of representations including the representations of From the reviews of the first volume 7 This is the quivers and finite partially ordered sets and their first of two volumes which aim to take the theory of applications to finite dimensional algebras. The associative rings and their modules from fundamental revised Second Edition reviews the most important definitions to the research frontier. The book is written recent developments in the theory of special ring at a level intended to be accessible to students who classes including Frobenius, quasi-Frobenius and have taken standard basic undergraduate courses others. in linear algebra and abstract algebra. … has been written with considerable attention to accuracy, and 2007. Approx. 350 p. (Mathematics and Its Applications, has been proofread with care. … A very welcome Volume 586) Hardcover feature is the substantial set of bibliographic and ISBN 978-1-4020-5140-1 historical notes at the end of each chapter.” 7 Math- ematical Reviews

Elementary Number Theory

G. A. Jones, J. M. Jones, University of Southampton, UK 7 This book would make an excellent text for an undergraduate course on number theory. From the reviews 7 A welcome addition . . . a care- 7 Mathematical Reviews fully and well-written book. 7 The Mathematical Gazette 1st ed. 1998. Corr. 2nd printing 1998. XIV, 301 pp. (Springer Undergraduate Mathematics Series) Softcover ISBN 978-3-540-76197-6 Algebra springer.com

The Heat Kernel and Theta Inversion on SL2(C)

J. Jorgenson, City College of New York, NY, USA; S. Lang through periodization, and further expanded in an eigenfunction expansion. A theta inversion formula The purpose of the text is to provide a complete, is obtained by studying the trace of the heat kernel. self-contained development of the trace formula Following the author’s previous work, the inversion and theta inversion formula for SL(2,Z[i])\SL(2,C). formula then leads to zeta functions through the Unlike other treatments of the theory, the approach Gauss transform. taken here is to begin with the heat kernel on SL(2,C) associated to the invariant Laplacian, which 2007. Approx. 410 p. (Springer Monographs in is derived using spherical inversion. The heat kernel Mathematics) Hardcover on the quotient space SL(2,Z[i])\SL(2,C) is gotten ISBN 978-0-387-38031-5

Algebra

S. Lang, Yale University, New Haven, CT, USA both to the comprehensiveness of its coverage and its ability to be authoritative and lively at the same time. From the reviews 7 Lang’s Algebra changed the way … a revolutionary work, changing the way in which graduate algebra is taught, retaining classical topics graduate algebra was taught. … the author describes but introducing language and ways of thinking from the book as ‘very stable’, indicating that there is little category theory and homological algebra. It has that he has wished to change. This confidence is affected all subsequent graduate-level algebra books. reflected in the wider mathematical community, and 7 Notices of the Ams ... this new printing deserves a place in every univer- 7 The author has an impressive knack for presenting sity departmental library. 7 The Mathematical Gazette the important and interesting ideas of algebra in just the ‘right’ way, and he never gets bogged down in the 3rd rev. ed. 2002. Corr. 4th printing 2004. XV, 914 p. dry formalism which pervades some parts of algebra. (Graduate Texts in Mathematics, Volume 211) Hardcover 7 Mathematical Reviews ISBN 978-0-387-95385-4 7 Lang’s Algebra … has gained an iconic status, due

Additive Number Theory Density Theorems and the Growth of Sumsets Additive Number Theory: Density Theorems M. B. Nathanson, City University of New York, NY, USA and the Growth of Sumsets presents material that deals with the above problem. Ideas and techniques A central problem in additive number theory is from many parts of mathematics are used to prove the growth of sumsets. If A is a finite or infinite theorems in this subject. For example, the authors subset of the integers and the lattice points, or more use number theory, combinatorics, commutative generally, of any abelian group or semigroup G, algebra, ultrafilters and logic, and nonstandard then the h-fold sumset of A is the set LA consisting analysis. The book is self-contained, and includes of all elements of G that can be represented as the short introductions to the various techniques that sum of L not necessarily distinct elements of A. are not standard in this field. The goal is to understand the asymptotics of the Graduate students and researchers in mathematics sumsets LA , that is, the size and structure of LA, will find this book useful. Prerequisites include as L tends to infinity. IfA is finite, then the size of undergraduate elementary number theory and LA is its cardinality. If A is infinite, then the size of algebra. LA is measured by various duality functions. These problems have natural analogues when A is a subset 2007. Approx. 400 p. 40 illus (Graduate Texts in of a nonabelian group. Mathematics) Hardcover ISBN 978-0-387-70998-7 springer.com Algebra

Cohomology of Number Fields

J. Neukirch, A. Schmidt, K. Wingberg, University of Heidelberg, Germany Poitou-Tate duality, Hasse principles, theorem of Grunwald-Wang, Leopoldt’s conjecture, Riemann’s The present second edition is a corrected and existence theorem, the theorems of Iwasawa and extended version of the first. It is a textbook for of Šafarevic on solvable groups as Galois groups, students, as well as a reference book for the working Iwasawa theory, and anabelian principles. New mathematician, on cohomological topics in number material is introduced here on duality theorems for theory. The first part provides algebraic background: unramified and tamely ramified extensions, a careful cohomology of profinite groups, duality groups, free analysis of 2-extensions of real number fields and a products, and homotopy theory of modules, with complete proof of Neukirch’s theorem on solvable new sections on spectral sequences and on Tate Galois groups with given local conditions. cohomology of profinite groups. The second part deals with Galois groups of local and global fields: 2nd ed. 2008. Approx. 700 p. (Grundlehren der mathe Tate duality, structure of absolute Galois groups of matischen Wissenschaften, Volume 323) Hardcover local fields, extensions with restricted ramification, ISBN 978-3-540-37888-4

Lie Groups An Approach through Invariants and binary forms with fields ranging from pure algebra Representations to functional analysis.By covering sufficient back- C. Procesi, Università di Roma “La Sapienza”, Italy ground material, the book is made accessible to a reader with a relatively modest mathematical back- In Lie Groups: An Approach through Invariants and ground. Historical information, examples, exercises Representations, the author’s masterful approach are all woven into the text. This unique exposition gives the reader a comprehensive treatment of the is suitable for a broad audience, including advanced classical Lie groups along with an extensive intro- undergraduates, graduates, mathematicians in a duction to a wide range of topics associated with Lie variety of areas from pure algebra to functional groups: symmetric functions, theory of algebraic analysis and mathematical physics. forms, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic groups, group 2007. XXIII, 596 p. (Universitext) Softcover representations, invariants, Hilbert theory, and ISBN 978-0-387-26040-2

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Deformations of Algebraic Schemes

E. Sernesi, Università Roma Tre, Rome, Italy the algebraic results needed are proved. The style of exposition is kept at a level amenable to graduate This account of deformation theory in classical students with an average background in algebraic algebraic geometry over an algebraically closed geometry. field presents for the first time some results previ- ously scattered in the literature, with proofs that 2006. XI, 339 p. (Grundlehren der mathematischen are relatively little known, yet relevant to algebraic Wissenschaften, Volume 334) Hardcover geometers. Many examples are provided. Most of ISBN 978-3-540-30608-5 Analysis springer.com

Applied Linear Algebra and Matrix Analysis

T. S. Shores, University of Nebraska, Lincoln, NE, USA contains a rigorous and self-contained development of most of the traditional topics in a linear algebra This text is intended for a one or two semester course. It provides background for numerous proj- sophomore level course in linear algebra. It is ects, which frequently require computational tools, designed to provide a balance of applications, theory but is not tied to any one computational platform. and computation, and to emphasize their interde- pendence. The text has a strong orientation towards 2007. XII, 388 p. 27 illus. (Undergraduate Texts in numerical computation and the linear algebra Mathematics) Softcover needed in applied mathematics. At the same time, it ISBN 978-0-387-33195-9

Analysis

Understanding Analysis

S. Abbott, Middlebury College, Middlebury, VT, USA introductory analysis course; take a look at it next time you’re preparing that class. From the reviews 7 This is a dangerous book. 7 The Mathematical Association of America Understanding Analysis is so well-written and the 7 ... This book lives up to its title by helping the development of the theory so well-motivated that readers to develop an understanding of analysis. I exposing students to it could well lead them to expect wish I could say I wrote it! 7 The Mathematical Gazette such excellence in all their textbooks. ... Under- standing Analysis is perfectly titled; if your students 1st ed. 2001. Corr. 2nd printing 2002. XII, 257 p. 32 illus. read it that’s what’s going to happen. This terrific book (Undergraduate Texts in Mathematics) Hardcover will become the text of choice for the single-variable ISBN 978-0-387-95060-0

Topics in Banach Space Theory

F. Albiac, N. J. Kalton, University of Missouri, Columbia, proofs, while being reader friendly. … the book is MO, USA essentially self-contained. It is also written in a lively manner, and its involved mathematical proofs are The geometry of Banach spaces is a rich, beautiful, elucidated and illustrated … . I strongly recommend and rewarding subject. In this book the authors to every graduate student … . 7 Mathematical Reviews emphasize the isomorphic theory of Banach spaces 7 I think that any mathematician who is interested and techniques using the unifying viewpoint of in geometry of Banach spaces should … look over this basic sequences. The book is suitable for a semester- book. Undoubtedly, the book will be a useful addition long graduate course and it will become a standard to any mathematical library. 7 Zentralblatt MATH reference and textbook in the area. 2006. XI, 373 p. (Graduate Texts in Mathematics, From the reviews: 7 The authors of the book under Volume 233) Hardcover review succeeded admirably in creating a very helpful ISBN 978-0-387-28141-4 text, which contains essential topics with optimal

Direct Methods in the Calculus of Variations

B. Dacorogna graduate students. The book has been updated with some new material and examples added. Applica- This book is developed for the study of vectorial tions are included. problems in the calculus of variations. The subject is a very active one and almost half of the book 2nd ed. 2007. Approx. 600 p. (Applied Mathematical consists of new material. This is a new edition of the Sciences, Volume 78) Hardcover earlier book published in 1989 and it is suitable for ISBN 978-0-387-35779-9 springer.com Analysis

Shape Analysis and Structuring

L. d. Floriani, M. Spagnuolo, Università Genova, Italy environmental monitoring, or cultural heritage. This (Eds.) book covers a variety of topics related to preserving and enhancing shape information at a geometric Several techniques have been developed in the level, and to effectively capturing the structure of a literature for processing different aspects of the shape by identifying relevant shape components and geometry of shapes, for representing and manipu- their mutual relationships. lating a shape at different levels of detail, and for describing a shape at a structural level as a concise, 2007. Approx. 330 p. (Mathematics and Visualization) part-based, or iconic model. Such techniques are Hardcover used in many different contexts, such as industrial ISBN 978-3-540-33264-0 design, biomedical applications, entertainment,

Modern Methods in the Calculus of Variations Lp Spaces ments in the calculus of variations. It is divided into I. Fonseca, G. Leoni, Carnegie Mellon University, two parts: Part I is devoted to Calculus of Variations Pittsburgh, PA, USA in a Sobolev setting, and Part 2 addresses variational methods in function spaces allowing for disconti- This book presents in a unified way both clas- nuities of the underlying potentials, e.g. the space of sical and contemporary results in the Calculus of functions of bounded variation. Variations. It offers a comprehensive analysis of necessary and sufficient conditions for sequential 2007. Approx. 385 p. (Springer Monographs in lower semicontinuity of functionals on Lp spaces, Mathematics) Hardcover followed by relaxation techniques. The book brings ISBN 978-0-387-35784-3 together in one place the contemporary develop-

Introduction to Calculus and Classical Analysis

O. Hijab, Temple University, Philadelphia, PA, USA 7 complete avoidance of complex numbers 7 heavy emphasis on computational problems 7 applications Intended for an honors calculus course or for an from many parts of analysis, e.g. convex conjugates, introduction to analysis, this is an ideal text for Cantor set, continued fractions, Bessel functions, undergraduate majors since it covers rigorous the zeta functions, and many more 7 344 problems analysis, computational dexterity, and a breadth of with solutions in the back of the book. applications. The book contains many remarkable features: 7 complete avoidance of /epsilon-/delta 2nd ed. 2007. Approx. 332 p. 65 illus. (Undergraduate arguments by using sequences instead 7 defini- Texts in Mathematics) Softcover tion of the integral as the area under the graph, ISBN 978-0-387-69315-6 while area is defined for every subset of the plane Analysis springer.com

Numerical Solution of Time-Dependent Advection-Diffusion- Reaction Equations W. Hundsdorfer, J. G. Verwer, Center for Mathematics & the present authors’ choice of problems to be one of the Computer Science (CWI), Amsterdam, The Netherlands highlights of the book. 7 SIAM Review 7 Highly recommended... 7 Mathematical Reviews From the reviews 7 Let me say at the outset that I highly recommend this book to practitioners … end- 1st ed. 2003. Corr. 2nd printing 2007. X, 471 p. (Springer users, and those new to the field. One of its strengths Series in Computational Mathematics, Volume 33) is its in-depth presentation of temporal and spatial Hardcover discretizations and their interaction … . With each ISBN 978-3-540-03440-7 topic, key theoretical results are presented. … I found

Analysis and Probability Wavelets, Signals, Fractals tools from engineering (especially signal/image P. E. Jorgensen, The University of Iowa, Iowa City, IA, USA processing) and mathematics (harmonic analysis Drawings by: B. Treadway and operator theory). The book features an interdisciplinary focus addressed to a diverse audience of From the reviews 7 I find that the best texts … are students and workers in a variety of fields, meeting those drawn from lectures delivered to varied audi- at the crossroads where they merge and applying ences over time. This is such a book … . it also goes a hands-on approach with generous motivation further than many to clear a pathway to success for and new pedagogical techniques. The presentation the diligent reader. … discusses the content of the includes numerous exercises that are essential to recommended works and their specific topical relation reinforce fundamental concepts and hone computa- to each chapter in concluding sections entitled ‘Refer- tional skills. Graduate students, researchers, applied ences and remarks’. The additional remarks make all mathematicians, engineers and physicists alike will the difference. That form of presentation is why this benefit from this unique work in book form that fills text has excellent motivation throughout … 7 MathDL a gap in the literature.

This text, combining analysis and tools from 2006. XLVII, 276 p. 58 illus. (Graduate Texts in mathematical probability, focuses on a systematic Mathematics, Volume 234) Hardcover and novel exposition of a recent trend in pure and ISBN 978-0-387-29519-0 applied mathematics. The book brings together

Partial Differential Equations

J. Jost, Max-Planck-Institut für Mathematik in den Natur- This book offers an ideal introduction to the theory wissenschaften, Leipzig, Germany of partial differential equations. It focuses on elliptic equations and systematically develops the relevant From the reviews 7 Because of the nice global presen- existence schemes, always with a view towards tation, I recommend this book to students and young nonlinear problems. It also develops the main researchers who need the now classical properties methods for obtaining estimates for solutions of of these second-order partial differential equations. elliptic equations: Sobolev space theory, weak and Teachers will also find in this textbook the basis of an strong solutions, Schauder estimates, and Moser introductory course on second-order partial differen- iteration. It also explores connections between tial equations. 7 Mathematical Reviews elliptic, parabolic, and hyperbolic equations as well 7 Beautifully written and superbly well-organised, as the connection with Brownian motion and semi- I strongly recommend this book to anyone seeking a groups. This second edition features a new chapter stylish, balanced, up-to-date survey of this central on reaction-diffusion equations and systems. area of mathematics. 7 The Mathematical Gazette 2nd ed. 2007. XIV, 356 p. 10 illus. (Graduate Texts in Mathematics, Volume 214) Hardcover ISBN 978-0-387-49318-3 springer.com 10 Analysis

Dynamical Entropy in Operator Algebras

S. Neshveyev, E. Størmer, University of Oslo, Norway give precise definitions of the notions and in most cases complete proofs of the results which are used. The book addresses mathematicians and physicists, including graduate students, who are interested in 2006. IX, 296 p. (Ergebnisse der Mathematik und ihrer quantum dynamical systems and applications of Grenzgebiete. 3. Folge / A Series of Modern Surveys in operator algebras and ergodic theory. It is the only Mathematics, Volume 50) Hardcover monograph on this topic. Although the authors ISBN 978-3-540-34670-8 assume a basic knowledge of operator algebras, they

An Introduction to Echo Analysis

Scattering Theory and Wave Propagation Both potential and target scattering phenomena are investigated and extensions of the theory to G. F. Roach, Strathclyde University, UK the electromagnetic and elastic fields are provided. Throughout, the emphasis is on concepts and results Aimed at graduate and postgraduate students and rather than on the fine detail of proof. A bibliog- researchers in mathematics and the applied sciences, raphy at the end of each chapter points the inter- this book provides an introductory account of scat- ested reader to more detailed proofs of the theorems tering phenomena and a guide to the technical require- and suggests directions for further reading. ments for investigating wave scattering problems. It gathers together the principal mathematical topics 2007. Approx. 305 p. (Springer Monographs in which are required when dealing with wave propaga- Mathematics) Hardcover tion and scattering problems, and indicates how to use ISBN 978-1-84628-851-7 the material to develop the required solutions.

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Elementary Analysis The Theory of Calculus examples and exercises, which illuminate and extend K. A. Ross, University of Oregon, Eugene, OR, USA the material. The author has tried to write in an informal but precise style, stressing motivation and From the reviews 7 This book is intended for the methods of proof, and, in this reviewer’s opinion, has student who has a good, but naïve, understanding succeeded admirably. 7 Mathematical Reviews of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in 1st ed. 1980. Corr. 14th printing 2003. X, 351 p. 34 illus. analysis, such as continuity, convergence of sequences (Undergraduate Texts in Mathematics) Hardcover and series of numbers, and convergence of sequences ISBN 978-0-387-90459-7 and series of functions. There are many nontrivial Analysis 11 springer.com

Nonsmooth Analysis

W. Schirotzek, Technical University, Dresden, Germany lower semicontinuous functions. All basic tools are presented where they are needed: this concerns This book treats various concepts of generalized separation theorems, variational and extremal derivatives and subdifferentials in normed spaces, principles as well as relevant parts of multifunction their geometric counterparts and their application theory. Each chapter ends with bibliographic notes to optimization problems. It starts with the subdif- and exercises. ferential of convex analysis, passes to corresponding concepts for locally Lipschitz continuous func- 2007. Approx. 400 p. (Universitext) Softcover tions and then presents subdifferentials for general ISBN 978-3-540-71332-6

The Arithmetic of Dynamical Systems

J. Silverman, Brown University, Providence, RI, USA is that many of the fundamental problems in the theory of Diophantine equations have dynamical This book provides an introduction to the relatively analogs.This graduate-level text provides an entry new discipline of arithmetic dynamics. Whereas for students into an active field of research and classical discrete dynamics is the study of iteration serves as a standard reference for researchers. of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic 2007. Approx. 520 p. (Graduate Texts in Mathematics, properties of rational and algebraic points under Volume 241) Hardcover repeated application of a polynomial or rational ISBN 978-0-387-69903-5 function. A principal theme of arithmetic dynamics

An Introduction to Navier-Stokes Equation and Oceanography

L. Tartar, Carnegie Mellon University, Pittsburgh, PA, USA mentioned in the text, the purpose being to show that the creation of scientific knowledge is an inter- Introduction to Navier-Stokes Equation and national enterprise, and who contributed to it, from Oceanography corresponds to a graduate course in where, and when. mathematics, taught at Carnegie Mellon University in the spring of 1999. Comments were added to 2006. XXVII, 245 p. (Lecture Notes of the Unione the lecture notes distributed to the students, as well Matematica Italiana, Volume 1) Softcover as brief biographical information for all scientists ISBN 978-3-540-35743-8

An Introduction to Sobolev Spaces and Interpolation Spaces

L. Tartar, Carnegie Mellon University, Pittsburgh, PA, USA the internet for a few years. The author has now revised and polished it into a text accessible to a After publishing an introduction to the Navier– larger audience. Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture 2007. Approx. 250 p. (Lecture Notes of the Unione notes based on a graduate course in two parts, as Matematica Italiana, Volume 3) Softcover indicated by the title. A draft has been available on ISBN 978-3-540-71482-8 springer.com 12 Applications of Mathematics

