Abcd London Bookfair 2011

ABCD springer.com

LONDON BOOKFAIR 2011 Title Selection - MATHEMATICS

A.A. Agrachev, Y. Sachkov subsets" of the phase space. Such systems lead to com- V. Arnol'd, S. Novikov plicated motion (so-called "chaos"). The book begins Control Theory from the with a discussion of the topological manifestations Dynamical Systems VII Geometric Viewpoint of uniform and total hyperbolicity: hyperbolic sets, Integrable Systems. Nonholonomic Dynamical Smale's Axiom A, structurally stable systems, Anosov Systems This book presents some facts and methods of Math- systems, and hyperbolic attractors of dimension or ematical Control Theory treated from the geomet- codimension one. There are various modifications of This volume contains five surveys on dynamical sys- ric viewpoint. It is devoted to finite-dimensional hyperbolicity and in this connection the properties tems. The first one deals with nonholonomic mechan- deterministic control systems governed by smooth of Lorenz attractors, pseudo-analytic Thurston dif- ics and gives an updated and systematic treatment ordinary differential equations. The problems of con- feomorphisms, and homogeneous flows with expand- ofthe geometry of distributions and of variational trollability, state and feedback equivalence, and opti- ing and contracting foliations are investigated. These problems with nonintegrable constraints. The mod- mal control are studied. Some of the topics treated by last two questions are discussed in the general context ern language of differential geometry used throughout the authors are covered in monographic or textbook of the theory of homeomorphisms of surfaces and of the survey allows for a clear and unified exposition of literature for the first time while others are presented homogeneous flows. the earlier work on nonholonomic problems. There is a detailed discussion of the dynamical properties in a more general and flexible setting than elsewhere. More on www.springer.com/978-3-642-08168-2 Although being fundamentally written for mathe- of the nonholonomic geodesic flow and of various maticians, the authors make an attempt to reach both Available related concepts, such as nonholonomic exponen- the practitioner and the theoretician by blending the 1995. VII, 235 p. 39 illus. (Encyclopaedia of Mathematical tial mapping, nonholonomic sphere, etc. Other sur- theory with applications. They maintain a good bal- Sciences, 66) veys treat various aspects of integrable Hamiltonian ance between the mathematical integrity of the text 978-3-642-08168-2 ▶ 109,95 € systems, with an emphasis on Lie-algebraic construc- and the conceptual simplicity that might be required tions. Among the topics covered are: the generalized by engineers. It can be used as a text for graduate Calogero-Moser systems based on root systems of courses and will become most valuable as a reference simple Lie algebras, a general r-matrix scheme for work for graduate students and researchers. constructing integrable systems and Lax pairs, links with finite-gap integration theory, topologicalaspects More on www.springer.com/978-3-642-05907-0 of integrable systems, integrable tops, etc. One of Available the surveys gives a thorough analysis of a family of 2004. XIV, 412 p. 35 illus. (Encyclopaedia of Mathematical quantum integrable systems (Toda lattices) using the Sciences, 87) machinery of representation theory. Readers will find 978-3-642-05907-0 ▶ 119,95 € all the new differential geometric and Lie-algebraic methods which are currently used in the theory of integrable systems in this book. It will be indispensable to graduate students and researchers in mathematics and theoretical physics. E. Arbarello, M. Cornalba, P.A. Griffiths More on www.springer.com/978-3-642-05738-0 Available T.S. Angell, A. Kirsch Geometry of Algebraic Curves 1994. VII, 341 p. 9 illus. (Encyclopaedia of Mathematical Volume II with a contribution by Joseph Daniel Sciences, 16) Optimization Methods in Harris 978-3-642-05738-0 ▶ 104,95 € Electromagnetic Radiation The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of This book considers problems of optimization aris- moduli of algebraic curves. Its authors are research ing in the design of electromagnetic radiators and mathematicians who have actively participated in the receivers. The authors develop a systematic general development of the Geometry of Algebraic Curves. theory that can be applied to a wide class of struc- The subject is an extremely fertile and active one, both tures. The theory is illustrated with familiar, simple within the mathematical community and at the inter- W. Arveson examples and indications of how the results can be face with the theoretical physics community. The applied to more complicated structures. The final approach is unique in its blending of algebro-geo- Noncommutative Dynamics and chapter introduces techniques from multicriteria opti- metric, complex analytic and topological/combi- mization in antenna design. The material is intended natorial methods. It treats important topics such as E-Semigroups for a dual audience of mathematicians