Biorthogonal Systems in Banach Spaces

J. Vanderwerff, La Sierra University, Riverside, CA, USA; Banach spaces. It achieves this in a manner acces- P. Hajek, Institute of Computer Science, Prague, Czech sible to graduate students and researchers who Republic; V. Montesinos Santalucia, Universidad Politec- have a foundation in Banach space theory. The nica de Valencia, Valencia, Spain; V. Zizler, University of authors have included numerous exercises, as well Alberta, Edmonton, AB, Canada as open problems that point to possible directions of research. This book introduces the reader to some of the basic concepts, results and applications of biorthogonal 2007. Approx. 315 p. (CMS Books in Mathematics) systems in infinite dimensional geometry of Banach Hardcover spaces, and in topology and nonlinear analysis in ISBN 978-0-387-68914-2 Applications of Mathematics

Iterative Learning Control Robustness and Monotonic Convergence for tonic convergence for typical uncertainty models, Interval Systems including parametric interval uncertainties, itera- H. Ahn, ETRI Intelligent Robot Research, Dajeon, Korea; tion-domain frequency uncertainty, and iteration- K. L. Moore, Colorado School of Mines, Golden, CO, USA; domain stochastic uncertainty. The book shows how Y. Chen, Utah State University, Logan, UT, USA to use robust iterative learning control in the face of model uncertainty. This monograph studies the design of robust, monotonically-convergent iterative learning 2007. Approx. 248 p. 36 illus. (Communications and controllers for discrete-time systems. It presents a Control Engineering) Hardcover unified analysis and design framework that enables ISBN 978-1-84628-846-3 designers to consider both robustness and mono-

Digital Noise Monitoring of Defect Origin

T. Aliev, Azerbaijan National Academy of Sciences, problems is how oil and gas extraction in construc- Baku City, Azerbaijan tion, power engineering, transportation, seismology, aviation, and medicine is done. The applications This book explores the initial stage of the origin of also show the improved results of mathematical the defect taking into account technical, biological, modeling, recognition, identification, and control. and other features of several technologies. These This book appeals to a wide audience focused on technologies allow the defect monitoring at the solving numerous problems where the processing beginning of the defect origin to be performed at and analysis of signals in various fields of science the expense of extracting information from the and technology is required. noise. By duplicating and combining technology advances a degree of reliability is reached. These 2007. Approx. 275 p. (Lecture Notes Electrical Engi- technologies are theoretically proven, and numerous neering, Volume 3) Hardcover examples of their applications at the beginning of ISBN 978-0-387-71753-1 the defect origin are included. One example of these Applications of Mathematics 13 springer.com

Piecewise-smooth Dynamical Systems

Theory and Applications bifurcation, which generalises diverse phenomena such as grazing, border-collision, sliding, chattering M. di Bernardo, University of Bristol, UK; University of and the period-adding route to chaos. The results Naples Federico II, Italy; C. Budd, University of Bath, UK; are presented in an informal style and illustrated A. Champneys, University of Bristol, UK; P. Kowalczyk, with copious examples, both theoretical and experi- University of Bristol, UK; University of Exeter, UK mental. Aimed at a wide audience of applied mathemati- The primary purpose of this book is to introduce cians, engineers and scientists at the early post- a coherent framework for understanding the graduate level, the book assumes only the standard dynamics of piecewise-smooth and hybrid systems. background of basic calculus and algebra and will An informal introduction asserts the ubiquity of be an indispensable resource for students and such models with examples drawn from mechanics, researchers. electronics, control theory and physiology. The main thrust is to classify complex behaviour via 2007. Approx. 496pp. (Applied Mathematical Sciences, bifurcation theory in a systematic yet applicable way. Volume 163) Hardcover The key concept is that of discontinuity-induced ISBN 978-1-84628-039-9

Least-Squares

Finite Element Methods tions. These methods are used in incompressible fluid flow, heat, transfer, and other problems. P. B. Bochev, Sandia National Laboratories, Albuquerque, This book provides researchers and practitioners NM, USA; M. D. Gunzburger, Florida State University, with a concise guide to the theory and practice of Tallahassee, FL, USA least-square finite element methods, their strengths and weaknesses, established successes, and open Since their emergence, finite element methods problems. have taken a place as one of the most versatile and powerful methodologies for the approximate 2007. Approx. 285 p. Hardcover numerical solution of Partial Differential Equa- ISBN 978-0-387-30888-3

Superior Beings. If They Exist, How Would We Know? Game-Theoretic Implications of that rational analysis need not stop where issues Omnipotence, Omniscience, Immortality, and involving faith and emotion begin. 7 New Scientist Incomprehensibility S. J. Brams, New York University, New York, NY, USA This book examines theology and the idea of a superior being in the context of game theory. The central Reviews from the first edition 7 [Brams’s] arguments, question posed in this book is: If there existed a some of them quite complicated, are presented clearly superior being who possessed the supernatural and enough background information is given to qualities of omniscience, omnipotence, immortality, enable the non-expert in game theory to follow what and incomprehensibility, how would he/she act is going on. 7 Nature differently from us? 7 Superior Beings is an extraordinary book... He The mathematical theory of games is used to define [Brams] uses strikingly simple models and generally each of these qualities, and different assumptions transparent logic to make some surprising infer- about the rules of play in several theological games ences about superiority. His inquiry is carried out that might be played between ordinary human with great inventiveness and care, and his book is beings and superior beings like God are posited. highly recommended to those interested in religion, philosophy, and the contribution of logical analysis. 2nd ed. 2007. XXII, 202 p. 32 illus. Softcover 7 American Scientist ISBN 978-0-387-48065-7 7 Brams has performed a service in demonstrating springer.com 14 Applications of Mathematics

Handbook of Mathematics

I. Bronshtein, K. Semendyayev, G. Musiol, H. Muehlig, the concept of the book has been completely re- Dresden, Germany arranged. The new emphasis is on those fields of mathematics that became more important for the This guide book to mathematics contains in hand- formulation and modeling of technical and natural book form the fundamental working knowledge of processes, namely Numerical Mathematics, Prob- mathematics which is needed as an everyday guide ability Theory and Statistics, as well as Information for working scientists and engineers, as well as for Processing. students. Easy to understand, and convenient to use, this guide book gives concisely the informa- 5th ed. 2007. XLII, 1157 p. 745 illus., 142 tabs. Softcover tion necessary to evaluate most problems which ISBN 978-3-540-72121-5 occur in concrete applications. For the 4th edition,

Introduction to Discrete Event Systems

C. G. Cassandras, Boston University, Boston, MA, USA; supervisory control, Petri net theory, Markov chains S. Lafortune, University of Michigan, Ann Arbor, MI, USA and queuing theory, discrete-event simulation, and concurrent estimation techniques. This edition Introduction to Discrete Event Systems is a includes recent research results pertaining to the comprehensive introduction to the field of discrete diagnosis of discrete event systems, decentralized event systems, offering a breadth of coverage that supervisory control, and interval-based timed makes the material accessible to readers of varied automata and hybrid automata models. backgrounds. The book emphasizes a unified modeling framework that transcends specific 2nd ed. 2007. Approx. 904 p. Hardcover application areas, linking the following topics in a ISBN 978-0-387-33332-8 coherent manner: language and automata theory,

New Computational Paradigms Changing Conceptions of What is Computable tional topics in Computability Theory are also S. Cooper, University of Leeds, UK; B. Löwe, Institute of covered as well as relationships between Proof Logic, Amsterdam, The Netherlands; A. Sorbi, Universita Theory, Computability and Complexity Theory, new di Siena, Italy (Eds.) paradigms of computation arising from biology and quantum physics and issues related to computability The recent necessity to deal with computability with/on the real numbers. The book is addressed to in the real world (computing on continuous data, researchers and graduate students in mathematics, biological computing, physical computing, etc.) has philosophy and computer science with a special switched attention to new paradigms of computa- interest in logic and foundational issues. Logicians tion, based on biological and physical models. This and theoretical physicists will also benefit from this book looks at new developments in the theory book. and practice of computation from a mathematical and predominantly logical perspective, with topics 2007. Approx. 650 p. 40 illus. Hardcover ranging from classical computability to complexity, ISBN 978-0-387-36033-1 biocomputing and quantum computing. Tradi-

Media Theory Interdisciplinary Applied Mathematics one of those feature. A simple example of a `state’ D. Eppstein, J. Falmagne, University of California, Irvine, is a partial solution of a jigsaw puzzle, which can be CA, USA; S. Ovchinnikov, San Francisco State University, transformed into another partial solution or into the CA, USA final solution just by adding or removing a single adjoining piece. The evolution of such a system over The focus of this book is a mathematical struc- time is considered. Such a structure is analyzed from ture modeling a physical or biological system that algebraic and probabilistic (stochastic) standpoints. can be in any of a number of `states.’ Each state is characterized by a set of binary features, and differs 2007. Approx. 320 p. 60 illus., some in color. Hardcover from some other neighbor state or states by just ISBN 978-3-540-71696-9 Applications of Mathematics 15 springer.com

Complexity Explained

P. Érdi, Kalamazoo College, Center for Complex Systems of very different fields, such as physics, chemistry, Studies, Kalamazoo, MI, USA biology, economics, psychology and sociology etc. have similar architecture. “Complexity Explained” This introductory textbook explains why complex is not highly technical and mathematical, but systems research is important in understanding teaches and uses the basic mathematical notions of the structure, function and dynamics of complex dynamical system theory making the book useful natural and social phenomena. It illuminates how for students of science majors and graduate courses, complex collective behavior emerges from the parts but it should be readable for a more general audi- of a system, due to the interaction between the ence; actually for those, who ask: What complex system and its environment. You will learn the basic systems really are? concepts and methods of complex system research. It is shown that very different complex phenomena 2007. Approx. 300 p. Hardcover of nature and society can be analyzed and under- ISBN 978-3-540-35777-3 stood by nonlinear dynamics since many systems

Wave Propagation and Time Reversal in Randomly Layered Media

J. Fouque, North Carolina State University, Raleigh, NC, addressed to a wide audience of graduate students USA; J. Garnier, Université de Paris VII, Paris, France; and researchers interested in the intriguing G. Papanicolaou, Stanford University, Stanford, CA, USA; phenomena related to waves propagating in random K. Solna, University of California, Irvine, CA, USA media. At the end of each chapter there is a section of notes where the authors give references and addi- The content of this book is multidisciplinary by tional comments on the various results presented in nature. It uses mathematical tools from the theories the chapter. of probability and stochastic processes, partial differential equations, and asymptotic analysis, 2007. X, 440 p. (Stochastic Modelling and Applied Prob- combined with the physics of wave propagation ability, Volume 56) Hardcover and modeling of time reversal experiments. It is ISBN 978-0-387-30890-6

Genetic Algorithms The Design of Innovation innovation researcher – from the social and behav- D. Goldberg, K. Sastry, University of Illinois at Urbana- ioral sciences, the natural sciences, the humanities, Champaign, IL, USA or the arts – or for the specialist in GAs and evolutionary computation. Genetic Algorithms: The Design of Innovation illustrates how to design and implement scalable This book illustrates how to design and implement genetic algorithms that solve hard problems quickly, scalable genetic algorithms that solve hard problems reliably, and accurately. This revised edition of the quickly, reliably, and accurately. This revised edition landmark The Design of Innovation includes recent includes recent results and new groundbreaking results and new groundbreaking material. The core material. The book combines two decades of hard- chapters have been updated and some chapters won research results in a single volume to provide a have been thoroughly rewritten. The chapter on step-by-step guide to designing genetic algorithms scalable GA design introduces other key techniques, that scale well with problem size and difficulty. A including the Dependency Structure Matrix GA major new chapter demonstrates practical scalability (DSMGA), which sheds light on probabilistic model of GAs on a problem with over a billion variables, builders such as the Bayesian Optimization Algo- and shows how these results can be used to obtain rithm. A major new chapter demonstrates practical routine solutions to important problems. This book scalability of GAs on a problem with over a billion is an essential reference. variables, and shows how these results can be used to obtain routine solutions to important problems. 2nd ed. 2007. Approx. 350 p. Hardcover Genetic Algorithms is an essential reference for the ISBN 978-0-387-35374-6 springer.com 16 Applications of Mathematics

Einstein’s General Theory of Relativity

With Modern Applications in Cosmology ously covered by textbooks, including Kaluza-Klein O. Gron, Oslo Engineering College, Oslo, Norway; theory, Israel’s formalism and branes. Anisotropic S. Hervik, Dalhousie University, Halifax, NS, Canada cosmological models are also included. The book contains a large number of new exercises and This book introduces the general theory of rela- examples, each with separate headings. The reader tivity and includes applications to cosmology. The will benefit from an updated introduction to general book provides a thorough introduction to tensor relativity including the most recent developments in calculus and curved manifolds. After the necessary cosmology. mathematical tools are introduced, the authors offer a thorough presentation of the theory of relativity. 2007. Approx. 545 p. Hardcover Also included are some advanced topics not previ- ISBN 978-0-387-69199-2

Front Tracking for Hyperbolic Conservation Laws

H. Holden, Norwegian University of Science and Tech- it displays a lot of details and information about nology, Trondheim, Norway; N. H. Risebro, University of numerical approximation for the Cauchy problem. Oslo, Norway 7 Mathematical Reviews

From the reviews 7 The present book is an excellent 1st ed 2002. Corr. 2nd printing 2007. XI, 363 p. 40 illus. compromise between theory and practice. Since it (Applied Mathematical Sciences, Volume 152) Hardcover contains a lot of theorems, with full proofs, it is a true ISBN 978-3-540-43289-0 piece of mathematical analysis. On the other hand,

Modeling and Control of Discrete-event Dynamical Systems with Petri Nets and Other Tools state charts, formal languages and max-plus algebra. B. Hrùz, Slovak University of Technology, Bratislava, Industrial examples illustrate the concepts and Slovakia; M. Zhou, New Jersey Institute of Technology, methods discussed. Using them, readers will be Newark, NJ, USA able to understand DEDs quickly and to master the control methods to analyze and improve the perfor- Discrete-event dynamic systems (DEDs) permeate mance of their systems. our world, being of great importance in modern Final-year undergraduates and graduates embarking manufacturing processes, transportation and on further courses in control, manufacturing and various forms of computer and communications process engineering, computer studies or opera- networking. tions research will find this text an invaluable aid in Modeling and Control of Discrete-event Dynamic learning about the control of this important class of Systems begins with the mathematical basics systems. required for the study of DEDs and moves on to present various tools used in their modeling and 2008. Approx. 400 p. 150 illus. (Advanced Textbooks in control. Among the instruments explained are many Control and Signal Processing) Softcover forms of Petri net, the sequential function chart, ISBN 978-1-84628-872-2 Applications of Mathematics 17 springer.com

Parallel Coordinates

A. Inselberg, Tel Aviv University, Israel Key features 7 Systematic presentation of topics Parallel coordinates has emerged as the leading interlaced with applications to visual and automatic methodology for Multidimensional Visualization. data mining, collision avoidance algorithms for air Starting from geometric foundations, this is the first traffic control, geometric modeling and computer systematic and rigorous exposition of the method- vision, decision support, information visualization ology’s mathematical and algorithmic components 7 A large collection of exercises from the basics to on the visualization of multidimensional lines, advanced project topics and open research questions minimum distances, planes, hyperplanes, clusters 7 Companion text for courses on informational of “near” planes, proximities, multidimensional visualization, multivariate statistics, linear algebra, transformations, curves, surfaces, hypersurfaces, and optimization 7 Interactive CD designed for convexity, and interior-point construction algo- classroom use, with visualizations of key topics and rithms. The last chapter explains in a non-technical examples, coordinated with cross-references in the way the methodology’s application to visual and text 7 Extensive bibliography on multivariate/ automatic data mining with principles, guidelines, multidimensional visualization techniques and strategies and algorithms illustrated in detail on real excellent index. “Parallel Coordinates” is well-suited high-dimensional datasets. for the classroom, as a reference text, or for reference, requiring only a sound foundation in linear algebra.

2007. 494 p. 416 illus. Hardcover ISBN 978-0-387-21507-5

Applied Partial Differential Equations: A Visual Approach including the flow of fluids and gases, granular P. A. Markowich, University of Vienna, Austria flows, biological processes like pattern forma- tion on animal skins, kinetics of rarified gases and This book presents topics of science and engi- semiconductor devices. Each topic is presented in neering which occur in nature or are part of daily its scientific or engineering context, followed by an life. It describes phenomena which are modelled by introduction of applicable mathematical models in partial differential equations, relating to physical the form of partial differential equations. variables like mass, velocity and energy, etc. to their spatial and temporal variations. The author has 2007. IX, 206 p. With CD-ROM. Hardcover chosen topics representing his career-long interests, ISBN 978-3-540-34645-6

Elements of Mathematics for Economics and Finance

V. C. Mavron, University of Wales, Aberystwyth, UK; This book equips undergraduates with the T. N. Phillips, University of Cardiff, UK mathematical skills required for degree courses in economics, finance, management, and business From the reviews 7 This book in every way provides studies. The fundamental ideas are described in the the elements of mathematics to be used in economics simplest mathematical terms, highlighting threads and finance. … The presentation of the examples of common mathematical theory in the various is extremely detailed, something like a step-by-step topics. Coverage helps readers become confident analysis of the solution. … This is a very easy read … and competent in the use of mathematical tools 7 MathDL and techniques that can be applied to a range of problems.

2007. X, 312 p., 77 illus. Softcover ISBN 978-1-84628-560-8 springer.com 18 Applications of Mathematics

Networks and Grids

Technology and Theory to networking theory to fundamental stochastic T. G. Robertazzi, Stony Brook University, Stony Brook, models, basics from queueing theory, fundamental NY, U.S.A. deterministic algorithms and an extensive tutorial on divisible load scheduling theory. Numerous This well-written text is intended for an undergrad- problems at the end of each chapter provide suffi- uate or graduate course on computer networks or cient material for practice and assignments. performance evaluation in electrical/computer engineering or computer science. It adopts a balanced 2007. Approx. 296 p. 113 illus. (Information Technology: approach between technology and mathematical Transmission, Processing and Storage) Hardcover modeling. Topics progress from an introduction ISBN 978-0-387-36758-3

An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces M. Schlichenmaier, Université du Luxembourg tional, more advanced geometric techniques: the modern language and modern view of Algebraic This book gives an introduction to modern geom- Geometry and Mirror Symmetry. etry. Starting from an elementary level, the author develops deep geometrical concepts that play an 2nd ed. 2007. Approx. 240 p. (Theoretical and important role in contemporary theoretical physics, Mathematical Physics) Hardcover presenting various techniques and viewpoints along ISBN 978-3-540-71174-2 the way. This second edition contains two addi-

Multidisciplinary Methods and Numerical Tools for UAV Design Applications French - Australian Advanced Workshop in for UAV applications. This book covers theoretical, Sydney, Australia 14-16 July 2003 numerical and experimental aspects, as well as K. Srinivas, University of Sydney, Australia; J. Periaux, practical applications. The topics of the papers Pôle Scientifique, Saint-Cloud, France; K. Wong, Univer- include Aerodynamics, Electromagnetics, Guid- sity of Sydney, Australia (Eds.) ance and Control as well as Propulsion and Energy Management. This research promotes the advanced This volume contains the proceedings of UAV- technologies necessary for continued development MMNT 03 workshop held in Sydney, Australia, in the field of UAV design applications. entitled “Multidisciplinary Methods and Numerical Tools for UAV Design Applications”. This work- 2007. Approx. 350 p. (Notes on Numerical Fluid shop brought together invited leading experts in Mechanics and Multidisciplinary Design (NNFM) the relatively new field of UAVs (Unmanned Aerial Hardcover Vehicles), to deliver lectures on advanced multi- ISBN 978-3-540-25134-7 disciplinary design methods and numerical tools Applications of Mathematics 19 springer.com

Advances in Unmanned Aerial Vehicles

State of the Art and the Road to Autonomy small and miniature unmanned aerial vehicles of K. P. Valavanis, University of South Florida, Tampa, USA both fixed and rotary wing designs. From historical (Ed.) background to proposed new applications, this is the most comprehensive reference yet. The past decade has seen tremendous interest in the production and refinement of unmanned 2007. Approx. 530 p. (Intelligent Systems, Control and aerial vehicles, both fixed-wing, such as airplanes Automation: Science and Engineering, Volume 33) and rotary-wing, such as helicopters and vertical Hardcover takeoff and landing vehicles. This book provides a ISBN 978-1-4020-6113-4 diversified survey of research and development on

Game Theory

Decisions, Interaction and Evolution Detailed solutions to the numerous exercises are J. N. Webb, Nottingham, UK provided at the back of the book, making it ideal for self-study. This introduction to game theory is The outstanding feature of this book is that it intended as a first course for undergraduate students provides a unified account of three types of decision of mathematics, but it will also interest advanced problem. It covers the basic ideas of decision theory, students or researchers in biology and economics. classical game theory, and evolutionary game theory in one volume. No background knowledge 2007. IX, 241 p. (Springer Undergraduate Mathematics of economics or biology is required as examples Series) Softcover have been carefully selected for their accessibility. ISBN 978-1-84628-423-6 springer.com 20 Computational Mathematics and Numerical Analysis

General Relativity

N. Woodhouse, Mathematical Institute, Oxford, UK Based on a course taught for years at Oxford, this book offers a concise exposition of the central ideas From the reviews 7 I have the opportunity to of general relativity. The focus is on the chain of comment on General Relativity … . I am happy reasoning that leads to the relativistic theory from to recommend … for an advanced undergraduate the analysis of distance and time measurements in course on relativity or for self-study. … marvelous the presence of gravity, rather than on the under- faithfulness to historical developments … character- lying mathematical structure. Includes links to izes the entire treatment. … In fact, the whole book recent developments, including theoretical work and is distinguished by this high quality of exposition. … observational evidence, to encourage further study. It’s a fine book, beautifully written and clear, and I highly recommend it. 7 MathDL 2007. IX, 219 p. 33 illus. (Springer Undergraduate Mathematics Series) Softcover ISBN 978-1-84628-486-1

A Course in Enumeration

M. Aigner, Freie Universität Berlin, Germany to offer a sophisticated source of information for professional mathematicians desiring to learn more. Combinatorial enumeration is a readily accessible There are 666 exercises, and every chapter ends with subject full of easily stated, but sometimes tantaliz- a highlight section, discussing in detail a particularly ingly difficult problems. This book leads the reader beautiful or famous result. in a leisurely way from basic notions of combinatorial enumeration to a variety of topics, ranging from 2007. X, 561 p. (Graduate Texts in Mathematics, algebra to statistical physics. The book is organized Volume 238) Hardcover in three parts: Basics, Methods, and Topics. The aim ISBN 978-3-540-39032-9 is to introduce readers to a fascinating field, and Computational Mathematics and Numerical Analysis

Numerical Linear Algebra

G. Allaire, École Polytechnique Palaiseau, France; covers core standard material and contains an S. M. Kaber, Université Pierre et Marie Curie, Lab. excellent variety of exercises. Scilab exercises are Jacques-Louis Lions, France also included online. In recent years, the use of computers in many areas of engineering and science This book distinguishes itself from the many has made it essential for students to get training in other textbooks on the topic of linear algebra by numerical methods and computer programming. including mathematical and computational chapters along with examples and exercises with Matlab. 2007. Approx. 400 p. Hardcover Using both Matlab and SciLab software, the book ISBN 978-0-387-34159-0 Computational Mathematics and Numerical Analysis 21 springer.com

Java Methods for Financial Engineering Applications in Finance and Investment applications. It is the first book to cover the topic of P. Barker, BWA Technologies LTD, Roslin, Midlothian, Java implementations for finance/investment appli- Scotland cations and is written specifically to be accessible to software practitioners without prior accoun- This book describes the principles of model building tancy/finance training. A series of packaged classes in financial engineering. It explains those models is explained and designed to allow the financial as designs and working implementations for Java- engineer complete flexibility. based applications. The book provides software professionals with an accessible source of numerical 2007. Approx. 500 p. Hardcover methods or ready-to-use code for use in business ISBN 978-1-85233-832-9

Mathematical Modelling, Analysis and Simulation of Problems

L. L. Bonilla, University of Madrid, Spain (Ed.) of mathematical modeling, analysis and numerical methods when addressing and solving problems ECMI is synonymous with European Mathematics from today’s real world applications. for Industry and organizes successful biannual The accessible presentation of real problems from conferences. The 14th European Conference for industry and finance, modeling, solutions via appro- Mathematics in Industry held in Leganés (Madrid) priate numerical and mathematical techniques are a focused on Aerospace, Information and Commu- source of fresh ideas and inspiration. nications, Materials, Energy and Environment, Imaging, Biology and Biotechnology, Life Sciences, 2007. Approx. 950 p. (Mathematics in Industry / The Finances and other topics including Education in European Consortium for Mathematics in Industry, Industrial Mathematics and web learning. Attendees Volume 12) Hardcover came from all over the world. Overall, these ISBN 978-3-540-71991-5 proceedings give a lively overview of the importance

Modeling and Simulation in Scilab/Scicos

S. Campbell, North Carolina State University, NC, USA; the second is dedicated to modeling and simulation J. Chancelier, CERMICS ENPC, France; R. Nikoukhah, of dynamical systems in Scicos. The concepts are INRIA, France illustrated through numerous examples, and all code used in the book is available to the reader. Scilab and its Scicos block diagram graphical editor, with a special emphasis on modeling and simulation 2006. XI, 313 p. Hardcover tools. The first part is a detailed Scilab tutorial, and ISBN 978-0-387-27802-5 springer.com 22 Computational Mathematics and Numerical Analysis

Spectral Methods Fundamentals in Single Domains sion of direct and iterative solution methods is also C. Canuto, Politecnico di Torino, Italy; M. Hussaini, greatly expanded. Florida State University, Tallahassee, FL, USA; A. Quarteroni, EPFL, Lausanne, Switzerland and Politec- From the reviews 7 The main aim of the book is to nico di Milano, Italy; T. Zang, NASA Langley Research discuss the approximations of solutions to ordinary Center, Hampton, VA, USA and partial differential equations in single domains by expansions in smooth, global basis functions. … Since the publication of “Spectral Methods in Fluid furnishes a comprehensive discussion of the math- Dynamics” 1988, spectral methods have become ematical theory of spectral methods in single domains firmly established as a mainstream tool for scientific … . All chapters are enhanced with material on and engineering computation. The authors of that Galerkin method … . The discussion of direct and book have incorporated into this new edition the iterative solution methods is endowed with numerical many improvements in the algorithms and the examples that illustrate the key properties of various theory of spectral methods that have been made spectral approximations and solution algorithms. since then. This latest book retains the tight integra- 7 Zentralblatt MATH tion between the theoretical and practical aspects of spectral methods, and the chapters are enhanced 2006. XXII, 563 p. 106 illus. (Scientific Computation) with material on the Galerkin with numerical Hardcover integration version of spectral methods. The discus- ISBN 978-3-540-30725-9

Spectral Methods Evolution to Complex Geometries and dynamics stability analyses is greatly expanded. The Applications to Fluid Dynamics chapter on spectral algorithms for incompressible C. G. Canuto, Politecnico di Torino, Italy; M. Y. Hussaini, flow focuses on algorithms that have proven most Florida State University, Tallahassee, FL, USA; useful in practice, has much greater coverage of A. M. Quarteroni, EPFL, Lausanne, Switzerland and algorithms for two or more non-periodic direc- Politecnico di Milano, Italy; T. A. Zang, NASA Langley tions, and shows how to treat outflow boundaries. Research Center, Hampton, VA, USA Material on spectral methods for compressible flow emphasizes boundary conditions for hyperbolic Following up the seminal Spectral Methods in systems, algorithms for simulation of homogeneous Fluid Dynamics, Spectral Methods: Evolution to turbulence, and improved methods for shock fitting. Complex Geometries and Applications to Fluid This book is a companion to Spectral Methods: Dynamics contains an extensive survey of the essen- Fundamentals in Single Domains. tial algorithmic and theoretical aspects of spectral methods for complex geometries. These types of 2007. Approx. 630 p. 183 illus. (Scientific Computation) spectral methods were only just emerging at the Hardcover time the earlier book was published. The discussion ISBN 978-3-540-30727-3 of spectral algorithms for linear and nonlinear fluid

Evolutionary Algorithms for Solving Multi-Objective Problems

C. A. Coello Coello, CINVESTAV-IPN, México City, México; rating state-of-the-art research. The book dissemi- G. B. Lamont, Air Force Institute of Technology, WPAFB, nates the application of evolutionary algorithm Dayton, OH, USA; D. A. Van Veldhuizen, AFMC/DR, techniques to a variety of practical problems. There Wright-Patterson AFB, OH, USA is an accompanying CD-ROM with a complete set of teaching tutorials, exercises and solutions, and This textbook is a second edition of Evolutionary the book contains exhaustive appendices, index and Algorithms for Solving Multi-Objective Prob- bibliography. lems, significantly expanded and adapted for the classroom. The various features of multi-objective 2nd ed. 2007. Approx. 700 p. (Genetic and Evolutionary evolutionary algorithms are presented here in an Computation) Hardcover innovative and student-friendly fashion, incorpo- ISBN 978-0-387-33254-3 Computational Mathematics and Numerical Analysis 23 springer.com

An Introduction to Scientific Computing Twelve Computational Projects Solved with more. The final section of each project contains MATLAB the solutions to proposed exercises and guides I. Danaila, P. Joly, S. M. Kaber, M. Postel, Université the reader in using the MATLAB scripts available Pierre et Marie Curie, Paris, France online.

This book demonstrates scientific computing From the reviews 7 In An Introduction to Scientific by presenting twelve computational projects in Computing, the authors present approaches to the several disciplines including Fluid Mechanics, numerical solution of problems drawn from a variety Thermal Science, Computer Aided Design, Signal of applications. … This is a graduate-level introduc- Processing and more. Each follows typical steps of tion and the pace is brisk. … This is a strong text on scientific computing, from physical and math- scientific computing for advanced students in applied ematical description, to numerical formulation and mathematics. … the book is most appropriate for programming and critical discussion of results. The students with some prior experience in scientific text teaches practical methods not usually available computing … 7 MathDL in basic textbooks: numerical checking of accuracy, choice of boundary conditions, effective solving of 2007. XV, 294 p. Hardcover linear systems, comparison to exact solutions and ISBN 978-0-387-30889-0

Newton Methods for Nonlinear Problems Affine Invariance and Adaptive Algorithms invariant under one out of four subclasses of affine P. Deuflhard, Zuse Institute Berlin (ZIB), Berlin, Germany transformations of the problem to be solved. Compared to traditional textbooks, the distin- This book deals with the efficient numerical solution guishing affine invariance approach leads to shorter of challenging nonlinear problems in science and theorems and proofs and permits the construction engineering, both in finite dimension (algebraic of fully adaptive algorithms. systems) and in infinite dimension (ordinary and partial differential equations). Its focus is on local 1st ed. 2004. Corr. 2nd printing 2006. XII, 424 p. 48 illus. and global Newton methods for direct problems or (Springer Series in Computational Mathematics, Gauss-Newton methods for inverse problems. The Volume 35) Hardcover term ‘affine invariance’ means that the presented ISBN 978-3-540-21099-3 algorithms and their convergence analysis are

Numerical Techniques for Chemical and Biological Engineers Using MATLAB® A Simple Bifurcation Approach provides detailed mathematics and engineering S. Elnashaie, Pennsylvania State University at Harrisburg, background in the appendixes, including an intro- Middletown, PA, USA; F. Uhlig, University of Auburn, AL, duction to Matlab and a guide to the user friendly USA CD included in this book. The text will be useful to undergraduate students in chemical/biological engi- This interdisciplinary book presents numerical neering, and in applied mathematics and numerical techniques needed for chemical and biological engi- analysis. neers using Matlab. The book begins by exploring general cases, and moves on to specific ones. The 2007. XVI, 590 p. With CD-ROM. Hardcover text includes a large number of detailed illustra- ISBN 978-0-387-34433-1 tions, exercises and industrial examples. The book springer.com 24 Computational Mathematics and Numerical Analysis

Computer Algebra Recipes An Introductory Guide to the Mathematical chemistry, economics, biology, and pre-medicine. Models of Science The spiral design allows the book to be effectively R. H. Enns, Simon Fraser University, Burnaby, BC, Canada; used as a computational science text, with each G. C. McGuire, University College of the Fraser Valley, section of recipes followed by a set of problems. The Abbotsford, BC, Canada book may also be used for self-study and may form the basis of an online course. This self-contained text is organized along a spiral, revisiting the general topics of graphics, symbolic From the reviews 7 Computer Algebra Recipes . . . is computation, and numerical simulation in greater an eclectic collection of application stories together detail and more depth at each turn of the spiral. with associated Maple computer algebra worksheets The heart of this text is a large number of computer or recipes. . . . The authors have designed this book to algebra worksheets or “recipes” that have been show how a computer algebra system such as Maple designed using MAPLE (Version 10). No prior can be a valuable tool for computer modeling. . . . knowledge of MAPLE is assumed. All relevant Any student who works through this text will develop commands are introduced on a need-to-know basis a very good sense of what mathematical modeling is and are indexed for easy reference. All recipes are about. . . . This text would work well for self-study or included on the CD-ROM enclosed with the book. as a source of material for projects. 7 MathDL Aimed at first- and second-year science and engineering undergraduates, the presentation is driven 2006. X, 430 p. With CD-ROM. Softcover by examples from a variety of disciplines to appeal ISBN 978-0-387-25767-9 to students in mathematics, physics, engineering,

Geometric Modelling, Numerical Simulation, and Optimization: Applied Mathematics at SINTEF recovery. The book also discusses local wind predic- G. Hasle, K. Lie, E. Quak, SINTEF, Oslo, Norway (Eds.) tions to increase aviation safety, sustainable long- term forest treatment, and optimization of natural This edited volume addresses the importance of gas value chains. The contributions are written in mathematics for industry and society by presenting a tutorial style to provide material for educational highlights from contract research at the Department purposes, such as a course or seminar on industri- of Applied Mathematics at SINTEF, the largest inde- ally relevant mathematics. pendent research organization in Scandinavia. Examples range from computer-aided geometric 2007. IX, 540 p. With many illus. in color. Hardcover design, via general purpose computing on graphics ISBN 978-3-540-68782-5 cards, to reservoir simulation for enhanced oil

More Math Into LaTeX, 4th Edition

G. Grätzer, University of Manitoba, Winnipeg, MB, From earlier reviews of Math into Latex 7 There Canada are several Latex guides, but this one wins hands down for the elegance of its approach and breadth of This is the fourth edition of the standard introduc- coverage. 7 Amazon.com, Best of 2000, Editor’s Choice tory text and complete reference for scientists in all 7 A very helpful and useful tool for all scientists and disciplines, and engineers. This fully revised version engineers. 7 Review of Astronomical Tools includes important updates on articles and books 7 A novice reader will be able to learn the most essen- as well as information on a crucial new topic: how tial features of Latex sufficient to begin typesetting to create transparencies and computer projections, papers within a few hours of time...An experienced both for classrooms and professional meetings. The Tex user, on the other hand, will find a systematic and text maintains its user-friendly, example-based, detailed discussion of all Latex features, supporting visual approach, gently easing readers into the software, and many other advanced technical issues. secrets of Latex with The Short Course. Then it 7 Reports on Mathematical Physics introduces basic ideas through sample articles and documents. It includes a visual guide and detailed 2007. Approx. 610 p. 80 illus. Softcover exposition of multiline math formulas, and even ISBN 978-0-387-32289-6 provides instructions on preparing books for publishers. Computational Mathematics and Numerical Analysis 25 springer.com

Topology-based Methods in Visualization

H. Hauser, H. Hagen, TU Kaiserslautern, Germany; the 2005 workshop “Topology-Based Methods in H. Theisel (Eds.) Visualization” that was initiated to enable additional stimulation in this field. It contains a longer chapter Enabling insight into large and complex datasets is a dedicated to a survey of the state-of-the-art, as well prevalent theme in visualization research for which as a great deal of original work by leading experts different approaches are pursued. that has not been published before, spanning both Topology-based methods are built on the idea of theory and applications. It captures key concepts abstracting characteristic structures such as the and novel ideas and serves as an overview of current topological skeleton from the data and to construct trends in topology-based visualization research. the visualizations accordingly. There are currently new demands for and renewed interest in topology- 2007. X, 222p. With colour appendix. (Mathematics and based visualization solutions. This book presents Visualization) Hardcover 13 peer-reviewed papers as written results from ISBN 978-3-540-70822-3

Nodal Discontinuous Galerkin Methods Algorithms, Analysis, and Applications classic systems of PDE’s, e.g., Maxwell’s equations, J. S. Hesthaven, Brown University, Providence, RI, USA; Euler equations, incompressible Navier-Stokes equa- T. Warburton, Rice University, Houston, TX, USA tions, and Poisson- and Helmholtz equations. These developments are done in detail in 1 and 2 dimen- The text offers an introduction to the key ideas, basic sions on general unstructured grids with high-order analysis, and efficient implementation of discon- elements and all essential routines for 3D extensions tinuous Galerkin finite element methods (DG-FEM) are also included and discussed briefly. Appendices for the solution of partial differential equations. contain an overview of orthogonal polynomials and All key theoretical results are either derived or associated library routines, a brief introduction to discussed, including an overview of relevant results grid generation, and an overview of the associated from approximation theory, convergence theory software. for numerical PDE’s, orthogonal polynomials etc. Through embedded Matlab codes, the algorithms 2008. Approx. 275 p. Hardcover are discussed and implemented for a number of ISBN 978-0-387-72065-4

Network Performance Analysis Using the J Programming Language issues. Topics covering Network Calculus include A. Holt wide sense increasing functions, mini-plus algebra, convolution and arrival, departure and services Network Calculus is a mathematical theory curves. Comprehensive examples in the applica- concerned with deriving performance bound tion of Network Calculus are given, models for networks and this book aims to show that it can simulating network traffic and network systems are provide useful methods for designing and engi- discussed and congestion control is explored. neering networks. Examples are implemented in J This book brings Network Calculus closer to the making the subject more accessible to those that, network professional and will equally appeal to although have a mathematical background, are not postgraduates studying network performance. pure mathematicians. Basic and advanced concepts of J are introduced 2007. Approx. 240 p. 52 illus. Hardcover throughout when required to illustrate different ISBN 978-1-84628-822-7 springer.com 26 Computational Mathematics and Numerical Analysis

Microflows and Nanoflows Fundamentals and Simulation theory and treasures of numerical methods. 7 Euro- G. Karniadakis, Brown University, Providence, RI USA; pean Journal of Mechanics B/Fluids A. Beskok, Texas A&M University, College Station, TX USA; 7 Microflows and Nanoflows will become an impor- N. Aluru, University of Illinois at Urbana-Champaign, tant reference for any researcher interested in the Urbana, IL USA fundamental science and simulation techniques for flow in microchannels and nanopores.7 Mathematical From the reviews 7 For those who want to compute Reviews flows at the micro scale, this monograph is a must. It describes the state of the art and helps by providing 2005. XXI, 817 p. 395 illus. (Interdisciplinary Applied coefficients, such as [are] needed in situations of slip. Mathematics, Volume 29) Hardcover Those who wonder what new fluid dynamics there ISBN 978-0-387-22197-7 is in the microworld are served by the overview of

An Introduction to Kolmogorov Complexity and Its Applications

M. Li, University of Waterloo, ON, Canada; P. M. Vitányi, science. Included are also numerous problem sets, CWI, Amsterdam, The Netherlands comments, source references, and hints to solutions of problems. New topics in this edition include Written by two experts in the field, this is the Omega numbers, Kolmogorov-Loveland random- only comprehensive and unified treatment of the ness, universal learning, communication complexity, central ideas and their applications of Kolmogorov Kolmogorov’s random graphs, time-limited complexity. The book presents a thorough treatment universal distribution, Shannon information and of the subject with a wide range of illustrative appli- others. cations. Such applications include the randomness of finite objects or infinite sequences, Martin-Loef From the reviews 7 The book is outstanding and tests for randomness, information theory, computa- admirable in many respects. ... is necessary reading for tional learning theory, the complexity of algorithms, all kinds of readers from undergraduate students to and the thermodynamics of computing. It will be top authorities in the field. 7 Journal of Symbolic Logic ideal for advanced undergraduate students, graduate 7 It is clear that this book will become ‘the’ students, and researchers in computer science, Kolmogorov complexity book. 7 Mathematical Reviews mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics. The 2008. Approx. 800 p. 41 illus. (Texts in Computer Science) book is self-contained in that it contains the basic Hardcover requirements from mathematics and computer ISBN 978-0-387-33998-6