and theoreti- Teichmüller theory, the cellular decomposition of The term Noncommutative Dynamics can be inter- cally-inclined engineers. References to both the math- moduli and its consequences and the Witten conjec- ematics and engineering literature help guide the preted in several ways. It is used in this book to refer ture. The careful and comprehensive presentation of to a set of phenomena associated with the dynamics reader through the necessary mathematical back- the material will be of value to students who wish to ground. of quantum systems of the simplest kind that involve learn the subject and to experts as a reference source. rigorous mathematical structures associated with More on www.springer.com/978-1-4419-1914-4 The first volume appeared 1985 as volume 267 of the infinitely many degrees of freedom. The dynamics Due April 2011 same series. of such a system is represented by a one-parameter 2004. 331 p. 92 illus. (Springer Monographs in More on www.springer.com/978-3-540-42688-2 group of automorphisms of a noncommutative alge- Mathematics, ) Due April 2011 bra of observables, and the author focuses primarily 978-1-4419-1914-4 ▶ 84,95 € on the most concrete case in which that algebra con- 2011. XXX, 963 p. (Grundlehren der mathematischen sists of all bounded operators on a Hilbert space. This Wissenschaften, 268) subject overlaps with several mathematical areas of 978-3-540-42688-2 ▶ 89,95 € current interest, including quantum field theory, the D. Anosov dynamics of open quantum systems, noncommutative geometry, and both classical and noncommuta- Dynamical Systems IX tive probability theory. This is the first book to give Dynamical Systems with Hyperbolic Behaviour a systematic presentation of progress during the past The book deals with smooth dynamical systems with fifteen years on the classification of E-semigroups up hyperbolic behaviour of trajectories filling out "large to cocycle conjugacy. There are many new results that springer.com 3 cannot be found in the existing literature, as well as ing a detailed exposition of many of the cohomolog- significant reformulations and simplifications of the ical results one obtains from having a torus action theory as it exists today. William Arveson is Profes- with fixed points. Many examples, such as toric vari- sor of Mathematics at the University of California, eties and flag varieties, are discussed in detail. W.M. Berkeley. He has published two previous books with McGovern studies the actions of a semisimple Lie Springer-Verlag, An Invitation to C*-algebras (1976) or algebraic group on its Lie algebra via the adjoint and A Short Course on Spectral Theory (2001). action and on itself via conjugation. His contribution More on www.springer.com/978-1-4419-1803-1 focuses primarily on nilpotent orbits that have found the widest application to representation theory in the Due April 2011 last thirty-five years. 2003. X, 434 p. (Springer Monographs in Mathematics, ) More on www.springer.com/978-3-642-07745-6 978-1-4419-1803-1 ▶ 91,95 € M. Bartholomew-Biggs Available Nonlinear Optimization with 2002. V, 242 p. (Encyclopaedia of Mathematical Sciences, 131) Engineering Applications 978-3-642-07745-6 ▶ 104,95 € This textbook examines a broad range of problems in science and engineering, describing key numerical methods applied to real life. The case studies presented are in such areas as data fitting, vehicle route planning and optimal control, scheduling and resource allocation, sensitivity calculations and worst-case analysis.Among the main topics covered:* one-variable optimization — optimality conditions, direct search and gradient * unconstrained optimization in n variables — solution methods including H. Bahouri, J. Chemin, R. Danchin Nelder and Mead simplex, steepest descent, New- ton, Gauss–Newton, and quasi-Newton techniques, Fourier Analysis and Nonlinear trust regions and conjugate gradients * constrained Partial Differential Equations optimization in n variables — solution methods including reduced-gradients, penalty and barrier T.R. Bielecki, M. Rutkowski In recent years, the Fourier analysis methods have methods, sequential quadratic programming, and expereinced a growing interest in the study of par- interior point techniques * an introduction to global Credit Risk: Modeling, Valuation tial differential equations. In particular, those tech- optimization* an introduction to automatic differ- niques based on the Littlewood-Paley decomposition entiationChapters are self-contained with exercises and Hedging have proved to be very efficient for the study of evolu- provided at the end of most sections. Nonlinear Opti- Mathematical finance and financial engineering have tion equations. The present book aims at presenting mization with Engineering Applications is ideal for been rapidly expanding fields of science over the self-contained, state- of- the- art models of those tech- self-study and classroom use in engineering courses past three decades. The main reason behind this phe- niques with applications to different classes of par- at the senior undergraduate or