Triangulated Manifolds

F. Lutz, TU Berlin, Germany The list of topics comprises: classification results, PL structures and Hauptvermutung, recognition Written from a Computational Topology point- techniques, computation of invariants, explicit of-view the intention of this book is to provide the constructions of examples, enumeration proce- reader with an easy and up-to-date access to a wide dures, f-vectors of triangulations, vertex-minimal, range of topics concerning topological, combinato- vertex-transitive, and centrally symmetric examples, rial, and geometric aspects of triangulated mani- realizability issues, polytopality and tightness of folds. triangulations. As a compendium of many classical results, comple- mented with new material, the book is equipped 2007. Approx. 350 p. Hardcover with an extensive bibliography. An atlas of small ISBN 978-3-540-34502-2 triangulations is also included. Computational Mathematics and Numerical Analysis 27 springer.com

Numerical Mathematics

A. Quarteroni, R. Sacco, Politecnico di Milano, Milan, authors are quite thorough in their discussion of the Italy; F. Saleri, Universitá di Milano, Milan, Italy theory underlying each of the topics…This text uses MATLAB for programming the numerical codes. This This book provides the mathematical foundations of is a very good choice…It contains a lot of interesting numerical methods and demonstrates their perfor- and useful information for experienced users of mance on examples, exercises and real-life applica- numerical methods… 7 Siam Review tions. This is done using the MATLAB software 7 This is an excellent and modern textbook in environment, which allows an easy implementation numerical mathematics! It is primarily addressed and testing of the algorithms for any specific class to undergraduate students in mathematics, physics, of problems. The book is addressed to students in computer science and engineering. But you will need Engineering, Mathematics, Physics and Computer a weekly 4 hour lecture for 3 terms lecture to teach Sciences. In the second edition of this extremely all topics treated in this book! .... In the reviewers popular textbook on numerical analysis, the read- opinion, the presented book is the best textbook in ability of pictures, tables and program headings has numerical mathematics edited in the last ten years. been improved. Several changes in the chapters on 7 Zentralblatt MATH iterative methods and on polynomial approximation have also been added. 2nd ed. 2007. XVIII, 655 p. 135 illus. (Texts in Applied From the reviews of the first edition 7 I found many Mathematics, Volume 37) Hardcover of the examples to be quite interesting. I find no fault ISBN 978-3-540-34658-6 with any of the theoretical portions of the text. The

Numerical Treatment of Partial Differential Equations

H. Roos, C. Grossmann, TU Dresden, Germany Moreover it also guides to actual developments in Transl. German: M. Stynes, University College Cork, research. Ireland For instance, relatively detailed introductions are given into a posteriori error estimation, discon- This book deals with discretization techniques for tinuous Galerkin methods or optimal control with partial differential equations of elliptic, parabolic partial differential equations, very recent subjects, and hyperbolic type. It provides an introduction to that are rarely to find in other books. The book is main principles of discretization as well as it pres- mainly dedicated to finite element methods, but ents the reader the ideas and analysis of advanced discusses as well difference methods and finite numerical methods in this area. volume techniques. The main motivation is to give students and Further, basic facts are given for solving the gener- mathematically interested engineers and scientists ated discrete problems and chapters on singularly a textbook which contains all basic discretization perturbed problems and variational inequalities and techniques for the fundamental types of partial optimal control illuminate special topics reflecting differential equations and in which the reader can research interests of the authors. find analytical tools, properties of the discretization techniques and hints to algorithmic aspects. 2007. Approx. 600 p. (Universitext) Softcover ISBN 978-3-540-71582-5 springer.com 28 Computational Mathematics and Numerical Analysis

Mathematics and Technology

C. Rousseau, Y. Saint-Aubin, Université de Montreal, context and not just the practical one. Mathematics QC, Canada and Technology is intended for undergraduate With contrib. by: I. Ascah-Coallier, H. Antaya students in mathematics, instructors and high school teachers. Additionally, its lack of calculus This book introduces the student to numerous centricity as well as a clear indication of the more modern applications of mathematics in technology. difficult topics and relatively advanced references The authors write with clarity and present the math- make it suitable for any curious individual with a ematics in a clear and straightforward way making decent command of high school math. it an interesting and easy book to read. Numerous exercises at the end of every section provide prac- Approx. 440 p. 100 illus. 2008. Approx. 440 p., 100 illus. tice and reinforce the material in the chapter. An (Springer Undergraduate Series in Mathematics and engaging quality of this book is that the authors also Technology) Softcover present the mathematical material in a historical ISBN 978-0-387-69215-9

Numerical Approximation Methods for Elliptic Boundary Value Problems Finite and Boundary Elements of linear elastostatics and the Stokes system. While O. Steinbach, Technische Universitat Graz, Austria there are textbooks on the finite element method, this is one of the first books on Theory of Boundary This book presents a unified theory of the Finite Element Methods. It is suitable for self study and Element Method and the Boundary Element exercises are included. Method for a numerical solution of second order elliptic boundary value problems. This includes the 2006. X, 390 p. (Texts in Applied Mathematics, solvability, stability, and error analysis as well as effi- Volume 54) Hardcover cient methods to solve the resulting linear systems. ISBN 978-0-387-31312-2 Applications are the potential equation, the system

Galerkin Finite Element Methods for Parabolic Problems

V. Thomée, Chalmers University of Technology, Göte- have also been added, dealing with problems in borg, Sweden polygonal, particularly noncovex, spatial domains, and with time discretization based on using Laplace This book provides insight into the mathematics transformation and quadrature. of Galerkin finite element method as applied to parabolic equations. The revised second edition has 2nd ed. 2006. XII, 370 p. (Springer Series in Computa- been influenced by recent progress in application tional Mathematics, Volume 25) Hardcover of semigroup theory to stability and error analysis, ISBN 978-3-540-33121-6 particulatly in maximum-norm. Two new chapters Computational Science and Engineering 29 springer.com

The Mathematica GuideBook for Numerics

M. Trott, Wolfram Research Inc., Champaign, IL, USA ematics capabilities. The available types of arithmetic (machine, high-precision, and interval) are Mathematica is today’s most advanced technical introduced, discussed, and put to use. Fundamental computing system, featuring a rich programming numerical operations, such as compiling programs, environment, two-and three-dimensional graphics fast Fourier transforms, minimization, numerical capabilities and hundreds of sophisticated, powerful solution of equations, ordinary/partial differential programming and mathematical functions using equations are analyzed in detail and are applied to a state-of-the-art algorithms. Combined with a user- large number of examples in the main text and solu- friendly interface and a complete mathematical tions to the exercises. typesetting system, Mathematica offers an intuitive, easy-to-handle environment of great power and 7 For PC and Mac. For the complete system require- utility. ments see: springer.com “The Mathematica GuideBook for Numerics” (text and code fully tailored for Mathematica 5.1) 2006. XXVIII, 1208 p. 1364 illus. With DVD. Hardcover concentrates on Mathematica’s numerical math- ISBN 978-0-387-95011-2 Computational Science and Engineering

Tensor Calculus for Engineers Analytical and Computational Aspects representations are discussed. The formulation of R. d. Boer, J. Schroeder, University of Essen, Germany isotropic and anisotropic elasticity is performed within a basis-independent formalism. As far as This textbook introduces to the vector and tensor possible illustrative approaches are chosen although calculus as it is used in continuum mechanics. some of the concepts require axiomatic introduc- Therefore, it limits itself to the 3-dimensional tion. All chapters widely consist of examples and Euclidian space. It contains, in addition, an intro- exercises. This book is written mainly for students duction to continuum mechanics and linear shell in civil and mechanical engineering and bridges theory. The theoretical concepts of small and finite the gap between mathematics and its engineering strain elasticity, its numerical formulation and application. essential implementation aspects are presented in detail. After setting the variational framework of 2008. Approx. 450 p. Softcover boundary value problems, several Finite Element ISBN 978-3-540-24224-6

Scientific Computing in Electrical Engineering SCEE 2006 coupled problems and general mathematical and G. Ciuprina, D. Ioan, Politehnica University of Bucharest, computational methods. This book is particularly Romania (Eds.) important for engineers, physicists and mathematicians who want to know the state of the art with This book is a collection of selected papers respect to scientific challenges arising from prob- presented at the last Scientific Computing in lems of interest for industry. Electrical Engineering (SCEE) Conference, held in Sinaia, Romania, in 2006. The series of SCEE 2007. XXII, 486 p. With colour appendix. (Mathematics in conferences aims at addressing mathematical Industry / The European Consortium for Mathematics in problems which have a relevance to industry, with Industry, Volume 11) Hardcover an emphasis on modeling and numerical simulation ISBN 978-3-540-71979-3 of electronic circuits, electromagnetic fields but also springer.com 30 Computational Science and Engineering

Spectral Clustering, Ordering and Ranking Statistical Learning with Matrix Factorizations trate the ideas. A key feature are the mathematical C. Ding, Lawrence Berkeley National Laboratory, proofs outlined throughout the text in reasonable Berkeley, CA, USA; H. Zha, Penn State University, State detail which highlight the rigorous and principled College, PA, USA quality of spectral clustering. A concise introduction to data clustering methods is followed by advanced Data mining methods are essential for analyzing spectral clustering, ordering and ranking topics the ever-growing massive quantities of data. Data which then lead to applications in web and text clustering is one of the key data mining techniques. mining and genomics. An Appendix covering the In recent years, spectral clustering has been devel- preliminaries makes this text self-contained. oped as an effective approach to data clustering. This exposition presents recent advances in this new 2007. Approx. 400 p. Hardcover subfield. New concepts are carefully developed and ISBN 978-0-387-30448-9 practical examples are extensively utilized to illus-

Design Patterns for e-Science

H. Gardner, Australian National University, Canberra, important design patterns for object-oriented soft- NSW, Australia; G. Manduchi, Consorzio RFX, Padova, ware. The final product is ready for porting onto the Italy Grid. Object-oriented design patterns are taught in a real-world context which is relevant to compu- This book is for readers with backgrounds in science tational science. A comprehensive CD of the case engineering who have experience in computer study accompanies the book. programming but who lack a training in software engineering. The treatment is centered around a 2007. XX, 388 p. 60 illus.,with CD-ROM. Also available case study in software development in “e-Science’’ online. (Texts in Computational Science and Engineering, using the Java™ programming language. A graphical Volume 4) Hardcover front-end for browsing and visualising scientific ISBN 978-3-540-68088-8 waveform data is progressively refactored using

Numerical Simulation in Molecular Dynamics Numerics, Algorithms, Parallelization, algorithms and their parallel implementation with Applications MPI on computer systems with distributed memory. M. Griebel, University of Bonn, Germany; S. Knapek, Furthermore, detailed explanations are given to the TWS Partners, Munich, Germany; G. Zumbusch, Univer- different steps of numerical simulation, and code sity of Jena, Germany examples are provided. With the description of the algorithms and the presentation of the results of Particle models play an important role in many various simulations from the areas material science, applications in physics, chemistry and biology. nanotechnology, biochemistry and astrophysics, They can be studied on the computer with the help the reader of this book will be able to write his own of molecular dynamics simulations. This book programs for molecular dynamics step by step and presents in detail both the necessary numerical to run successful experiments. methods and techniques (linked-cell method, SPME-method, tree codes, multipole technique) 2007. Approx. 500 p. (Texts in Computational Science and the theoretical background and foundations. and Engineering, Volume 5) Hardcover It illustrates the aspects modelling, discretization, ISBN 978-3-540-68094-9 Differential Equations and Dynamical Systems 31 springer.com

Computational Turbulent Incompressible Flow Applied Mathematics: Body and Soul 4 tional finite element methodology in the form of J. Hoffman, C. Johnson, Royal Institute of Technology - General Galerkin (G2) up against the challenge of KTH, Stockholm, Sweden computing turbulent solutions of the inviscid Euler equations and the Navier-Stokes equations with This is Volume 4 of the book series of the Body and small viscosity. This is an outstanding textbook Soul mathematics education reform program. It presenting plenty of new material with an excellent presents a unified new approach to computational pedagogical approach. simulation of turbulent flow starting from the general basis of calculus and linear algebra of Vol 2007. XIX, 397 p. Hardcover 1-3. The book puts the Body and Soul computa- ISBN 978-3-540-46531-7

Python Scripting for Computational Science

H. P. Langtangen, Simula Research Laboratory, Lysaker, scripting with Python increases the productivity and and University of Oslo, Norway reliability of your scientific work and lets you have more fun - under Unix, Windows and MacIntosh. Hans Petter Langtangen teaches you how to develop tailored, flexible, and efficient working 2nd ed. 2006. XXIV, 736 p. 62 illus. (Texts in Computa- environments built from small programs written in tional Science and Engineering, Volume 3) Hardcover Python. The focus is on examples and applications ISBN 978-3-540-29415-3 of relevance to computational science. In short, Differential Equations and Dynamical Systems

An Introduction to Sequential Dynamical Systems

H. S. Mortveit, Virginia Tech, Blacksburg, VA, USA; C. M. broad range of topics on structure theory - equiva- Reidys, Los Alamos Labs., Santa Fé, NM, USA lence, fixed points, invertibility and other phase space properties - thereafter SDS relations to graph This introductory text to the class of Sequential theory, classical dynamical systems as well as SDS Dynamical Systems (SDS) is the first textbook on applications in computer science are explored. This this timely subject. Driven by numerous examples is a versatile interdisciplinary textbook. and thought-provoking problems throughout, the presentation offers good foundational material on 2007. X, 250 p. 20 illus. Hardcover finite discrete dynamical systems, which then leads ISBN 978-0-387-30654-4 systematically to an introduction of SDS. From a

Synchronization in Oscillatory Networks

G. V. Osipov, Nizhny Novgorod University, Nizhny the field for graduate students in physics and applied Novgorod, Russia; J. Kurths, C. Zhou, Universität mathematics as well as being a compendium for Potsdam, Germany researchers from any field of application interested in quantitative models. This work systematically investigates a large number of oscillatory network configurations that are able 2007. Approx. 330 p. (Springer Series in Synergetics) to describe many real systems such as electric power Hardcover grids, lasers or even the heart muscle, to name but ISBN 978-3-540-71268-8 a few. The book is conceived as an introduction to springer.com 32 Differential Equations and Dynamical Systems

Chaos and Fractals New Frontiers of Science tion on nearly every angle of the topic... 7 Zentralblatt H. Peitgen, H. Jürgens, University of Bremen, Germany; Mathematik D. Saupe, University of Konstanz, Germany 7 This is the second … edition of what has been a bestseller since its first publication in 1992. … All the From the reviews 7 Numerous books have appeared laudatory comments heard twelve years ago about in recent years that either explore the beauty of fractal this fascinating book remain entirely valid. No one art, describe techniques for its creation, or investigate has succeeded in better presenting … . the presenta- some aspect of the related field of chaotic behavior. tion has not aged at all – the comprehensiveness of the The present work attempts to accomplish all three underlying mathematics and the illustrative power goals in one huge volume...the authors should be of the figures has never been surpassed. Twelve years applauded for their ambitions undertaking. 7 Math- after its first edition this book remains a must buy. ematical Reviews 7 Physicalia 7 This book … contains all one ever wanted to know about fractals, and more. Written by–next to 2nd ed. 2004. XIII, 864 p. 606 illus., 40 in color. Hardcover Mandelbrot–the greatest popularizer of the concept of ISBN 978-0-387-20229-7 fractal geometry … It contains a wealth of informa-

Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics M. Pettini, Osservat. Astrofisico Arcetri, Firenze, Italy relating topology changes of microscopic configura- tion space with the generation of singularities of This book covers a new explanation of the origin thermodynamic observables. The book contains of Hamiltonian chaos and its quantitative charac- numerous illustrations throughout and it will terization. The author focuses on two main areas: interest both mathematicians and physicists. Riemannian formulation of Hamiltonian dynamics, providing an original viewpoint about the relation- 2007. Approx. 331 p. (Interdisciplinary Applied ship between geodesic instability and curvature Mathematics, Volume 33) Hardcover properties of the mechanical manifolds; and a topo- ISBN 978-0-387-30892-0 logical theory of thermodynamic phase transitions,

Averaging Methods in Nonlinear Dynamical Systems

J. A. Sanders, Free University of Amsterdam, The Nether- manifolds. One of the most striking features of the lands; F. Verhulst, State University of Utrecht, The Neth- book is the collection of examples, which range erlands; J. Murdock, Iowa State University, Iowa, USA from the very simple to some that are elaborate, realistic, and of considerable practical importance. Perturbation theory and in particular normal form Most of them are presented in careful detail and theory has shown strong growth in recent decades. illustrated with illuminating diagrams. This book is a drastic revision of the first edition of the averaging book. The updated chapters represent 2nd ed. 2007. XX, 433 p. (Applied Mathematical Sciences, new insights in averaging, in particular its relation Volume 59) Hardcover with dynamical systems and the theory of normal ISBN 978-0-387-48916-2 forms. Also new are survey appendices on invariant General Mathematics 33 springer.com

Functional Equations and How to Solve Them

C. G. Small, University of Waterloo, ON, Canada carefully. The most difficult will challenge students studying for the International Mathematical Olym- Many books have been written on the theory of piad or the Putnam Competition. An appendix functional equations, but few help readers solve provides a springboard for further investigation of functional equations in mathematics competitions the concepts of limits, infinite series and continuity. and mathematical problem solving. This book fills that gap. Each chapter includes a list of problems 2007. Approx. 132 p. (Problem Books in Mathematics) associated with the covered material. These vary Softcover in difficulty, with the easiest being accessible to ISBN 978-0-387-34539-0 any high school student who has read the chapter General Mathematics

Proofs from THE BOOK

M. Aigner, Freie Universität Berlin, Germany; pages, one gem after another. Some of the proofs are G. M. Ziegler, Technische Universität Berlin, Germany classics, but many are new and brilliant proofs of Illustrations by: K. Hofmann classical results. ...Aigner and Ziegler do not claim to have presented the definitive collection of great From the reviews 7 ... This is a wonderful book that mathematics. In their brief introduction they write: can be recommended to anybody who is in any way “We have no definition or characterization of what connected to mathematics. Those who have ever expe- constitutes a proof from THE BOOK: all we offer is rienced the beauty of mathematics will experience the examples that we have selected, hoping that our the chill again. For those who have never experienced readers will share our enthusiasm about brilliant that, this book is just the right one to start. 7 Acta ideas, clever insights and wonderful observations.” I Scientiarum Mathematicarum do. ... 7 Notices of the American Mathematical Society 7 ... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever 3rd ed. 2004. VIII, 239 p. 250 illus. Hardcover insights and beautiful ideas combine in astonishing ISBN 978-3-540-40460-6 and glorious ways. There is vast wealth within its

Approval Voting

S. Brams, New York University, New York, NY, USA; benefits of approval voting are its propensity to elect P. C. Fishburn, Basking Ridge, NJ, USA the majority candidate, its relative invulnerability to insincere or strategic voting, and a probable increase This volume presents a simple and logical potential in voter turnout. electoral reform. Under this system voters may vote for, or approve of, as many candidates as they 2nd ed. 2007. XXII, 200 p. 4 illus. Softcover like in multicandidate elections. Among the many ISBN 978-0-387-49895-9

The Heart of Mathematics An invitation to effective thinking … . It is really true that the ideas presented in this E. B. Burger, Williams College, Williamstown, MA, USA; book are some of the most fascinating and beautiful M. Starbird, The University of Texas at Austin, Austin, ones around. … The reader will have something to TX, USA explore, to learn, to think, to enjoy, and to add new aspects to his view of everything. 7 Zentralblatt MATH From the reviews 7 In this book, the reader will see that mathematics is a network of intriguing ideas 2nd ed. 2005. XXIV, 760 p. With CD ROM and Glasses. … . It is a really nice book. … This attractive book Hardcover contains a lot of well-known and interesting problems ISBN 978-1-931914-41-3 springer.com 34 General Mathematics

The IMO Compendium A Collection of Problems Suggested for The want to be without a copy, nor will anyone involved in International Mathematical Olympiads: 1959- mathematics competitions … 7 MathDL 2004

D. Djukic, University of Toronto, ON, Canada; This is the ultimate collection of challenging high- V. Z. Jankovic, Belgrade University, Serbia and Monte- school-level mathematics problems. It is the result negro; I. Matic, University of California, Berkeley, CA, of a two year long collaboration to rescue these USA; N. Petrovic, Institute of Physics, Belgrade, Serbia problems from old and scattered manuscripts, and Montenegro and produce the definitive source of IMO practice problems in book form for the first time. This book From the reviews 7 The International Mathematical attempts to gather all the problems and solutions Olympiad, or IMO is the premier international appearing on the IMO and contains a grand total competition for talented high school mathematics of 1900 problems. It is an invaluable resource for students. … This book collects statements and high-school students preparing for mathematics solutions of all of the problems ever set in the IMO, competitions, and for anyone who loves math. together with many problems proposed for the contest. … serves as a vast repository of problems at the Olym- 2006. XIV, 740 p. 200 illus. (Problem Books in piad level, useful both to students … and to faculty Mathematics) Hardcover looking for hard elementary problems. No library will ISBN 978-0-387-24299-6

Problem-Solving Strategies

A. Engel, Johann Wolfgang Goethe-Universität, Frankfurt, Germany

1st ed. 1998. Corr. 2nd printing 1999. X, 403 p. 223 illus. (Problem Books in Mathematics) Softcover ISBN 978-0-387-98219-9

Putnam and Beyond

R. Gelca, Texas Tech University, Lubbock, TX, USA; the reader is eased into transitioning from problem- T. Andreescu, The University of Texas at Dallas, solving at the high school level to the university and Richardson, TX, USA beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam and Beyond takes the reader on a journey Putnam exam, as a text for many different problem- through the world of college mathematics, focusing solving courses, and as a source of problems for on some of the most important concepts and results standard courses in undergraduate mathematics. in the theories of polynomials, linear algebra, real Putnam and Beyond is organized for self-study analysis in one and several variables, differential by undergraduate and graduate students, as well as equations, coordinate geometry, trigonometry, teachers and researchers in the physical sciences elementary number theory, combinatorics, and who wish to expand their mathematical horizons. probability. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring 2007. Approx. 808 p. 50 illus. Hardcover symbol to build an appropriate math background ISBN 978-0-387-25765-5 for graduate studies in pure or applied mathematics, Geometry and Topology 35 springer.com

Geometric Modeling and Algebraic Geometry

B. Jüttler, Johannes-Kepler-Universität Linz, Austria; which rely on theinteraction of both fields. Some R. Piene, University of Oslo, Norway (Eds.) of these results have been obtainedin the frame of the European GAIA II project (IST 2001-35512) The two fields of Geometric Modeling and Algebraic entitled`Intersection algorithms for geometry- Geometry, thoughclosely related, are tradition- based IT applications usingapproximate algebraic ally represented by two almost disjointscientific methods’. communities. Both fields deal with objects defined byalgebraic equations, but the objects are studied 2007. Approx. 240 p. Hardcover in different ways.This contributed book presents, in ISBN 978-3-540-72184-0 12 chapters written byleading experts, recent results Geometry and Topology

Squaring the Circle Geometry in Art and Architecture the fine art from the book in full color, as well as P. Calter, Vermont Technical College, Randolph Center, exclusive teaching resources. The text will appeal VT, USA both to mathematicians and to artists and will generally be used in courses that bridge the two This book introduces geometry concepts by subjects. analyzing well-known buildings and works of art. The book includes an access code which allows the 2007. Approx. 400 p. Also available online. Softcover reader into a dedicated web site presenting most of ISBN 978-1-930190-82-5

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Inequalities for Differential Forms

R. P. Agarwal, Florida Institute of Technology, ties, Lipschitz classes, Orlicz spaces and inequalities Melbourne, Florida, USA; S. Ding, Seattle University, in Carnot groups are discussed in the concluding Seattle, Washington, USA chapter. An abundance of bibliographical references and historical material supplement the text This monograph is the first one to systematically throughout. This rigorous presentation requires a present a series of local and global estimates and familiarity with topics such as differential forms, inequalities for differential forms, in particular the topology and Sobolev space theory. It will serve as ones that satisfy the A-harmonic equations. The an invaluable reference for researchers, instructors presentation focuses on the Hardy-Littlewood, and graduate students in analysis and partial differ- Poincare, Cacciooli, imbedded and reverse Holder ential equations and could be used as additional inequalities. Integral estimates for operators, such as material for specific courses in these fields. homotopy operator, the Laplace-Beltrami operator, and the gradient operator are discussed next. Addi- 2007. Approx. 400 p. Hardcover tionally, some related topics such as BMO inequali- ISBN 978-0-387-36034-8 springer.com 36 Geometry and Topology

Combinatorial Algebraic Topology

D. Kozlov, ETH Zentrum, Zürich, Switzerland and Univer- sion of the major research techniques of Combina- sity of Bremen, Germany torial Algebraic Topology. Our presentation of standard topics is quite different from the existing texts. Combinatorial Algebraic Topology is a fascinating In addition several new themes, such as spectral and dynamic field on the crossroads of Algebraic sequences, are included. Although applications are Topology and Discrete Mathematics. This volume sprinkled throughout the second part, this reaches is the first comprehensive treatment of the subject its climax in the third part, which is entirely devoted in book form. The first part of the book constitutes to developing the topological structure theory for a swift walk through the main tools of Algebraic graph homomorphisms. Topology, including Stiefel-Whitney characteristic- classes, which are needed for the later parts. The 2007. Approx. 407 p. (Algorithms and Computation in reader - graduate students and working mathemati- Mathematics, Volume 21) Hardcover cians alike - will probably find particularly useful ISBN 978-3-540-71961-8 the second part, which contains an in-depth discus-

A Topological Picturebook

G. K. Francis, University of Illinois at Urbana-Champaign, 7 Bravo to Springer for reissuing this unique and Urbana, IL, USA beautiful book! It not only reminds the older generation of the pleasures of doing mathematics by hand, Fromt the reviews 7 I was every pleasantly surprised but also shows the new generation what ‘hands when I opened the book. … this is really a much on’ really means. 7 John Stillwell, University of San richer book. Indeed, the approach it offers to drawing Francisco can have a significant impact on how we teach and 7 The Topological Picturebook has taught a whole think about mathematics. … If you are good at generation of mathematicians to draw, to see, and to visualization and illustration, this book can help you think. 7 Tony Robbin, artist and author of “Shadows of become better yet. … this will give you concrete and Reality” specific suggestions for developing your skills. If you just appreciate skillful drawing and illustration, this 1st ed 1987. 2nd printing 2007. XV, 194 p. 87 illus. book deserves a look. 7 MathDL Softcover ISBN 978-0-387-34542-0

Convex and Discrete Geometry

P. M. Gruber, Vienna University of Technology, Vienna, cations. Besides being a graduate-level introduction Austria to the field, it is a practical source of information and orientation for convex geometers, and useful to Convex and Discrete Geometry is an area of math- people working in the applied fields. ematics situated between analysis, geometry and discrete mathematics with numerous relations to 2007. Approx. 600 p. (Grundlehren der mathematischen other subdisciplines. This book provides a compre- Wissenschaften, Volume 336) Hardcover hensive overview of major results, methods and ISBN 978-3-540-71132-2 ideas of convex and discrete geometry and its appli- Geometry and Topology 37 springer.com springer.com 38 Geometry and Topology

MESH A Journey Through Discrete Geometry Mesh have never before been portrayed with computer B. Janzen, Zipheron Design Labs, Culver City, CA, USA; graphics … 7 (www.webwire.com, January, 2007) K. Polthier, Freie Universität Berlin, Germany MESH is a mathematical video on polyhedral From the reviews 7 Alle Körper und Formen lassen meshes and their role in geometry, numerics sich als ein Netz vieler kleiner Flächen darstellen, and computer graphics. The film is completely so genannte polyedrische Flächen, mit denen sich computer-generated using the latest technology and im Computer besonders gut arbeiten lässt. Was sich spans the range from ancient Greek mathematics trocken anhört, kommt in dem Film als unterhalt- to the area of geometric modelling of today. MESH same und spannende Geschichte daher. Es spannt has already won several science awards worldwide. den Bogen von den griechischen Philosophen wie The authors are Konrad Polthier, a professor of Platon bis zur modernen Computer-Grafik und zur mathematics, and Beau Janzen, a professional film modernen Wissenschaft;- alles faszinierend animiert. director. Die Zielgruppe sind nicht Forscher, sondern Lehrer, The film is an excellent teaching tool for courses Schüler oder Hobby-Mathematiker”, sagt Polthier. on geometry, visualization, scientific computing Seine Filme wurden bereits mehrfach international and geometric modeling at universities and centers ausgezeichnet. 7 Der Tagesspiegel, 18.11.2006 for computational science, and can also be used in 7 The mathematical film Mesh … has already won schools. numerous international prizes. Mesh is a ground breaking 40-minute computer animation that explores 2007. DVD-Video PAL. Length 39 minutes, booklet 23 p. the advancement of discrete geometry from the ancient (Springer VideoMATH) Greeks to contemporary research topics. … With its ISBN 978-3-540-28478-9 synthesis of cutting-edge visualization, breathtaking artistry, storytelling and humor, Mesh presents 2007. DVD-Video NTSC. Length 39 minutes, booklet 23 p. complex ideas in a way that is palpable and relevant (Springer VideoMATH) to even a novice audience. … Many of the topics in ISBN 978-3-540-28484-0

The Interactive Geometry Software Cinderella.2 Single user edition Windows/Macintosh/Solaris/ 7 The Mathematical Intelligencer Linux-Version U. H. Kortenkamp, Pädagogische Hochschule, Cinderella.2, the new version of the well-known Schwäbisch Gmünd, Germany; J. Richter-Gebert, interactive geometry software, has become an even Technische Universität, München, Germany more versatile tool than its predecessor. The geometry component extends the functionality to such From the reviews 7 Cinderella is a gem: this interac- spectacular objects as dynamic fractals, and the soft- tive geometry package offers an environment in which ware includes two major new components: physical the user can do classic or original constructions with simulation such as of mechanical objects, virtual extreme accuracy and ease... The fact that Cinderella electronic devices, and electromagnetic proper- is written entirely in JAVA allows for a high level ties. Cinderella.2: Math in Motion offers complete of portability. The ease of both construction and instruction and techniques for using Cinderella.2, exporting applets is amazing... Highly recommended and includes the program on CD-ROM with a single for all teachers and students of geometry from high user licence in the purchase price. school through undergraduate level. 7 CHOICE 7 [...] The first thing that attracted me in Cinderella 7 For PC und Mac. For the complete system require- was its human interface. [...] At this point you face ments see: springer.com one of the strongest features of Cinderella: its support of different geometric views. [...] Let me conclude with Version 2.0 2007. CD-ROM, with handbook (also avail- a good word about the software installation: It’s a able as netlicence edition). Special type piece of cake. After 30 seconds or so, you can play. ISBN 978-3-540-33422-4

Geometry and Topology 39 springer.com

The Cinderella.2 Manual

U. Kortenkamp, Pädagogische Hochschule, Schwäbisch Gmünd, Germany; J. Richter-Gebert, Technische Univer- sität, München, Germany

2007. Approx. 300 p. Softcover ISBN 978-3-540-34924-2

Semiparallel Submanifolds in Space Forms

Ü. Lumiste, University of Tartu, Estonia subclasses are given. In later chapters Lumiste introduces the concept of main symmetric orbit and This book offers the most comprehensive survey presents all known results concerning umbilic-like to date of the theory of semiparallel submanifolds. main symmetric orbits. Introduced only in 1985, semiparallel submanifolds Covering both background material and the most have emerged as an important area of research recent developments in semiparallel submani- within differential geometry and topology. folds, this book will appeal to both researchers and Lumiste begins with the necessary background graduate students. material: symmetric and semisymmetric Reim- manian manifolds, smooth manifolds in space 2007. Approx. 315 p. (Springer Monographs in forms, and parallel submanifolds. Semiparallel Mathematics) Hardcover submanifolds are introduced in chapter 4, where ISBN 978-0-387-49911-6 some characterizations for their class and several

Algorithmic Topology and Classification of 3-Manifolds

S. Matveev, Chelyabinsk State University, Russia contributes to keep the level of the exposition really elementary. From the reviews of the 1st edition 7 This book In conclusion, the reviewer subscribes to the quota- provides a comprehensive and detailed account of tion from the back cover: “the book fills a gap in the different topics in algorithmic 3-dimensional topology, existing literature and will become a standard refer- culminating with the recognition procedure for Haken ence for algorithmic 3-dimensional topology both for manifolds and including the up-to-date results in graduate students and researchers. 7 Zentralblatt für computer enumeration of 3-manifolds. Originating Mathematik 1048 (2004) from lecture notes of various courses given by the For this 2nd edition, new results, new proofs, and author over a decade, the book is intended to combine commentaries for a better orientation of the reader the pedagogical approach of a graduate textbook have been added. (without exercises) with the completeness and reli- 7 Recommended. 7 Choice ability of a research monograph… All the material, with few exceptions, is presented 2nd ed. 2007. Approx. 500 p. (Algorithms and Computa- from the peculiar point of view of special poly- tion in Mathematics, Volume 9) Hardcover hedra and special spines of 3-manifolds. This choice ISBN 978-3-540-45898-2

An Invitation to Morse Theory

L. Nicolaescu, University of Notre Dame, IN, USA and equivariant cohomology, and complex Morse theory. In addition, many examples, problems, and This book offers readers a taste of the “unreason- illustrations further enhance the value of this useful able effectiveness” of Morse theory. It covers many introduction to Morse Theory. of the most important topics in Morse theory along with applications. The book details topics such as 2007. XIV, 242 p. 32 illus. (Universitext) Softcover Morse-Smale flows, min-max theory, moment maps ISBN 978-0-387-49509-5 springer.com 40 Geometry and Topology

Elementary Differential Geometry

A. Pressley, King’s College, London, UK is a very good first book on the topic.7 Internationale Mathematische Nachrichten From the reviews 7 By the inclusion of 200 exercises with full solutions, this book has become a helpful tool 1st ed. 2001. Corr. 2nd printing 2001. X, 332 pp. (Springer for everyone teaching in its field. Summing up, it Undergraduate Mathematics Series) Softcover ISBN 978-1-85233-152-8

The Four Pillars of Geometry

J. Stillwell, University of San Francisco, CA, USA geometry, and transformations and non-Euclidean geometry. … The writing style is both student-friendly From the reviews 7 This is an introductory book on and deeply informed. The pleasing brevity of the book geometry, easy to read, written in an engaging style. … makes the book especially suitable as an instruc- The author’s goal is … to increase one’s overall under- tion to geometry for the large and critically important standing and appreciation of the subject. … Along the population of undergraduate mathematics majors … . way, he presents elegant proofs of well-known theo- Each chapter concludes with a well-written discussion rems … . The advantage of the author’s approach is section that combines history with glances at further clear: in a short space he gives a brief introduction to results. There is a good selection of thought-provoking many sides of geometry and includes many beautiful exercises. 7 Mathematical Reviews results, each explained from a perspective that makes it easy to understand. 7 SIAM Review 2005. XII, 229 p. 138 illus. (Undergraduate Texts in 7 The pillars of the title are … Euclidean construc- Mathematics) Hardcover tion and axioms, coordinates and vectors, projective ISBN 978-0-387-25530-9

An Introduction to Manifolds

L. W. Tu, Tufts University, Medford, MA, USA and logical organization lend clarity to the book. Examples and exercises are provided throughout The aim of this textbook is to introduce advanced the text and solutions to selected exercises are also undergraduate and graduate level students - in included. A novice to manifolds needs a semester either a mathematics or physics field of study of abstract algebra and a year of real analysis. The - to manifolds. In the first section of the book, author covers prerequisites from point-set topology the Euclidean space and point-set topology are in an elaborate appendix. An Introduction to presented to create a smooth transition from Manifolds should enable students to do calculus undergraduate calculus. At a quick, yet accessible on manifolds and recognize their applications in pace, the text then continues to explore manifolds in analysis and topology. terms of their relationship to tangent spaces, such as Lie groups and their Lie algebras. The focus within 2007. Approx. 310 p. 30 illus. (Universitext) Softcover each chapter consists of only the most fundamental ISBN 978-0-387-48098-5 topics in manifold theory. This modesty of scope History of Mathematics 41 springer.com History of Mathematics

Mr Hopkins’ Men: Cambridge Reform and British Mathematics in the 19th Century A. D. D. Craik, University of St. Andrews, UK life at Cambridge to give the reader a glimpse inside its colleges, and it charts the evolution of the curric- This wide-ranging book tells the story of the ulum and the slow reforms that led to Cambridge’s remarkable William Hopkins, and his top “wran- dominance of British higher education. glers”, many of whom went on to illustrious careers as bishops, judges, politicians, scientists or educa- 2007. Approx. 432pp. 78 illus., 48 in colour Hardcover tors. It draws on first-hand accounts of 19th Century ISBN 978-1-84628-790-9

Ernst Zermelo An Approach to His Life and Work one or the other of these threads. The presentation H. Ebbinghaus, Universität Freiburg, Germany of his work explores motivations, aims, acceptance, In cooperation with: V. Peckhaus and influence. Selected proofs and information gleaned from unpublished notes and letters add to This biography attempts to shed light on all facets of the analysis. Zermelo’s life and achievements. Personal and scientific aspects are kept separate as far as coherence 2007. XIV, 356 p. 42 illus. Hardcover allows, in order to enable the reader to follow the ISBN 978-3-540-49551-2

David Hilbert’s Lectures on the Foundations of Arithmetic and Logic, 1894-1917 W. Ewald, University of Pennsylvania, Philadelphia, USA; Cantor and Dedekind; his early investigations into M. Hallett, McGill University, Montreal, Canada; W. Sieg, the relationship between arithmetic, set theory, Carnegie Mellon University, Pittsburgh, USA; U. Majer, and logic; his advocation of the use of the axiom- University of Göttingen, Germany (Hrsg.) atic method generally; his first engagement with the logical and semantical paradoxes; and the first This volume focuses on notes for lectures on the formal attempts to develop a logical calculus. The foundations of the mathematical sciences held by Volume also contains Hilbert’s address from 1895 Hilbert in the period 1894-1917. They document which formed the preliminary version of his famous Hilbert’s first engagement with ‘impossibility’ Zahlbericht (1897). proofs; his early attempts to formulate and address the problem of consistency, first dealt with in his 2007. Approx. 700 p. Hardcover work on geometry in the 1890s; his engagement ISBN 978-3-540-20605-7 with foundational problems raised by the work of

A Remarkable Collection of Babylonian Mathematical Texts Manuscripts in the Schøyen Collection: objects. The book is carefully written and organized. Cuneiform Texts The tablets are classified according to mathematical J. Friberg, Chalmers University of Technology, Sweden content and purpose, while drawings and pictures are provided for the most interesting tablets. The book analyzes the mathematical tablets from the private collection of Martin Schoyen. It includes 2007. Approx. 555 p. 259 illus. (Sources and Studies analyses of tablets which have never been studied in the History of Mathematics and Physical Sciences) before. This provides new insight into Babylonian Hardcover understanding of sophisticated mathematical ISBN 978-0-387-34543-7 springer.com 42 History of Mathematics

Tales of Mathematicians and Physicists

S. Gindikin, Rutgers University, Piscataway, NJ, USA enjoyed by those who love mathematics and physics. Transl. Russian: A. Shuchat 7 Choice

From the reviews 7 This lively and entertaining book This revised and greatly expanded second edition of tells “tales’’ of Cardano, Galileo, Huygens, Pascal, the Russian text contains a wealth of new informa- Gauss.... The reasoning of the scientists discussed is tion about the lives and accomplishments of more modernized so as to ease the reader’s path; thus this than a dozen scientists throughout five centuries book is not a scholarly discussion of the history of of history: from the first steps in algebra up to science readable only by experts, but a far more valu- new achievements in geometry in connection with able work: a readable introduction to the scientific physics. The heroes of the book are renowned work discussed and the historical context (both scien- figures from early eras, as well some scientists of last tific and social) in which it took place. Addressed to century. A unique mixture of mathematics, physics, a “general audience,” it deserves to have a wide one... and history, this volume provides biographical 7 Zentralblatt MATH glimpses of scientists and their contributions in the 7 This book will be enjoyable reading for anyone context of the social and political background of interested in the history of science. 7 Mathematical their times. Reviews 7 [T]he work is engagingly written and will be 2nd ed. 2007. XX, 382 p. Softcover ISBN 978-0-387-36026-3