graduate level. The nomenon has been the success of sophisticated quan- tial differential equations: transport, heat, wave and book will also appeal to postdocs and advanced titative methodologies in helping professionals to Schrödinger equations. It also offers more sophis- researchers interested in the development and use of manage financial risks. The newly developed credit ticated models originating from fluid mechanics optimization algorithms.Also by the author: Nonlin- derivatives industry has grown around the need to (in particular the incompressible and compressible ear Optimization with Financial Applications,ISBN: handle credit risk, which is one of the fundamental Navier-Stokes equations) or general relativity. It is 978-1-4020-8110-1, (c)2005, Springer. factors of financial risk. In recent years, we have wit- either directed to anyone with a good undergradu- More on www.springer.com/978-1-4419-4621-8 nessed a tremendous acceleration in research efforts ate level of knowledge in analysis or useful for experts aimed at better apprehending, modeling and hedg- Available who are eager to know the benefit that one might gain ing of this kind of risk. One of the objectives has been from Fourier analysis when dealing with nonlinear to understand links between credit risk and other 2008. XVI, 280 p. 15 illus. (Springer Optimization and partial differential equations. Its Applications, 19) major sources of uncertainty, such as the market risk or the liquidity risk. The main objective of this mono- More on www.springer.com/978-3-642-16829-1 978-1-4419-4621-8 46,95 € ▶ graph is to present a comprehensive survey ofthe past Available developments in the area of credit risk research, as 2011. XVI, 522 p. (Grundlehren der mathematischen well as put forth the most recent advancements in Wissenschaften, 343) A. Bialynicki-Birula, J. Carrell, W. McGovern this field. An important aspect of this text is that it 978-3-642-16829-1 ▶ 99,95 € attempts to bridge the gap between the mathematical Algebraic Quotients. Torus theory of credit risk and the financial practice, which Actions and Cohomology. The serves as the motivation for the mathematical modeling studied in the book. Mahtematical developments Adjoint Representation and the are presented in a thorough manner and cover the Adjoint Action structural (value-of-the-firm) and the reduced-form (intensity-based) approaches to credit risk model- This is the second volume of the new subseries ing, applied both to single and to multiple defaults. In "Invariant Theory and Algebraic Transformation particular, the book offers a detailed study of various Groups". The aim of the survey by A. Bialynicki-Bir- arbitrage-free models of defaultable term structures ula is to present the main trends and achievements of with several rating grades. This book will serve as a research in the theory of quotients by actions of alge- valuable reference for financial analysts and traders braic groups. This theory contains geometric invari- involved with credit derivatives. Some aspects of the ant theory with various applications to problems of book may also be useful for market practitioners with moduli theory. The contribution by J. Carrell treats managing credit-risk sensitives portfolios. Gradu- the subject of torus actions on algebraic varieties, giv- ate students and researchers in areas such as finance 4 springer.com theory, mathematical finance, financial engineering stretchings, but not tearing. This book deals with versity Press 1997) and Algebraic Geometry (World and probability theory will benefit from the book as the topology of curves and surfaces as well as with Scientific 1998). well. On the technical side, readers are assumed to be the fundamental concepts of homotopy and homol- More on www.springer.com/978-1-4419-1937-3 familiar with graduate level probability theory, the- ogy, and does this in a lively and well-motivated way. ory of stochastic processes, and elements of stochastic There is hardly an area of mathematics that does not Due April 2011 analysis and PDEs; some acquaintance with arbitrage make use of topological results and concepts. The pricing theory is also importance of topological methods for different areas 2004. XI, 451 p. 50 illus. (Graduate Texts in Mathematics, 225) More on www.springer.com/978-3-642-08707-3 of physics is also beyond doubt. They are used in field theory and general relativity, in the physics of low 978-1-4419-1937-3 ▶ 55,95 € Available temperatures, and in modern quantum theory. The 2002. XVIII, 501 p. (Springer Finance, ) book is well suited not only as preparation for stu- 978-3-642-08707-3 ▶ 79,95 € dents who plan to take a course in algebraic topology L. Bunimovich, D. Szasz, D. Burago, N. Chernov, E. Cohen, C. but also for advanced undergraduates or beginning Dettmann, J. Dorfman, S. Ferleger, R. Hirschl, A. Kononenko, graduates interested in finding out what topology J. Lebowitz, C. Liverani, T. Murphy, J. Piasecki, H. Posch, N. is all about. The book has more than 200 problems, Simanyi, Y. Sinai, D. Szasz, T. Tel, H.v. Beijeren, R.v. Zon, J. many examples, and