Worlds Out of Nothing A Course in the History of Geometry in the selections and translations from original sources. It 19th Century provides both an overview of the growth of a major J. Gray, The Open University, Buckinghamshire, UK part of mathematics and offers practical guidance on the teaching of the history of mathematics. Based on the latest historical research, this is the first book to provide a course on the history of 2007. XXIII, 376 p. (Springer Undergraduate Mathematics geometry in the 19th century. The book is a compre- Series) Softcover hensive resource with full background material and ISBN 978-1-84628-632-2

Wolfgang Doeblin A Mathematician Rediscovered Academy of Sciences in Paris. The film of Agnes A. Handwerk, Hamburg, Germany; H. Willems, Handwerk and Harrie Willems documents scientific Amsterdam, The Netherlands and human aspects of this amazing discovery and throws new light on the startling circumstances of Wolfgang Doeblin, one of the great probabilists his death at the age of 25. I recommend it in the of the 20th century, was already widely known in strongest terms. the 1950s for his fundamental contributions to the Hans Föllmer, Faculty of Mathematics, Humboldt theory of Markov chains. His coupling method University, Berlin became a key tool in later developments at the interface of probability and statistical mechanics. But the 2007. DVD-Video NTSC (Springer VideoMATH) full measure of his mathematical stature became ISBN 978-3-540-71960-1 apparent only in 2000 when the sealed envelope containing his construction of diffusion processes 2007. DVD-Video PAL. (Springer VideoMATH) in terms of a time change of Brownian motion ISBN 978-3-540-71959-5 was finally opened, 60 years after it was sent to the History of Mathematics 43 springer.com

Set Theory The Third Millennium Edition, revised and chapter ends with a valuable historical survey and expanded there is an extensive bibliography. This will continue T. Jech, Mathematical Institute of the Academy of to be the bible for set theorists in the new century. Sciences of Czech Republic 7 The Mathematical Gazette 7 One of the classical textbooks and reference books From the reviews 7 Thomas Jech’s text has long in set theory is Jech’s Set Theory …7 Mathematical been considered a classic survey of the state of the Reviews set theory … . As every logician will know, this is a work of extraordinary scholarship, essential for 3rd rev. ed. Corr. 4th printing 2006. XIII, 769 p. (Springer any graduate logician who needs to know where the Monographs in Mathematics) Hardcover current boundaries of research are situated. Each ISBN 978-3-540-44085-7

Mathematical Masterpieces Further Chronicles by the Explorers a masterpiece of mathematical achievement. The A. Knoebel, Albuquerque, NM, USA; R. Laubenbacher, book includes numerous exercises and historical Virginia Bioinformatics Institute, Blacksburg, VA, USA; photographs. The authors’ goal is illuminate the J. M. Lodder, D. Pengelley, New Mexico State University, mathematical world in which we live, and in the Las Cruces, NM, USA process, to introduce students to the exciting world of mathematical discovery, conveying the thrill of This book introduces advanced undergraduates to exploration that motivates great mathematicians. the excitement of mathematical discovery, through close examination of original historical sources. 2007. Approx. 336 p. 74 illus. (Undergraduate Texts in Each chapter is anchored by a different story Mathematics / Readings in Mathematics) Softcover sequence of selected primary sources showcasing ISBN 978-0-387-33061-7

Mechanics and Natural Philosophy before the Scientific Revolution

W. R. Laird, Carleton University, Ottawa, ON, Canada; concerned with ancient mechanics and its transfor- S. Roux, Université Grenoble II, Grenoble, France (Eds.) mations in the Middle Ages; the second part, with the reappropriation of ancient mechanics and espe- This volume deals with a variety of moments in the cially with the reception of the Pseudo-Aristotelian history of mechanics when conflicts arose within Mechanica in the Renaissance; and the third and one textual tradition, between different traditions, final part, with early-modern mechanics in specific or between textual traditions and the wider world social, national, and institutional contexts. of practice. Its purpose is to show how the accom- modations sometimes made in the course of these 2007. Approx. 300 p. (Boston Studies in the Philosophy conflicts ultimately contributed to the emergence of of Science, Volume 254) Hardcover modern mechanics. The first part of the volume is ISBN 978-1-4020-5966-7 springer.com 44 History of Mathematics

David Hilbert’s Lectures on the Foundations of Physics, 1915-1927: Relativity, Quantum Theory and Epistemology U. Majer, University of Göttingen, Germany; T. Sauer, in physics (1916), the intricate relation between California Institute of Technology, Pasadena, CA, USA; nature and mathematical knowledge (1921), and H. Schmidt, University of Osnabrück, Germany (Hrsg.) the subtle question whether what Hilbert calls the ‘world equations’ are physically complete (1923). This Volume has three sections, General Relativity, The last section deals with quantum theory in its Epistemological Issues, and Quantum Mechanics. early, advanced and mature stages. Hilbert held The core of the first section is Hilbert’s two semester lecture courses on the mathematical foundations of lecture course on ‘The Foundations of Physics’ quantum theory twice, before and after the break- (1916/17). This is framed by Hilbert’s published through in 1926. These documents bear witness to ‘First and Second Communications’ on the one of the most dramatic changes in the foundations ‘Grundlagen der Physik’ (1915, 1917). The section of science. closes with a lecture on the new concepts of space and time held in Bucharest in 1918. The episte- 2008. Approx. 650 p. Hardcover mological issues concern the principle of causality ISBN 978-3-540-20606-4

Mathematics and Culture in Europe

M. Manaresi (Ed.) something about prime numbers, Galois’ theory, or simply about the relationship between science, It is not true that mathematics has never been able mathematics and power at Napoleon’s times. to arouse people’s interest. At least, this is our feeling This volume, which has its origin in the activities as mathematicians when we meet the general public performed in Bologna in 2004, is dedicated to all to explain what we are dealing with in our work, those who are curious about mathematics, but also what is the usefulness of mathematics and how it more generally about theatre, cinema, literature, arts becomes possible to catch its harmony and beauty. and science. Also the cinema changed its attitude on the matter, Thanks to the DVD one can relive various events and some screenplays started to show mathemati- through the voices and the images of the partici- cians engaged in their work while some recent pants. theatrical pieces have a mathematician as a main character. 7 For PC und Mac. For the complete system require- These considerations stimulated some of us to orga- ments see: springer.com nize the review Mathematics and Theatre, which offered to a general audience the opportunity to 2007. Approx. 401 p., 192 figures, With DVD. Softcover attend performances and, at the same time, to hear ISBN 978-3-540-71963-2

Thomas Harriot’s Artis Analyticae Praxis An English Translation with Commentary relates to corresponding pages in the manuscript M. Seltman, Eltham, London, UK; R. Goulding, Univer- papers, enabling exploration of Harriot’s novel and sity of Notre Dame, IN, USA advanced mathematics. This publication provides the basis for a reassessment of the development of This is the first English translation of Thomas algebra. Harriot’s seminal Artis Analyticae Praxis, first published in Latin in 1631. It has recently become 2007. Approx. 315 p. 30 illus. (Sources and Studies in the clear that Harriot’s editor substantially rearranged History of Mathematics and Physical Sciences) Hardcover the work, and omitted sections beyond his compre- ISBN 978-0-387-49511-8 hension. Commentary included with this translation Mathematical Biology 45 springer.com

MacLaurin’s Physical Dissertations

I. Tweddle, University of Strathclyde, UK This book presents important works by the Scottish mathematician Colin MacLaurin (1698-1746), From the reviews 7 Anyone seriously interested translated in English for the first time. It includes in Colin Maclaurin (1698-1746) or in eighteenth- three of the mathematician’s less known and often century mathematical physics will welcome this hard to obtain works. A general introduction book. … the assiduous reader will be rewarded in puts the works in context and gives an outline of many ways, both by working through Tweddle’s MacLaurin’s career. Each translation is also accom- introductions, notes, and appendices, and by reading panied by an introduction and analyzed both in Maclaurin’s own words in Tweddle’s clear and accu- modern terms and from a historical point of view. rate translations. I find the book refreshing … we have the result of years of profound study and deliberation, 2007. VII, 220 p. (Sources and Studies in the History of careful textual analysis, and sound understanding Mathematics and Physical Sciences) Hardcover and explanation of the relevant mathematics and ISBN 978-1-84628-593-6 physics. 7 MathDL Mathematical Biology

Mathematical Biology I and II I. An Introduction readers quickly find key words. ... I recommend the II. Spatial Models and Biomedical Applications new and expanded third edition to any serious young J. D. Murray, University of Washington, Seattle, WA, USA student interested in mathematical biology who already has a solid basis in applied mathematics. From the reviews 7 Murray has produced a magnifi- 7 Siam cent compilation of mathematical models and their applications in biology. 7 Nature 3rd ed. 2002. Corr. 2nd printing 2004. XXIII, 551 p. 7 Murray’s Mathematical Biology belongs on the shelf 189 illus. (Interdisciplinary Applied Mathematics, of any person with a serious interest in mathematical Volume 17) Hardcover biology. 7 Bulletin of Mathematical Biology ISBN 978-0-387-95223-9 7 Murray’s Mathematical Biology is a classic that belongs on the shelf of any serious student or 3rd ed. 2003. XXV, 811 p. 296 illus. (Interdisciplinary researcher in the field. Together the two volumes Applied Mathematics, Volume 18) Hardcover contain well over 1000 references, a rich source of 978-0-387-95228-4 7 material, together with an excellent index to help

Bulletin of Mathematical Biology A Journal Devoted to Research at the Junction JOURNAL of Computational, Theoretical and Experimental gists alike. An ideal article would be a symbiotic Biology combination of theory and experiment. Also very Official Journal of The Society for Mathematical welcome are papers that provide documentation of Biology a purely theoretical advance together with a clear exposition of how this advance furthers biological P. K. Maini, Centre for Mathematical Biology, understanding. Mathematical Institute, Oxford, UK ISSN 0092-8240 (print version) TheBulletin of Mathematical Biology aims to be of ISSN 1522-9602 major interest to theorists and experimental biolo-

available on SPRINGERLINK springer.com 46 Optimization and Operations Research

Mathematical Biology An Introduction with Maple and Matlab interest. It includes new chapters on parasites, R. W. Shonkwiler, Georgia Institute of Technology, cancer, and phylogenetics, as well as an introduc- Atlanta, Georgia, USA tion to online resources for DNA and protein lookups and popular pattern matching tools such A greatly expanded and updated edition of the as BLAST. One major new topic presented in is popular Introduction to the Mathematics of Biology that of genomics, a rapidly growing field. Just as (Yeargers, Shonkwiler and Herod, Birkhäuser mathematics once became indispensable for the 1996), this textbook aims to present mathematical study of physics, with genomics mathematics has biology as not merely the intrusion of one science become indispensable for biology. The discussion into another, but rather as a field with a unity of its of genomics in this book also presents the many own. It retains and expands on the concept of the subdisciplines it has given rise to, and it intro- “computer biology laboratory,” giving students a duces the emerging field of algebraic statistics as a general perspective of the field before proceeding powerful tool in genomics. to more specialized topics. The book is a product Mathematical Biology includes extensive exercises, of extensive classroom experience, and the student problems and examples to help students grasp response to it has been exhilarating due to its focus the concepts fully. A year of calculus is required on problems of contemporary interest such as to understand the material presented, while no cancer, genetics and aging. previous coursework in biology is necessary. The A unique feature of the book is its integration of a mathematics presented proceeds from the simple to computer algebra system into the flow of ideas, in a the more complex, while the biology proceeds from supporting but unobtrusive role. Syntax for both the the study of populations down to the molecular Maple and Matlab systems is provided in a side-by- level. Overall, the book will be appropriate for side format. The use of a computer algebra system undergraduate and graduate students studying gives students the opportunity to examine “what mathematics or biology, and it also lends itself well if” scenarios, thereby allowing them to to grasp to self-study for scientists and researchers who wish important mathematical and biological concepts in to explore this exciting frontier of the applications of a way not otherwise possible. For students without mathematics and computers in the natural sciences. access to Maple or Matlab, each topic presented is complete. Graphic visualizations are provided for all 2nd ed. 2007. Approx. 430 p. 156 illus. Hardcover mathematical results. ISBN 978-0-387-70983-3 This book focuses on problems of contemporary Optimization and Operations Research

Topics on Concentration Phenomena and Problems with Multiple Scales A. Braides, Università di Roma ‘Tor Vergata’, Italy; passage from atomistic systems to continuous func- V. Chiadò Piat, Politecnico di Torino, Italy (Eds.) tionals, from competition between bulk and surface energies, from various types of homogenization The study of variational problems showing multi- processes, and on concentration effects in Ginzburg- scale behaviour with oscillation or concentration Landau energies and in subcritical growth problems. phenomena is a challenging topic of very active research. This volume collects lecture notes on the 2006. XI, 316 p. (Lecture Notes of the Unione Matematica asymptotic analysis of such problems when multi- Italiana, Volume 2) Softcover scale behaviour derives from scale separation in the ISBN 978-3-540-36241-8 Optimization and Operations Research 47 springer.com

Set-Valued Analysis and Enlargements of Monotone Operators

R. Burachik, University of South Australia, Mawson ferentials and of sums of monotone operators. Lakes, Australia; A. Iusem, IMPA, Rio de Janiero, Brazil The second part of the monograph contains new results, all of them established during the last This book gives a clear presentation of set-valued decade, on a concept of enlargements of monotone analysis and monotone operators and also pres- operators, which is then applied to several fields ents several important new results in the field. The of interest in applied mathematcs like bundle-type first part of the book begins with a self-contained methods, augmented Lagrangian methods or varia- and encompassing overview of several key topics tional inequalities and recently developed versions within set-valued analysis. The authors present basic of proximal point algorithms. The results in the notions of set convergence, and of continuity of set- second part use extensively the concepts presented valued mappings, together with the many important in the first one. results in infinite-dimensional convex analysis, leading to the classical fixed point results due to 2007. Approx. 300 p. (Springer Optimization and Its Ekeland, Caristi and Kakutani. Next, an in-depth Applications, Volume 8) Hardcover introduction to monotone operators is developed, ISBN 978-0-387-69755-0 emphasizing results related to maximality of subdif-

Time-Varying Network Optimization

X. Cai, D. Sha, C. Wong, The Chinese University of Hong and the Chinese postman problem are presented in Kong, China a chapter together with the time-varying generalized problem. While these topics are examined within This text describes a series of models, proposi- the framework of time-varying networks, each tions, and algorithms developed in recent years on chapter is self-contained so that each can be read time-varying networks. References and discus- – and used – separately. sions on relevant problems and studies that have appeared in the literature are integrated in the book. 2007. XVI, 224 p. (International Series in Operations Its eight chapters consider problems including the Research & Management Science, Volume 103) Hard- shortest path problem, the minimum-spanning tree cover problem, the maximum flow problem, and many ISBN 978-0-387-71214-7 more. The time-varying traveling salesman problem

Stochastic Learning and Optimization A Sensitivity-Based Approach applied. This book provides a unified framework X. Cao, Hong Kong University of Sciences and Tech- based on a sensitivity point of view. It also intro- nology, Hong Kong, China duces new approaches and proposes new research topics within this sensitivity-based framework. This Performance optimization is vital in the design and new perspective on a popular topic is presented by a operation of modern engineering systems, including well respected expert in the field. communications, manufacturing, robotics, and logistics. Most engineering systems are too compli- 2007. Approx. 500 p. Hardcover cated to model, or the system parameters cannot be ISBN 978-0-387-36787-3 easily identified, so learning techniques have to be springer.com 48 Optimization and Operations Research

Throughput Optimization in Robotic Cells

M. W. Dawande, University of Texas at Dallas, Rich- over the last 25 years for the various realistic models ardson, TX, USA; H. N. Geismar, Prairie View A&M Univer- of robotic cells. This book is ideally suited for use in sity, Texas, USA; S. P. Sethi, C. Sriskandarajah, University a graduate course or a research seminar on robotic of Texas at Dallas, Richardson, TX, USA cells.

Throughput Optimization In Robotic Cells 2007. Approx. 430 p. (International Series in Opera- provides practitioners, researchers, and students tions Research & Management Science, Volume 101) with up-to-date algorithmic results on sequencing of Hardcover robot moves and scheduling of parts in robotic cells. ISBN 978-0-387-70987-1 It brings together the structural results developed

Network Science, Nonlinear Science and Dynamic Game Theory Applied to the Study of Infrastructure Systems T. L. Friesz, Pennsylvania State University, Philadelphia, better solve problems from transportation networks PA, USA (Ed.) to telecommunications, Internet, supply chains and more. This book is written by leading scholars in Network Science, Nonlinear Science and Infrastructure 2007. Approx. 332 p. (International Series in Opera- Systems, expressly to develop common theoretical tions Research & Management Science, Volume 102) underpinnings for better solutions to modern Hardcover infrastructural problems. The book is dedicated to ISBN 978-0-387-71080-8 the formulation of infrastructural tools that will

Foundations of Optimization in Finite Dimensions

O. Guler, University of Maryland, Baltimore, MD, USA of mathematical programming, such as necessary and sufficient optimality conditions for optimality, This book is intended as a textbook to be used convex analysis and duality, are covered in great in a first graduate level course, and covers the detail, often from multiple points of view. A distinc- fundamental principals of optimization in finite tive feature of this book is its set of worked-out dimensions. It develops the necessary background examples and problems, including hundreds of well- material in multivariable calculus using coordinates chosen problems and important examples. as well as in a coordinate-free manner, so that the recent developments such as semidefinite program- 2006. Approx. 350 p. Hardcover ming can be dealt with ease. All the standard topics ISBN 978-0-387-34431-7

Ordinal Optimization Soft Computing for Hard Problems sive models involving possible stochastic effects Y. Ho, Harvard University, Cambridge, MA; Q. Zhao, and discrete choices. This book establishes distinct Q. S. Jia, Tsinghua University, Beijing, China advantages of the “softer” ordinal approach for search-based type problems, analyzes its general Performance evaluation of increasingly complex properties, and shows the many orders of magnitude human-made systems requires the use of simula- improvement in computational efficiency that is tion models. However, these systems are difficult possible. to describe and capture by succinct mathematical models. The purpose of this book is to address the 2007. Approx. 400 p. Hardcover difficulties of the optimization of complex systems ISBN 978-0-387-37232-7 via simulation models or other computation-inten- Optimization and Operations Research 49 springer.com

Integrated Methods for Optimization

J. N. Hooker, Carnegie Mellon University, Pittsburgh, This book integrates the key concepts of mathemat- PA, USA ical programming (MP) and constraint programming (CP) into a unified framework that allows From the reviews 7 Presents a synthesis of the them to be generalized and combined. The unifica- integer programming and constraint programming tion of MP and CP creates optimization methods approaches. … The book includes numerous examples that have much greater modeling power, increased and exercises. Hooker has done a particularly good computational speed, and a sizeable reduction job of organizing the … array of options within the computational coding. This integration along with framework. … the book will help readers to under- constraint programming being incorporated into a stand the algorithms used within various software number of programming languages, brings the field packages … . This book is highly recommended, both a step closer to being able to simply state a problem as a reference for researchers working at the intersec- and having the computer solve it. tion of constraint programming and integer programming and as a textbook for graduate level courses … 2007. XIV, 486 p. (International Series in Operations 7 MathDL Research & Management Science, Volume 100) Hard- cover ISBN 978-0-387-38272-2

Nonlinear Integer Programming

D. Li, The Chinese University of Hong Kong, China; aims to bring the theoretical foundation and solu- X. Sun, Shanghai University, China tion methods for nonlinear integer programming to students and researchers in optimization, operations A combination of both Integer Programming and research, and computer science. Nonlinear Optimization, this is a powerful book that surveys the field and provides a state-of-the-art 2006. XXII, 440 p. (International Series in Operations treatment of Nonlinear Integer Programming. It Research & Management Science, Volume 84) Hardcover is the first book available on the subject. The book ISBN 978-0-387-29503-9

Models and Solutions in Inventory Management

J. A. Muckstadt, A. Sapra, Cornell University, Ithaca, NY, tries to establish relationships between the dicussed USA models and real situations and discusses some examples in detail. Not directly competitive with This textbook presents models and solutions in other textbooks in this field, (more mathematical inventory management. It begins with a “must-read” than some, less than others) this graduate textbook chapter discussing basic terminology, concepts, will appeal to senior and first year graduate students taxonomy, and tenets of inventory system and in operations research, industrial engineering, and common mathematical assumptions underlying the quantitative MBA programs and can also serve as a models. With a systematic organization, it then pres- reference to persons in the industry. ents various models such as the EOQ model, lot- sizing models, Newsvendor model, periodic review 2008. Approx. 305 p. (Springer Series in Operations models with variable and fixed ordering cost, and Research and Financial Engineering) Hardcover a continuous time model. Additionally, it discusses ISBN 978-0-387-24492-1 methods in multiechelon systems. In summary it springer.com 50 Optimization and Operations Research

Numerical Optimization

J. Nocedal, Northwestern University, Evanston, IL, USA; Optimization is an important tool used in decision S. Wright, University of Wisconsin, WI, USA science and for the analysis of physical systems used in engineering. One can trace its roots to the From the reviews 7 The books looks very suitable to Calculus of Variations and the work of Euler and be used in an graduate-level course in optimization Lagrange. This natural and reasonable approach for students in mathematics, operations research, to mathematical programming covers numerical engineering, and others. Moreover, it seems to be very methods for finite-dimensional optimization prob- helpful to do some self-studies in optimization, to lems. It begins with very simple ideas progressing complete own knowledge and can be a source of new through more complicated concepts, concentrating ideas.... I recommend this excellent book to everyone on methods for both unconstrained and constrained who is interested in optimization problems. 7 Math- optimization. ematical Methods of Operations Research 2nd ed. 2006. XXII, 664 p. (Springer Series in Operations Research and Financial Engineering) Hardcover ISBN 978-0-387-30303-1

Introduction to Mathematical Systems Theory A Behavioral Approach This is a book about modelling, analysis and control J. W. Polderman, University of Twente, Enschede, The of linear time- invariant systems. The book uses Netherlands; J. C. Willems, University of Leuven, Belgium what is called the behavioral approach towards mathematical modelling. An essential feature of From the reviews 7 The present book is a major using the behavioral approach is that it allows original contribution to the literature and is of high these and similar concepts to be introduced in a quality. The most original chapters are the ‘strongly representation-free manner. Thus a system is viewed behavioural’ Chapters 1-6 and the historical preface. as a dynamical relation between manifest and latent The introduction is carefully written and each chapter variables. The emphasis is on dynamical systems ends with a precise recapitulation of what has been that are represented by systems of linear constant done. It is well organized, technically well written, coefficients. The book contains numerous exercises, philosophically nice, and contains a wealth of exam- including simulation problems, and examples, ples and exercises. It is also well self-contained for its notably of mechanical systems and electrical audience…scientific honesty dictates to congratulate circuits. the authors and to recommend this book as a textbook to a large public of systems and control students, and 2nd ed. 2007. Approx. 455 p. 89 illus. (Texts in Applied especially for those having already followed a first Mathematics, Volume 26) Hardcover course on linear systems. 7 International Journal of ISBN 978-0-387-35763-8 Robust and Nonlinear Control

Handbook of Optimization in Telecommunications

M. G. Resende, AT & T Labs Research, Florham Park, NJ, networks, routing, network protection, grooming, USA; P. M. Pardalos, University of Florida, Gainesville, FL, restoration, wireless communications, network loca- USA (Eds.) tion and assignment problems, Internet protocol, World Wide Web, and stochastic issues in telecom- This comprehensive handbook brings together munications. The book’s objective is to provide a experts who use optimization to solve problems that reference tool for the increasing number of scientists arise in telecommunications. It is the first book to and engineers in telecommunications who depend cover in detail the field of optimization in telecom- upon optimization. munications. Recent optimization developments that are frequently applied to telecommunica- 2006. XXXI, 1134 p. Hardcover tions are covered. The spectrum of topics covered ISBN 978-0-387-30662-9 includes planning and design of telecommunication Probability Theory and Statistics 51 springer.com Probability Theory and Statistics

Random Fields and Geometry

R. Adler, Israel Institute of Technology, Haifa, Israel; J. new relationships between geometry and prob- Taylor, Stanford University, CA, USA ability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text This monograph is devoted to a completely new will serve as a basic reference for all those inter- approach to geometric problems arising in the study ested in the companion volume of the applications of random fields. The groundbreaking material of the theory. These applications, to appear in a in Part III, for which the background is carefully forthcoming volume, will cover areas as widespread prepared in Parts I and II, is of both theoretical and as brain imaging, physical oceanography, and practical importance, and striking in the way in astrophysics. which problems arising in geometry and probability are beautifully intertwined. 2007. XVIII, 454 p. (Springer Monographs in Math- “Random Fields and Geometry” will be useful for ematics) Hardcover probabilists and statisticians, and for theoretical and ISBN 978-0-387-48112-8 applied mathematicians who wish to learn about

Applied Probability and Queues

S. Asmussen, University of Lund, Sweden resource to all those interested in applied probability and stochastic modelling. It provides a clear and From the reviews 7 I would rate it as essential for any careful unified treatment of traditional queueing library … and I can happily recommend it, espe- theory … . The material is self-contained … . cially to young researchers starting out in the field. Researchers and graduate students interested in these 7 Journal of the Operational Research Society fields will no doubt want to acquire this book.7 Short 7 This makes APQ the major reference in applied Book Reviews probability. … is definitely indispensable for researchers in applied probability. 7 Operations 2nd ed. 2003. CDXXXVIII, 12 p. 46 illus. (Stochastic Research Letters Modelling and Applied Probability, Volume 51) Hard- 7 This book, which focuses mainly on queueing cover theory and the basic structures … will be a valuable ISBN 978-0-387-00211-8

Stochastic Simulation Algorithms and Analysis the ideas is illustrated by discussing a wide range S. Asmussen, University of Aarhus, Denmark; of applications and the models that have found P. W. Glynn, Stanford University, Stanford, CA, USA wide usage. Given the wide range of examples, exercises, and applications students, practitioners Sampling-based computational methods have and researchers in probability, statistics, operations become a fundamental part of the numerical toolset research, economics, finance, engineering, as well of practitioners and researchers across an enormous as biology and chemistry and physics will find the number of different applied domains and academic book of value. disciplines. This book provides a broad treatment of such sampling-based methods, as well as accom- 2007. Approx. 300 p. 44 illus. (Stochastic Modelling and panying mathematical analysis of the convergence Applied Probability, Volume 57) Hardcover properties of the methods discussed. The reach of ISBN 978-0-387-30679-7 springer.com 52 Probability Theory and Statistics

Stochastic Analysis and Applications The Abel Symposium 2005 over presented the newest developments within the Proceedings of the Second Abel Symposium, exciting and fast growing field of stochastic analysis. Oslo, July 29 - August 4th, 2005 This volume combines both papers from the invited F. E. Benth, G. Di Nunno, T. Lindstrøm, B. Øksendal, speakers and contributions by the presenting University of Oslo, Norway; T. Zhang, University of lecturers. In addition, it includes the Memoirs that Manchester, UK (Eds.) Kiyoshi Ito wrote for this occasion.

The Abel Symposium 2005 was organized as a 2007. Approx. 690 p. (Abel Symposia, Volume 2) Hard- tribute to the work of Kiyosi Ito on the occasion of cover his 90th birthday. Distinguished researchers from all ISBN 978-3-540-70846-9

Markovian Demand Inventory Models

D. Beyer, Hewlett-Packard Laboratories, CA, USA; is a central problem in Operations Management. F. Cheng, IBM Thomas J. Watson Research Center, NJ, The central problem is to find the amount to be USA; S. P. Sethi, University of Texas at Dallas, TX, USA; produced or purchased in order to maximize the M. Taksar, University of Missouri-Columbia, USA total expected profit, or minimize the total expected cost. This text provides a superbly researched insight into Markovian demand inventory models. The result 2007. Approx. 260 p. (International Series in Opera- of ten years of research, this work covers all aspects tions Research & Management Science, Volume 108) of demand inventory where they are modeled Hardcover by Markov processes. Inventory management is ISBN 978-0-387-71603-9 concerned with matching supply with demand and

A Basic Course on Probability Theory

R. Bhattacharya, University of Arizona, Tucson, AZ, USA; such as coin flips and conundrums such as the E. C. Waymire, Oregon State University, Corvallis, OR, Monty Hall problem. An alternative is to first USA develop measure theory and analysis, and then add interpretation. Bhattacharya and Waymire take A Basic Course in Probability Theoryis a pleasure the second path. To illustrate the authors’ frame of to read and provides a fine answer to the question: reference, consider the two definitions they give of How do you construct Brownian motion from conditional expectation. The first is as a projection scratch, given that you are a competent analyst? of L2 spaces. There are at least two ways to develop probability theory. The more familiar path is to treat it as its 2007. Approx. 220 p. (Universitext) Softcover own discipline, and work from intuitive examples ISBN 978-0-387-71938-2

Measure, Integral and Probability

M. Capinski, Nowy Sacz, Poland; P. E. Kopp, University 7 A clear, understandable treatment of a very of Hull, UK problematic area…The authors are to be commended for their lucid writing style. 7 Journal of the American From the reviews 7 The level of explanation is excel- Statistical Association lent and great care has gone into providing motivation for the study of all aspects of the material…Overall, 2nd ed. 2004. XV, 311 p. 23 illus. (Springer Undergrad- this is an excellent and interesting text. 7 Times Higher uate Mathematics Series) Softcover Education Supplement ISBN 978-1-85233-781-0 Probability Theory and Statistics 53 springer.com

An Introduction to the Theory of Point Processes, Volume II

D. Daley, Australian National University, Canberra, ACT, models and applications. It also has three appen- Australia; D. Vere-Jones, Victoria University, Wellington, dices that review the mathematical background New Zealand needed mainly in Volume II. Volume II sets out the basic theory of random Point processes and random measures find wide measures and point processes in a unified setting applicability in telecommunications, earthquakes, and continues with the more theoretical topics of image analysis, spatial point patterns and stereology, the first edition: limit theorems, ergodic theory, to name but a few areas. The authors have made a Palm theory, and evolutionary behaviour via major reshaping of their work in their first edition martingales and conditional intensity. The very of 1988 and now present their An Introduction to substantial new material in this second volume the Theory of Point Processes in two volumes with includes expanded discussions of marked point subtitles Volume I: Elementary Theory and Methods processes, convergence to equilibrium, and the and Volume II: General Theory and Structure. structure of spatial point processes. Volume I contains the introductory chapters from the first edition together with an account of basic 2nd ed. 2007. Approx. 560 p. (Probability and its Applica- models, second order theory, and an informal tions) Hardcover account of prediction, with the aim of making the ISBN 978-0-387-21337-8 material accessible to readers primarily interested in

Séminaire de Probabilités XL

C. Donati-Martin, Université Paris VI, Paris, France; on local time-space calculus. Other topics from M. Émery, Université Strasbourg I, France; A. Rouault, stochastic processes and stochastic finance include Université des Versailles, France; C. Stricker, Université three contributions by A.S. Cherny on general des Besançon, France (Eds.) approaches to arbitrage pricing.

Two noteworthy features of the 40th volume of 2007. Approx. 470 p. (Lecture Notes in Mathematics / Séminaire de Probabilités are L. Coutin’s advanced Séminaire de Probabilités, Volume 1899) Softcover course on calculus driven by fractional Brownian ISBN 978-3-540-71188-9 motion, and a series of seven interrelated works

The Random-Cluster Model

G. Grimmett, University of Cambridge, UK supercritical phases, together with clear statements of important open problems. It includes treatment The random-cluster model has emerged as a key of the first-order (discontinuous) phase transition. tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to 2006. XIII, 377 p. 37 illus. (Grundlehren der mathema- include Ising and Potts models, and its analysis is a tischen Wissenschaften, Volume 333) Hardcover mix of arguments from probability and geometry. ISBN 978-3-540-32890-2 This study contains accounts of the subcritical and

Multivariate Statistics: Exercises and Solutions

W. Härdle, Humboldt-Universität zu Berlin, Germany; The first part of this book is devoted to graphical Z. Hlavka, Charles University in Prague, Czech Republic techniques. The second deals with multivariate random variables and presents the derivation of The authors have cleverly used exercises and their estimators and tests for various practical situations. solutions to explore the concepts of multivariate The final section contains a wide variety of exercises data analysis. Broken down into three sections, in applied multivariate data analysis. this book has been structured to allow students in economics and finance to work their way through 2007. Approx. 390 p. Softcover a well formulated exploration of this core topic. ISBN 978-0-387-70784-6 springer.com 54 Probability Theory and Statistics

Brownian Motion and Stochastic Calculus

I. Karatzas, Columbia University, New York, NY, USA; The authors have done a good job.7 Mathematical S. E. Shreve, Carnegie Mellon University, Pittsburgh, PA, Reviews USA 2nd ed. 1991. Corr. 8th printing 2005. XXIII, 470 p. 10 From the reviews 7 A valuable book for every grad- illus. (Graduate Texts in Mathematics, Volume 113) uate student studying stochastic process, and for those Softcover who are interested in pure and applied probability. ISBN 978-0-387-97655-6

Queuing Theory A Linear Algebraic Approach numerous examples and exercises to illustrate L. Lipsky, University of Connecticut, Storrs, CT, USA crucial points.

This textbook is a very good introduction to 2nd ed. 2007. Approx. 500 p. Hardcover queueing analysis using matrix analytic techiques. ISBN 978-0-387-49704-4 The book is readable and the author provides

Stochastic Differential Equations An Introduction with Applications single resource for learning the stochastic calculus … B. Øksendal, University of Oslo, Norway 7 riskbook.com 7 [A] modern classic... 7 The Mathematical Gazette From the reviews 7 This is a highly readable and 7...certainly one of the best books on the subject, it refreshingly rigorous introduction to stochastic will be very helpful to any graduate students and also calculus. … This is not a watered-down treatment. It very valuable for any analysts of financial market. is a serious introduction that starts with fundamental 7 Physicalia measure-theoretic concepts and ends, coincidentally, with the Black-Scholes formula as one of several 6th ed. 2003. Corr. 4th printing 2007. XXX, 374 p. 15 illus. examples of applications. This is the best (Universitext) Softcover ISBN 978-3-540-04758-2

Heavy-Tail Phenomena Probabilistic and Statistical Modeling tical background, some familiarity with time series S. I. Resnick, Cornell University, Ithaca, NY, USA analysis, and ability to use a statistics package. This work will serve second-year graduate students and This comprehensive text gives an interesting and researchers in the areas of applied mathematics, useful blend of the mathematical, probabilistic statistics, operations research, electrical engineering, and statistical tools used in heavy-tail analysis. It and economics. is uniquely devoted to heavy-tails and emphasizes both probability modeling and statistical methods 2007. XIX, 404 p. (Springer Series in Operations Research for fitting models. and Financial Engineering) Hardcover Prerequisites for the reader include a prior course in ISBN 978-0-387-24272-9 stochastic processes and probability, some statis- Quantitative Finance 55 springer.com

Probability Volume I and II From the reviews 7 It is clear that this book contains A. N. Shiryaev, Steklov Mathematical Institute, Moscow, important and interesting results obtained through Russia a long time period, beginning with the classical Transl. Russian: S. S. Wilson, Technical Translation Bernoulli’s law of large numbers, and ending with Services, Cheltanham, UK very recent results concerning convergence of martingales and absolute continuity of probability This book contains a systematic treatment of prob- measures. Let us note especially that the great number ability from the ground up, starting with intuitive of ideas, notions and statements in the book are ideas and gradually developing more sophisticated well-motivated, explained in detail and illustrated subjects, such as random walks, martingales, by suitably chosen examples and a large number of Markov chains, ergodic theory, weak convergence exercises. Thus, the present book is a synthesis of all of probability measures, stationary stochastic significant classical ideas and results, and many of the processes, and the Kalman-Bucy filter. Many major achievements of modern probability theory. In examples are discussed in detail, and there are a the whole it is a welcome addition to mathematical large number of exercises. The book is accessible to literature and can become an indispensable textbook advanced undergraduates and can be used as a text for courses in stochastics. 7 Zentralblatt or for self-study. The third edition contains new problems and exer- Volume I. 3rd ed. 2007. XII, 520 p. 47 illus. (Graduate cises, new proofs, expanded material on financial Texts in Mathematics, Volume 95/1) Hardcover mathematics, financial engineering, and math- ISBN 978-0-387-72205-4 ematical statistics, and a final chapter on the history of probability theory. Volume II. 3rd ed. 2007. Approx. 430 p. (Graduate Texts in Mathematics, Volume 95/2) Hardcover ISBN 978-0-387-72207-8 Quantitative Finance

Interest Rate Models - Theory and Practice With Smile, Inflation and Credit pedagogically fresh. The authors’ applied background D. Brigo, F. Mercurio, Banca IMI, Milan, Italy allows for numerous comments on why certain models have (or have not) made it in practice. The theory is From the reviews 7 The text is no doubt my favorite interwoven with detailed numerical examples…For on the subject of interest rate modeling. It perfectly those who have a sufficiently strong mathematical combines mathematical depth, historical perspective background, this book is a must. 7 Short Book Reviews and practical relevance. The fact that the authors combine a strong mathematical (finance) background 2nd ed. Corr. 3rd printing 2007. LV, 981 p. 124 illus. with expert practice knowledge (they both work in a (Springer Finance) Hardcover bank) contributes hugely to its format. I also admire ISBN 978-3-540-22149-4 the style of writing: at the same time concise and

Mathematics for Finance An Introduction to Financial Engineering the topics in a mathematically rigorous manner. M. Capinski, National Louis University, Nowy Sacz, 7 Zentralblatt MATH Poland; T. Zastawniak, University of York, UK 7 The reviewer can only congratulate the authors with successful completion of a difficult task of writing From the reviews 7 This text is an excellent introduc- a useful textbook on a traditionally hard topic. 7 The tion to Mathematical Finance. Armed with a knowl- Australian Mathematical Society Gazette edge of basic calculus and probability a student can use this book to learn about derivatives, interest rates 1st ed. 2003. 3rd printing 2005. X, 310 p. 75 illus. and their term structure and portfolio management. (Springer Undergraduate Mathematics Series) Softcover The text serves as an easily understood introduction ISBN 978-1-85233-330-0 to the economic concepts but also manages to cover springer.com 56 Quantitative Finance

The Mathematics of Arbitrage

F. Delbaen, ETH Zürich, Switzerland; W. Schachermayer, notes along the way as they formally develop concepts. Technische Universität Wien, Austria … I recommend it highly to theoretically-inclined financial engineers and researchers. From the reviews 7 As a learning device, I think this 7 www.riskbook.com works really well. The second half of the book allows readers to ‘put to use’ the mathematics they learn in 2006. XVI, 373 p. (Springer Finance) Hardcover the first half. I really like the authors’ writing style. ISBN 978-3-540-21992-7 They provide plenty of intuitive insights and historical

Linear Estimation and Detection in Krylov Subspaces

G. K. Dietl, Technische Universität München, Germany which are typically desired in wireless communications systems. This book focuses on the foundations of linear esti- The investigations include mation theory which is essential for effective signal 7 exact computational complexity considerations processing. In its first part, it gives a comprehensive and overview of several key methods like reduced-rank 7 performance analysis based on extrinsic informa- signal processing and Krylov subspace methods of tion transfer charts as well as Monte-Carlo simula- numerical mathematics. Based on the derivation tions. of the multistage Wiener filter in its most general form, the relationship between statistical signal 2007. Approx. 200 p. (Foundations in Signal Processing, processing and numerical mathematics is presented. Communications and Networking) Hardcover In the second part, the theory is applied to iterative ISBN 978-3-540-68478-7 multiuser detection receivers (Turbo equalization)

Duality in Mathematical Finance

M. Frittelli, Università degli Studi di Firenze, Italy; The powerful tools of convex analysis and duality S. Biagini, Università degli Studi di Perugia, Italy; theory are systematically applied to investigate G. Scandolo, Università degli Studi di Firenze, Italy these topics, under very general assumptions on the financial markets. This monograph presents an advanced and unified This duality approach reveals the prominent role of treatment of four important issues that have the investor’s preferences in all these fundamental dominated the theoretical research in mathematical issues and contributes to a deeper understanding of finance for the last ten years: (1) the fundamental the economic aspects of the theory. theorem of asset pricing; (2) utility maximization in incomplete markets; (3) pricing in incomplete 2008. Approx. 150 p. (Springer Finance) Hardcover markets; (4) the risk measurement of a static payoff ISBN 978-3-540-40108-7 and of a cash-flow stream.