over 200 illustrations. Vollmer, L. Young More on www.springer.com/978-1-4419-2882-5 Hard Ball Systems and the Lorentz Due April 2011 Gas 2001. XII, 141 p. 210 illus. (Universitext, ) Hard Ball Systems and the Lorentz Gas are funda- 978-1-4419-2882-5 ▶ 44,95 € mental models arising in the theory of Hamiltonian dynamical systems. Moreover, in these models, some key laws of statistical physics can also be tested or even established by mathematically rigorous tools. The mathematical methods are most beautiful but J.F. Blowey, J.P. Coleman, A.W. Craig sometimes quite involved. This collection of surveys written by leading researchers of the fields - mathe- Theory and Numerics of D. Bump maticians, physicists or mathematical physicists - treat both mathematically rigourous results, and evolving Differential Equations Lie Groups physical theories where the methods are analytic or Durham 2000 computational. Some basic topics: hyperbolicity and This book is intended for a one year graduate course ergodicity, correlation decay, Lyapunov exponents, This book contains detailed lecture notes on six top- on Lie groups and Lie algebras. The author proceeds Kolmogorov-Sinai entropy, entropy production, irre- ics at the forefront of current research in numerical beyond the representation theory of compact Lie versibility. This collection is a unique introduction analysis and applied mathematics. Each set of notes groups (which is the basis of many texts) and pro- into the subject for graduate students, postdocs or presents a self-contained guide to a current research vides a carefully chosen range of material to give the researchers - in both mathematics and physics - who area and has an extensive bibliography. In addition, student the bigger picture. For compact Lie groups, want to start working in the field. most of the notes contain detailed proofs of the key the Peter-Weyl theorem, conjugacy of maximal tori More on www.springer.com/978-3-642-08711-0 results. The notes start from a level suitable for first (two proofs), Weyl character formula and more are year graduate students in applied mathematics, math- covered. The book continues with the study of com- Available ematical analysis or numerical analysis, and pro- plex analytic groups, then general noncompact Lie 2000. VIII, 458 p. 75 illus. (Encyclopaedia of Mathematical ceed to current research topics. The reader should groups, including the Coxeter presentation of the Sciences, 101) therefore be able to gain quickly an insight into the Weyl group, the Iwasawa and Bruhat decomposi- 978-3-642-08711-0 ▶ 109,95 € important results and techniques in each area with- tions, Cartan decomposition, symmetric spaces, Cay- out recourse to the large research literature. Current ley transforms, relative root systems, Satake diagrams, (unsolved) problems are also described and directions extended Dynkin diagrams and a survey of the ways for future research are given. This book is also suitable Lie groups may be embedded in one another. The for professional mathematicians who require a succint book culminates in a ``topics'' section giving depth and accurate account of recent research in areas par- to the student's understanding of representation the- allel to their own, and graduates in mathematical sci- ory, taking the Frobenius-Schur duality between the ences. representation theory of the symmetric group and More on www.springer.com/978-3-642-07533-9 the unitary groups as a unifying theme, with many Available applications in diverse areas such as random matrix theory, minors of Toeplitz matrices, symmetric alge- 2001. X, 280 p. 21 illus., 8 in color. (Universitext, ) bra decompositions, Gelfand pairs, Hecke algebras, representations of finite general linear groups and 978-3-642-07533-9 57,95 € ▶ the cohomology of Grassmannians and flag varieties. Daniel Bump is Professor of Mathematics at Stanford University. His research is in automorphic forms, rep- R. Busam, T. Epp resentation theory and number theory. He is a co- author of GNU Go, a computer program that plays Prüfungstrainer Analysis the game of Go. His previous books include Automor- 1000 Fragen und Antworten für Bachelor und phic Forms and Representations (Cambridge Uni- Vordiplom V. Boltyanskii, V. Efremovich Dieser „Prüfungstrainer“ wendet sich an Studierende Intuitive Combinatorial Topology mit Mathematik als Haupt- oder Nebenfach, die – insbesondere bei der Prüfungs- oder Klausurvor- Topology is a relatively young and very important bereitung – den Wunsch verspüren, als Ergänzung branch of mathematics. It studies properties of objects zu den Lehrbüchern den umfangreichen Stoff des that are preserved by deformations, twistings, and Analysisgrundstudiums noch einmal in pointierter springer.com 5

Form vorliegen zu haben, zugespitzt auf dasjenige, matikabsolventen – ist es sehr gut gelungen, mit der an exploration of a fascinating subfield of algebraic was man wirklich wissen und beherrschen sollte, Auswahl der Fragen ein realistisches Bild davon zu geometry for the latter. um eine Prüfung erfolgreich zu bestehen und exakte vermitteln, was einen Studenten in der mündlichen More on www.springer.com/978-3-642-17403-2 Antworten auf mögliche Fragen formulieren zu Prüfung oder einer Klausur typischerweise erwartet. können. In einem konzisen Frage-Antworten-Stil Durch die Gliederung des Stoffes in einzelne Fra- Available werden die zentralen Begriffe und Beweise der Analy- gen eignet sich das Buch ausgezeichnet dazu, Wissen 2011. XIII, 233 p. (Encyclopaedia of Mathematical Sciences, sis wiederholt. Mehr noch als auf die Rechenfähigkeit stichpunktartig zu trainieren und zu überprüfen; auch 139) (die sicherlich auch notwendig ist und nicht zu kurz höhere Semester können davon profitieren, wenn sie 978-3-642-17403-2 ▶ 89,95 € kommt) wird dabei Wert auf das grundsätzliche schon einmal Gelerntes noch einmal gezielt nach- Verständnis wichtiger Konzepte gelegt. Dem schlagen wollen. Eine besondere Attraktion stellen Autorenduo – einem Dozenten mit langjähriger Vor- die zahlreichen Abbildungen dar, die geometrische S. Carter, S. Kamada, M. Saito lesungs- und Prüfungserfahrung und einem Mathe- Sachverhalte veranschaulichen. matikabsolventen – ist es sehr gut gelungen, mit der More on www.springer.com/978-3-8274-1976-7 Surfaces in 4-Space Auswahl der Fragen ein realistisches Bild davon zu vermitteln, was einen Studenten in der mündlichen Available Surfaces in 4-Space, written by leading specialists Prüfung oder einer Klausur typischerweise erwartet. in the field, discusses knotted surfaces in 4-dimen- Durch die Gliederung des Stoffes in einzelne Fra- 2009. VIII, 245 S. 37 Abb. sional space and surveys many of the known results gen eignet sich das Buch ausgezeichnet dazu, Wissen 978-3-8274-1976-7 ▶ 18,64 € in the area. Results on knotted surface diagrams, con- stichpunktartig zu trainieren und zu überprüfen; auch structions of knotted surfaces, classically defined höhere Semester können davon profitieren, wenn sie invariants, and new invariants defined via quandle schon einmal Gelerntes noch einmal gezielt nach- homology theory are presented. The last chapter com- schlagen wollen. Eine besondere Attraktion stellen die prises many recent results, and techniques for com- ca. 180 Abbildungen dar, die geometrische Sachver- P. Bürgisser, M. Clausen, M.A. Shokrollahi putation are presented. New tables of quandles with halte veranschaulichen. a few elements and the homology groups thereof are Algebraic Complexity Theory included. This book contains many new illustrations More on www.springer.com/978-3-8274-1895-1 This is the first book to present an up-to-date and of knotted surface diagrams. The reader of the book Available self-contained account of Algebraic Complexity The- will become intimately aware of the subtleties in going ory that is both comprehensive and unified. Requir- from the classical case of knotted circles in 3-space to 2008. VIII, 374 S. 166 Abb. ing of the reader only some basic algebra and offering this higher dimensional case. As a survey, the book 978-3-8274-1895-1 ▶ 23,32 € over 350 exercises, it is well-suited as a textbook for is a guide book to the extensive literature on knotted beginners at graduate level. With its extensive bibli- surfaces and will become a useful reference for grad- ography covering about 500 research papers, this text uate students and researchers in mathematics and is also an ideal reference book for the professional physics. researcher. The subdivision of the contents into 21 More on www.springer.com/978-3-642-05913-1 more or less independent chapters enables readers to Available familiarize themselves quickly with a specific topic, and facilitates the use of this book as a basis for com- 2004. XIII, 213 p. (Encyclopaedia of Mathematical Sciences, plementary courses in other areas such as computer 142) algebra. 978-3-642-05913-1 ▶ 104,95 € More on www.springer.com/978-3-642-08228-3 Available 1997. XXIII, 618 p. 21 illus. (Grundlehren der R. Busam, T. Epp mathematischen Wissenschaften, 315) 978-3-642-08228-3 ▶ 99,95 € Prüfungstrainer Lineare Algebra 500 Fragen und Antworten für Bachelor und Vordiplom H.E. Campbell, D.L. Wehlau Dieser „Prüfungstrainer" wendet sich an Studierende Modular Invariant Theory mit Mathematik als Haupt- oder Nebenfach, die – insbesondere bei der Prüfungs- oder Klausurvorbere- This book covers the modular invariant theory of itung – den Wunsch verspüren, als Ergänzung zu den finite groups, the case when the characteristic of the Lehrbüchern den Grundstudiums-Stoff der Linearen field divides the order of the group. It explains a the- W. Cherry, Z. Ye Algebra noch einmal in pointierter Form vorliegen ory that is more complicated than the study of the zu haben, zugespitzt auf dasjenige, was man wirk- classical non-modular case, and it describes many Nevanlinna's Theory of Value lich wissen und beherrschen sollte, um eine Prüfung open questions.Largely self-contained, the book erfolgreich zu bestehen und exakte Antworten auf develops the theory from its origins up to modern Distribution mögliche Fragen formulieren zu können. In einem results. It explores many examples, illustrating the The Second Main Theorem and its