Implementing Models in Quantitative Finance: Methods and Cases

G. Fusai, Università del Piemonte Orientale, Novara, to a concrete problem arising in applied finan- Italy; A. Roncoroni, ESSEC, Cergy Pontoise, France cial management and guides the user towards a computer implementation. The appendices contain This book puts numerical methods in action for the “crash courses” in VBA and Matlab programming purpose of solving practical problems in quantita- languages. A companion CD provides ready-to-run tive finance. The first part develops a toolkit in codes (VBA, MATLAB). numerical methods for finance. The second part proposes twenty self-contained cases covering 2007. Approx. 650 p. With CD-ROM. (Springer Finance) model simulation, asset pricing and hedging, risk Hardcover management, statistical estimation and model ISBN 978-3-540-22348-1 calibration. Each case develops a detailed solution Quantitative Finance 57 springer.com

Monte Carlo Methods in Financial Engineering LANCHESTER P. Glasserman, Columbia University, New York, NY, USA 7 Glasserman’s new book is a remarkable presenta- PRIZE tion of the current state of the art of Monte Carlo From the reviews 7 Paul Glasserman has written an Methods in Financial Engineering. … lot of material astonishingly good book that bridges financial engi- which is sometimes hard to access has been composed neering and the Monte Carlo method. The book will into one volume. … a high quality monograph which appeal to graduate students, researchers, and most of is both suitable as a reference for practitioners and all, practicing financial engineers. It is an advanced researchers as well as a textbook … . The list of refer- book. … The presentation is masterful. … You will ences is by itself a valuable aspect. The refreshing learn plenty of financial engineering amidst the pages. writing style of the author is tailor-made for the The writing is a pleasure to read. Topics are timely thirsty reader … 7 www.mathfinance.de and relevant. Glasserman’s is a must-have book for financial engineers.7 www.riskbook.com 2003. XIII, 596 p. 99 illus. (Stochastic Modelling and 7 ...this book is very comprehensive, up-to-date and Applied Probability, Volume 53) Hardcover useful tool for those who are interested in imple- ISBN 978-0-387-00451-8 menting Monte Carlo methods in a financial context. 7 Mathematical Reviews

Mathematical Models of Financial Derivatives

Y. Kwok, Hong Kong University of Science & Technology, discussion of Ito calculus and Girsanovs Theorem, China and the risk-neutral measure and equivalent martin- gale pricing approach. A new chapter on credit risk This second edition, now featuring new material, models and pricing of credit derivatives has been focuses on the valuation principles that are common added. Up-to-date research results are provided by to most derivative securities. A wide range of many useful exercises. financial derivatives commonly traded in the equity and fixed income markets are analyzed, emphasizing 2nd ed. 2007. Approx. 500 p. (Springer Finance) Hard- aspects of pricing, hedging and practical usage. This cover second edition features additional emphasis on the ISBN 978-3-540-42288-4

Risk and Asset Allocation

A. Meucci, Lehman Brothers, Inc., New York, NY, USA primitives, and leading to portfolio optimization in a Bayesian context with parameter uncertainty. 7 Bob From the reviews 7 This exciting new book takes a Litterman, Head of Quantitative Resources, Goldman fresh look at asset allocation and offers up a masterly Sachs Asset Management account of this important subject. The quantitative 7 This book takes the reader on a journey through emphasis and included MATLAB software make it a portfolio management starting with the basics and must-read for the mathematically oriented investment reaching some fascinating terrain. Attilio Meucci professional. 7 Peter Carr, Head of Quantitative Research, shows a real talent for explaining the most difficult Bloomberg LP, Director of Masters in Mathematical of subjects in a very clear manner. 7 Paul Wilmott, Finance program, NYU wilmott.com 7 A wonderful book! Mathematically rigorous and yet practical, heavily illustrated with graphs 1st ed. 2005. Corr. 3rd printing 2007. XXVI, 532 p. and worked examples, Attilio Meucci has written a 141 illus. (Springer Finance) Hardcover comprehensive treatment of asset allocation starting ISBN 978-3-540-22213-2 from statistical concepts, covering investment springer.com 58 Quantitative Finance

Stochastic Calculus for Finance I and II The Binomial Asset Pricing Model volume of Shreves’s text is a wonderful display of the S. E. Shreve, Carnegie Mellon University, Pittsburgh, PA, use of mathematical probability to derive a large set of USA results from a small set of assumptions. In summary, this is a well-written text that treats the From the reviews 7 Steven Shreve’s comprehensive key classical models of finance through an applied two-volume Stochastic Calculus for Finance may well probability approach. It is accessible to a broad audi- be the last word, at least for a while, in the flood of ence and has been developed after years of teaching Master’s level books.... a detailed and authoritative the subject. It should serve as an excellent introduc- reference for “quants” (formerly known as “rocket tion for anyone studyin the mathematics of the clas- scientists”). The books are derived from lecture notes sical theory of finance.7 Siam that have been available on the Web for years and that have developed a huge cult following among Vol. I. 2005. XVI, 187 p. 33 illus. (Springer Finance) students, instructors, and practitioners. The key ideas Softcover presented in these works involve the mathematical ISBN 978-0-387-24968-1 theory of securities pricing based upon the ideas of classical finance. Vol. II. 2004. XIX, 550 p. 28 illus. (Springer Finance) ...the beauty of mathematics is partly in the fact that Hardcover it is self-contained and allows us to explore the logical ISBN 978-0-387-40101-0 implications of our hypotheses. The material of this

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Foreign Exchange Rate Forecasting using Artificial Neural Networks L. Yu, City University of Hong Kong, Kowloon, Hong an up-to-date review of the most recent research Kong; S. Wang, Chinese Academy of Sciences, Beijing, developments in forecasting foreign exchange China; K. K. Lai, City University of Hong Kong, Kowloon, rates coupled with a highly useful methodological Hong Kong approach to predicting rate changes in foreign currency exchanges. This book focuses on forecasting foreign exchange rates via artificial neural networks (ANNs), creating 2007. Approx. 350 p. (International Series in Opera- and applying the highly useful computational tions Research & Management Science, Volume 107) techniques of Artificial Neural Networks (ANNs) Hardcover to foreign-exchange rate forecasting. The result is ISBN 978-0-387-71719-7 New Journals in 2007 59 springer.com New Journals in 2007

Applied Mathematics-A Journal of Chinese Universities

Applied Mathematics, A Journal of Chinese Univer- environmental science, economics, and finance. sities, Series B seeks to promote the integration In addition, the latest developments and trends in of mathematics with other scientific disciplines, which mathematics interacts with other disciplines expanding its fields of study and promoting the are also reported. Readers include professors and development of relevant interdisciplinary subjects. students, professionals in applied mathematics, and The journal mainly publishes original research engineers at research institutes and in industry. papers which apply mathematical concepts, theories and methods to other subjects such as physics, ISSN 1005-1031 (print version) chemistry, biology, information science, energy, ISSN 1993-0445

Blätter der DGVFM

C. Hipp, Universität Karlsruhe, LS Versicherungswissen- survey paper, or papers of partical matter of actu- schaften arial work

Blätter der DGVFM invites papers for publication ISSN 1864-0281 (print version) that contribute to the area of insurance and finance. ISSN 1864-0303 Particularly welcome are innovative research papers,

Functional Analysis and Other Mathematics

Editor-in-Chief: V.I. Arnold; Managing Editor: L. Kotova coordinates) was developed to the point where, at the beginning of the twentieth century, the study of As its name implies, the journal Functional these areas came to be called “functional analysis.” Analysis and Other Mathematics publishes papers Today, this enormous branch of mathematics and not only on functional analysis, but in related areas physics (which has, for example, created the basis of as well. The editorial board is especially interested in quantum mechanics, constructed the geometry of work at the interface of functional analysis and other function spaces, and described the states of physical branches of mathematics, in areas that use ideas systems) has become one of the most important and methods of functional analysis and that expand domains both in fundamental mathematical its borders. The similarity between the geometry research and in applications to the natural sciences. of finite-dimensional spaces and properties of function spaces (such as between the theory of ISSN 1991-0061 (print version) Fourier series and the study of Cartesian orthogonal ISSN 1863-7941 (electronic version) springer.com 60 New Journals in 2007

Israel Journal of Mathematics

A. Mann, Hebrew University Jerusalem; E. London, 7 applied mathematics Hebrew University; E. Goldman, Hebrew University The prestigious interdisciplinary editorial board Jerusalem reflects the wide spectrum of mathematical fields covered. TheIsrael Journal of Mathematics is an inter- The Israel Journal of Mathematics is owned by the national journal publishing high-quality original Hebrew University of Jerusalem and publishes for research papers in a wide spectrum of pure and worldwide distribution under the Magnes Press. applied mathematics. These include, but are not Since its inception in 1963, its volumes can be found limited to, the following areas: in the libraries of major mathematical institutions 7 set theory 7 model theory 7 algebra 7 group around the world. More than 2300 pages per year theory 7 number theory 7 analysis 7 functional are published. analysis 7 ergodic theory 7 algebraic topology 7 geometry 7 combinatorics 7 theoretical ISSN 0021-2172 (print version) computer science 7 mathematical physics ISSN 1565-8511 (electronic version)

Journal d’Analyse Mathématique

L. Zalcman, Bar-Ilan University, Dept. Mathematics & differential equations, and quasiconformal mappings. Computer Science; E. Goldman, Hebrew University The Journal d’Analyse Mathématique is owned by Jerusalem the Hebrew University of Jerusalem and publishes three volumes totaling 1200 pages under the Magnes TheJournal d’Analyse Mathématique publishes Press. Since its founding in 1951 by B. Amira, its top-level original articles in English and French in volumes can be found in the libraries of major the field of classical analysis and in related areas. The mathematical institutions around the world. broad mathematical scope of this journal includes topics such as complex function theory, functional ISSN 0021-7670 (print version) analysis, ergodic theory, harmonic analysis, partial ISSN 1565-8538 (electronic version)

Journal of Applied and Industrial Mathematics

M. M. Lavrent’ev, Russian Academy of Sciences, Sobolev chemistry, biology, ecology, medicine, economics; Institute of Mathematics, Sibirian Branch control theory; applied problems in discrete analysis; information theory. The journal publishes articles on qualitative theory of differential equations in mechanics, physics, ISSN 1990-4789 (print version) biology, industrial and natural processes; math- ISSN 1990-4797 ematical modelling in mechanics, physics, technics,

Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)

The journal covers the following fields: Complex ISSN 1068-3623 (print version) and Real Analysis, Mathematical Physics, Differen- ISSN 1934-9416 tial Equations, Integral and Stochastic Geometry. New Journals in 2007 61 springer.com

Logic and Analysis

N. J. Cutland, University of York, Dept. Mathematics papers using or developing analytical methods having connections to any area of mathematical Logic and Analysis publishes papers of high quality logic. involving interaction between ideas or techniques Logic and Analysis is intended to be a natural home from mathematical logic and other areas of math- for papers with an essential interaction between ematics (especially - but not limited to - pure and mathematical logic and other areas of mathematics, applied analysis). The journal welcomes rather than for papers purely in logic or analysis. papers in nonstandard analysis and related areas of applied model theory; papers involving interplay ISSN 1863-3617 (print version) between mathematics and logic (including foun- ISSN 1863-3625 dational aspects of such interplay); mathematical

Mathematics and Financial Economics

Elyès Jouini, Université Paris-Dauphine and Institut reasoning. The work should have real economic Universitaire de France, Paris, France content and the mathematical reasoning should be new and correct. The primary objective of the journal is to provide a forum for work in finance which expresses ISSN 1862-9679 (print version) economic ideas using formal mathematical ISSN 1862-9660

Mathematical Methods of Statistics

The journalMathematical Methods of Statistics is an outlet for researches in advanced statistical meth- dedicated to the mathematical foundations of statis- odology and for studies where such methodology tical theory. It publishes primarily research papers is effectively used or which stimulate its further with complete proofs and occasionally survey papers development. on particular fields of statistics. Papers dealing with applications of statistics are also published if ISSN 1066-5307 (print version) they contain new theoretical developments to the ISSN 1934-8045 underlying statistical methods. The journal provides

Moscow University Computational Mathematics and Cybernetics

The Journal publishes original papers of high scientific or engineering problems are especially scientific value in all areas of Computational Math- welcome. ematics and Cybernetics. It works at the interface between applied mathematics, numerical computa- ISSN 0278-6419 (print version) tion, and applications. Papers that describe and ISSN 1934-8428 analyze new computational techniques for solving

Moscow University Mathematics Bulletin

The journal publishes original articles and brief control, mathematical logic, theory of algorithms, communications in the different areas of theoretical numbers theory, discrete mathematics, mathemat- and applied mathematics including mathematical ical cybernetics. analysis, theory of functions and functional analysis, algebra, geometry and topology, differential equa- ISSN 0027-1322 (print version) tions, mathematical physics, theory of probability, ISSN 1934-8444 mathematical statistics, random processes, optimal springer.com 62 New Journals in 2007

Proceedings Mathematical Sciences Theory in Biosciences

G. Misra, Indian Statistical Institute, Bangalore Centre published. Papers in applied areas are considered for publication only on the basis of the mathematical The Proceedings of the Indian Academy of Sciences content. Special issues devoted to advances in - Mathematical Sciences is a quarterly research specific areas of Mathematics and proceedings of journal in English published by the Indian Academy selected high quality conferences are also published. of Sciences. The journal publishes refereed papers covering current research in Mathematics. The ISSN 0253-4142 (print version) papers must normally present results of original ISSN 0973-7685 work. Critical reviews of important fields are also

Regular and Chaotic Dynamics

V. Kozlov, Russian Academy of Sciences, Steklov Math- The journal welcomes papers that establish original ematical Institute results, characterized by rigorous mathematical settings and proofs, and that also address practical Regular and Chaotic Dynamics seeks to publish problems. Founded in 1996 and primarily published leading research papers in dynamical systems theory works by Russian and Eastern European researchers, and its applications. Rooted in the Moscow school Regular and Chaotic Dynamics has grown into of mathematics and mechanics, the journal brings an international journal with a diverse range of together dynamical problems from all the sciences, contributors worldwide, including eminent experts successfully combining classical problems, modern in dynamical systems throughout the world. techniques and breakthroughs in the field. With its interdisciplinary approach, Regular and Chaotic ISSN 1560-3547 (print version) Dynamics helps bridge the gap between abstract ISSN 1468-4845 theory and phenomenological studies.

Russian Mathematics (Iz VUZ)

Founded in 1957 by the Ministry of Higher and have a thematic character, being at the same time of Special Secondary Education of USSR and the certain interest not only for “narrow” specialsts in Kazan State University, the journal embraces the those domains of the Contemporary Mathematics, most singificant research works in both Pure and but also for all those who actively work in other Applied Mathematics, which are carried out by fields. scientists of Russian Universities, Institutions of Higher Education, and Russian Academy of Science. ISSN 1066-369X (print version) The articles of well-known mathematicians of C.I.S. ISSN 1934-810X and other countries are also published. Some issues

Siberian Advances in Mathematics

This journal publishes high-level articles in funda- mathematical cybernetics, mathematical economics, mental and Applied Mathematics. It covers a broad mathematical problems of geophysics and tomog- spectrum of subjects: algebra and logic, real and raphy, numerical methods, and optimization theory. complex analysis, functional analysis, differential equations, mathematical physics, geometry and ISSN 1055-1344 (print version) topology, probability and mathematical statistics, ISSN 1934-8126 New Journals in 2007 63 springer.com

Theory in Biosciences

O. Breidbach, Universität Jena, Ernst-Haeckel-Haus, Inst. systems theory/dynamics, theoretical ecology/ Geschichte der Medizin; P. Stadler, J. Jost neurobiology, evolution, cognition, visual computation, simulation strategies, bioethics Theory in Biosciences, formerly “Biologisches Manuscripts present original work with a strong Zentralblatt”, focuses on new concepts in theoretical conceptual background. biology. It likewise deals with analytical or modelling approaches and biophilosophy or history of ISSN 1431-7613 (print version) ideas. Central topics are: ISSN 1611-7530

Vestnik St. Petersburg University: Mathematics

The journal publishes original contributions in all Petersburg State University. areas of fundamental and applied mathematics. It is the prime outlet for the researches of scientists ISSN 1063-4541 (print version) from Faculty of Mathematics and Mechanics of St. ISSN 1934-7855

ZDM The International Journal on Mathematics Education ZDM is one of the oldest mathematics education pre-dominantly mathematics education researchers research journals. The papers appearing in the six around the world interested in current develop- themed issues per year are strictly by invitation ments in the field. only followed by internal peer review by the issue- editors and external review by invited experts. The ISSN 1863-9690 (print version) journal exists to survey, discuss and extend current ISSN 1863-9704 research-based and theoretical perspectives as well as to create a forum for critical analyses of issues within mathematics education. The audience is springer.com 64 Author Index

Author Index

A Ding 30 I Pressley 40 Djukic 34 Procesi 6 Abbott 7 Inselberg 17 Donati-Martin 53 Q Adler 51 J E Agarwal 35 Quarteroni 27 Janzen 38 Ahn 12 Ebbinghaus 41 Jech 43 R Aigner 20, 33 Elnashaie 23 Jones 4 Albiac 7 Engel 34 Resende 50 Jorgensen 5, 9 Aliev 12 Enns 24 Resnick 54 Jost 9 Allaire 20 Eppstein 14 Roach 10 Jüttler 35 Andreescu 1 Érdi 15 Robertazzi 18 Asmussen 51 Erdmann 3 K Roos 27 Axler 1 Rose 18 Ewald 41 Karatzas 54 Ross 10 B F Karniadakis 26 Rousseau 28 Knoebel 43 Barker 21 Filloy 3 Kortenkamp 38, 39 S Benth 52 Floriani 8 Kozlov 36 Bernardo 13 Fonseca 8 Sanders 32 Kwok 57 Beyer 52 Fouque 15 Schirotzek 11 Bhattacharya 52 Francis 36 L Schlichenmaier 18 Bochev 13 Seltman 44 Friberg 41 Laird 43 Boer 29 Sernesi 6 Friesz 48 Lang 5 Bonilla 21 Shiryaev 55 Frittelli 56 Langtangen 31 Borwein 1 Shonkwiler 46 Fusai 56 Li, D. 49 Braides 46 Shores 7 G Li, M. 26 Brams 13, 33 Shreve 58 Lipsky 54 Brigo 55 Gardner 30 Silverman 11 Lumiste 39 Bronshtein 14 Gelca 34 Small 33 Lutz 26 Buchmann 1 Gindikin 42 Srinivas 18 Burachik 47 Glasserman 57 M Steinbach 28 Burger 33 Goldberg 15 Majer 44 Stillwell 40 Bushnell 2 Grätzer 24 Manaresi 44 T C Gray 42 Markowich 17 Tartar 11 Griebel 30 Matveev 39 Cai 47 Thomée 28 Grillet 4 Mavron 17 Calter 35 Trott 29 Grimmett 53 Meucci 57 Campbell 21 Tu 40 Gron 16 Mortveit 31 Canuto 22 Tweddle 45 Gruber 36 Muckstadt 49 Cao 47 Guler 48 Murray 45 V Capinski 52, 55 H Cassandras 14 N Valavanis 19 Ciuprina 29 Hall 4 Vanderwerff 12 Nathanson 5 Coello Coello 22 Handwerk 42 Neshveyev 10 W Cohen 2, 3 Härdle 53 Neukirch 6 Conway 3 Hasle 24 Webb 19 Nicolaescu 39 Cooper 14 Hauser 25 Willems 45 Nocedal 50 Craik 41 Hazewinkel 4 Woodhouse 20 O D Hesthaven 25 Y Hijab 8 Øksendal 54 Dacorogna 7 Yu 58 Ho 48 Osipov 31 Daley 53 Hoffman 31 Z Danaila 23 P Holden 16 Ziegler 33 Dawande 48 Holt 25 Peitgen 32 Delbaen 56 Hooker 49 Pettini 32 Deuflhard 23 Hrùz 16 Polderman 50 Dietl 56 Hundsdorfer 9

Algebra  Springer.Com Algebra

Algebra Springer.Com Algebra