Error Terms theory and its contrast with the better understood konzisen Frage-Antworten-Stil werden die zen- On the one hand, this monograph serves as a self- non-modular setting. It details techniques for the tralen Begriffe und Beweise der Linearen Algebra contained introduction to Nevanlinna's theory of computation of invariants for many modular rep- wiederholt. Mehr noch als auf die Rechenfähigkeit value distribution because the authors only assume resentations of finite groups, especially the case of (die sicherlich auch notwendig ist und nicht zu kurz the reader is familiar with the basics of complex anal- the cyclic group of prime order. It includes detailed kommt) wird Wert auf das Verständnis wichtiger ysis. On the other hand, the monograph also serves examples of many topics as well as a quick survey of Konzepte gelegt, deren grundsätzliche Bedeutung as a valuable reference for the research specialist the elements of algebraic geometry and commutative durch viele Querverweise auf Anwendungen in because the authors present, for the first time in book algebra as they apply to invariant theory. The book anderen Gebieten der Mathematik sowie der Natur- form, the most modern and refined versions of the is aimed at both graduate students and researchers und Computerwissenschaften illustriert wird. Dem Second Main Theorem with precise error terms, in —an introduction to many important topics in mod- Autorenduo – einem Dozenten mit langjähriger Vor- both the geometric and logarithmic derivative based ern algebra within a concrete setting for the former, lesungs- und Prüfungserfahrung und einem Mathe- approaches. A unique feature of the monograph is its 6 springer.com

"number theoretic digressions." These special sections Differential Equations and Stochastic Partial Differen- framework for solving stochastic optimization prob- assume no background in number theory and explore tial Equations, Infinite Dimensional Stochastic Geom- lems of finding the optimal contracts between two the exciting interconnections between Nevanlinna etry, Random Media and Interacting Particle Systems, parties, under various assumptions on the informa- theory and the theory of Diophantine approximation. Super-processes, Stochastic Filtering, Mathemati- tion they have access to, and the effect they have on More on www.springer.com/978-3-642-08568-0 cal Finance, etc. Stochastic Analysis has emerged as the underlying "profit/loss" values. This monograph a core area of late 20th century Mathematics and is surveys recent results of the theory in a systematic Available currently undergoing a rapid scientific development. way, using the approach of the so-called Stochastic 2001. XII, 202 p. (Springer Monographs in Mathematics, ) The special volume “Stochastic Analysis 2010” pro- Maximum Principle, in models driven by Brownian 978-3-642-08568-0 ▶ 79,95 € vides a sample of the current research in the different Motion. Optimal contracts are characterized via a branches of the subject. It includes the collected works system of Forward-Backward Stochastic Differential of the participants at the Stochastic Analysis section Equations. In a number of interesting special cases of the 7th ISAAC Congress organized at Imperial Col- these can be solved explicitly, enabling derivation of lege London in July 2009. many qualitative economic conclusions. More on www.springer.com/978-3-642-15357-0 More on www.springer.com/978-3-642-14199-7 Available Available 2011. VIII, 299 p. 2011. X, 280 p. (Springer Finance, 0) 978-3-642-15357-0 ▶ 109,95 € 978-3-642-14199-7 ▶ approx. 69,95 €

J. Cuntz, G. Skandalis, B. Tsygan Cyclic Homology in Non- A.M. Cohen, H. Cuypers, H. Sterk Commutative Geometry Some Tapas of Computer Algebra This volume contains contributions by three authors and treats aspects of noncommutative geometry This book arose from a series of courses on computer that are related to cyclic homology. The authors give algebra which were given at Eindhoven Technical rather complete accounts of cyclic theory from differ- University. Its chapters present a variety of topics in ent and complementary points of view. The connec- computer algebra at an accessible (upper undergrad- tions between topological (bivariant) K-theory and uate/graduate) level with a view towards recent devel- cyclic theory via generalized Chern-characters are dis- opments. For those wanting to acquaint themselves cussed in detail. This includes an outline of a frame- C. Czado, T. Schmidt somewhat further with the material, the book also work for bivariant K-theory on a category of locally contains seven 'projects', which could serve as prac- convex algebras. On the other hand, cyclic theory is Mathematische Statistik tical sessions related to one or more chapters. The the natural setting for a variety of general index the- contributions focus on topics like Gröbner bases, real Dieses Buch widmet sich den mathematischen orems. A survey of such index theorems (including algebraic geometry, Lie algebras, factorisation of poly- Grundlagen der Statistik und der Theorie von statis- the abstract index theorems of Connes-Moscovici and nomials, integer programming, permutation groups, tischen Schätz- und Testverfahren. Dabei wird of Bressler-Nest-Tsygan) is given and the concepts differential equations, coding theory, automatic theo- Wert auf die Herleitung von statistischen Fragestel- and ideas involved in the proof of these theorems are rem proving, and polyhedral geometry. This book is a lungen und deren tiefere Analyse gelegt. Um die explained. must-read for everybody interested in computer alge- Verständlichkeit zu erhöhen, werden zahlreiche bra. More on www.springer.com/978-3-642-07337-3 Beispiele ausgearbeitet und elementare Beweise More on www.springer.com/978-3-642-08335-8 Available gezeigt, so dass ein schneller Einstieg in dieses Fachgebiet möglich wird. Das Buch beginnt mit einer Available 2004. XIII, 137 p. (Encyclopaedia of Mathematical Sciences, 121) Zusammenfassung der verwendeten wahrschein- lichkeitstheoretischen Konzepte. Nach der For- 978-3-642-07337-3 104,95 € 1999. XIV, 352 p. 20 illus. (Algorithms and ▶ mulierung von parametrischen statistischen Modellen Computation in Mathematics, 4) werden grundlegende Schätzverfahren sowie deren 978-3-642-08335-8 ▶ 54,95 € Vergleich entwickelt. Dies beinhaltet die klassische Theorie vom unverzerrten Schätzer mit kleinster Var- ianz (UMVUE) nach Lehmann-Scheffé. Nach der statistischen Modellierung ist die Beantwortung von statistischen Hypothesen mit Hilfe von beobachteten Daten von Interesse. Dazu werden statistische Hypothesentests und Konfidenzintervalle hergeleitet. Mit Hilfe des Neymann-Pearson-Lemmas werden optimale Tests für einfache Testprobleme vorgestellt und unter Verwendung von Likelihood- Quotienten- tests allgemeinere Testprobleme betrachtet. Das Buch schließt mit der ausführlichen Behandlung von Lin- earen Modellen in Zusammenhang mit Suffizienz, J. Cvitanic, J. Zhang UMVUE, kleinsten Quadraten und zugehörigen Hypothesentests. Eine umfangreiche Aufgabensamm- Contract Theory in Continuous- D. Crisan Time Models Stochastic Analysis 2010 In recent years there has been a significant increase Stochastic Analysis aims to provide mathematical of interest in continuous-time Principal-Agent mod- tools to describe and model high dimensional random els, or contract theory, and their applications. Con- systems. Such tools arise in the study of Stochastic tinuous-time models provide a powerful and elegant springer.com 7 lung am Ende jeden Kapitels bietet eine bewährte Singulärwertzerlegung, CG-Verfahren oder finite Ele- ysis Topologie und Geometrie Numerik Stochastik Ergänzung für das Studium des Textes. mente Diskretisierungen. Mengenlehre und Logik Ein besonderes Augenmerk More on www.springer.com/978-3-642-17260-1 More on www.springer.com/978-3-540-76492-2 liegt auf einer knappen und präzisen, dabei aber nicht zu formalen Darstellung. Dadurch erlauben die Due April 2011 Available einzelnen Beiträge ein fokussiertes Nachlesen ebenso wie ein neugieriges Kennenlernen. Das Buch ist 2011. VIII, 280 S. 23 Abb. (Statistik und ihre 2008. XVIII, 633 S. 125 Abb., 5 in Farbe. (Springer- geschrieben für Studierende der Mathematik ab dem Anwendungen, 0) Lehrbuch, ) ersten Semester und möchte ein treuer Begleiter und 978-3-642-17260-1 ▶ 27,99 € 978-3-540-76492-2 ▶ 27,99 € eine zuverlässige Orientierungshilfe für das gesamte Studium sein. More on www.springer.com/978-3-8274-2297-2 Available G.B. Dantzig, M.N. Thapa 2011. X, 342 S. 39 Abb. Linear Programming 978-3-8274-2297-2 ▶ 18,64 € 2: Theory and Extensions Linear programming represents one of the major applications of mathematics to business, industry, and economics. It provides a methodology for optimizing an output given that is a linear function of a number of inputs. George Dantzig is widely regarded as the founder of the subject with his invention of the sim- W. Dahmen, A. Reusken plex algorithm in the 1940's. This second volume is intended to add to the theory of the items discussed in Numerik für Ingenieure und the first volume. It also includes additional advanced Naturwissenschaftler topics such as variants of the simplex method; interior point methods (early and current methods), GUB, Numerische Simulation erlaubt in immer stärkerem decomposition, integer programming, and game the- Maße die Erschließung von Bereichen in Tech- ory. Graduate students in the fields of operations nik und Naturwissenschaften, die Messungen oder research, industrial engineering and applied mathe- U. Dierkes, S. Hildebrandt, F. Sauvigny, A.J. Tromba Experimenten nicht mehr zugänglich sind. Der matics will find this volume of particular interest. Einsatz numerischer Methoden wird daher eine Minimal Surfaces More on www.springer.com/978-1-4419-3140-5 immer bedeutendere Rolle in einem sich wandel- The three-volume treatise consists of the volumes nden Aufgabenprofil zukünftiger Ingenieurstätigkeit Available Minimal Surfaces (GL 339), Regularity of Minimal spielen. Dieses Lehrbuch vermittelt dem Leser die Surfaces (GL 340), and Glolbal Theory of Minimal Wirkungsweise vieler unterschiedlicher Grund- 2003. XXV, 448 p. 45 illus. (Springer Series in Surfaces (GL 341) that replace the monograph Min- bausteine numerischer Algorithmen. Übergeordnete Operations Research and Financial Engineering, ) imal Surfaces I , II, published as volumes 295 and Zielsetzung ist die Stärkung der Fähigkeit, numerische 978-1-4419-3140-5 ▶ 80,95 € 296 of the Grundlehren der mathematischen Wis- Ergebnisse einschätzen und bewerten zu können, senschaft series.Ther first volume covers the classical sowie die numerischen Werkzeuge auch in komplex- theory as well as existence results concerning bound- eren Anwendungsszenarien flexibel, sachgemäß kom- ary value problems for minimal surfaces, in particu- binieren und anpassen zu können. Besonderer Wert lar results for Plateau's problem.The second volume wird dabei von Anfang an auf ein solides Verständnis deals with basic regularity results for minimal sur- der Konzepte Kondition (eines Problems) und faces concerning their boundary behaviour at Plateau Stabilität (eines Lösungsverfahrens) gelegt. Aufgrund boundaries and free boundaries. Moreover, exclosure der Vielfalt der in der Praxis benötigten numerischen theorems, isoperimetricc inequalities and existence Bausteine schließt sich dann eine methodenorien- theorems for surfaces of prescribed mean curvature tierte Einführung zu den relevanten Themenschw- in a Riemanian manifold and for the thread prob- erpunkten wie direkte und iterative Verfahren zur lem are discussed.Finally, the third volume deals with Lösung von Gleichungssystemen, Ausgleichsrech- geometric properties of minimal surfaces with free nung, Singulärwertzerlegung, Eigenwertberech- boundaries and with a priori gradient estimates for nung, Interpolation, schnelle Fouriertransformation, n-dimensional minimal surfaces, leading to various numerische Integration sowie numerische Verfahren O. Deiser, C. Lasser, E. Vogt, D. Werner Bernstein-type theorems. Secondly, a global theory für gewöhnliche und partielle Differentialgleichun- of minimal surfaces (as envisioned by Smale) is pre- gen an. In einem abschließenden Kapitel werden typ- 12 x 12 Schlüsselkonzepte zur sented, including index theorems. ische Kombinationen der behandelten numerischen Methoden anhand komplexerer Anwendungsbeispiele Mathematik More on www.springer.com/978-3-642-11715-2 illustriert. Die Aufbereitung mehrerer Themen ist Wie ist ein Ring definiert, wann kann man Gren- Available angesichts obiger Zielsetzung im folgenden Sinne zprozesse vertauschen, was sind lineare Ordnun- 2011. L, 1910 p. 3-volume-set. (Grundlehren der gestaffelt: Einfachen auch optisch hervorgehobenen gen und wozu benötigt man das Zornsche Lemma in mathematischen Wissenschaften, 339-341) "Pflichtinhalten" folgen je nach Anspruch überspring- der Linearen Algebra? Das Buch will seinen Lesern 978-3-642-11715-2 ▶ 259,00 € bare Vertiefungen, wobei dann konzeptionelle helfen, sich in der Fülle der grundlegenden mathe- Gesichtspunkte, übergreifende Zusammenhänge matischen Definitionen zurecht zu finden und exem- sowie rigorose Begründungen stärker betont wer- plarische mathematische Ergebnisse einordnen und den. Hierzu gehören elementare funktionalanalytis- ihre Eigenheiten verstehen zu können. Es behan- che Hilfsmittel im Umfeld von Normen wie auch delt hierzu je zwölf Schlüsselkonzepte der folgenden die Rolle von Projektionen in Ausgleichsrechnung, zwölf Themengebiete der Mathematik: Grundlagen Zahlen Zahlentheorie Diskrete Mathematik Lineare Algebra Algebra Elementare Analysis Höhere Anal- 8 springer.com

optimization and a real-world case study using important concepts from each chapter. Key Features: Provides well-written self-contained chapters, including problem sets and exercises, making it ideal for the classroom setting; Introduces applied optimization to the hazardous waste blending problem; Explores linear programming, nonlinear programming, discrete optimization, global optimization, optimization under uncertainty, multi-objective optimization, optimal control and stochastic optimal control; Includes an extensive bibliography at the end of each chapter and an index; GAMS files of case studies for Chapters 2, U. Dierkes, S. Hildebrandt, A.J. Tromba 3, 4, 5, and 7 are linked to http://www.springer.com/ R.M. Dudley, R. Norvaiša math/book/978-0-387-76634-8; Solutions manual Global Analysis of Minimal available upon adoptions. Introduction to Applied Concrete Functional Calculus Surfaces Optimization is intended for advanced undergraduate Concrete Functional Calculus focuses primarily on and graduate students and will benefit scientists from differentiability of some nonlinear operators on func- Many properties of minimal surfaces are of a global diverse areas, including engineers. tions or pairs of functions. This includes composi- nature, and this is already true for the results treated More on www.springer.com/978-1-4419-4570-9 tion of two functions, and the product integral, taking in the first two volumes of the treatise. Part I of the Available a matrix- or operator-valued coefficient function present book can be viewed as an extension of these into a solution of a system of linear differential equa- results. For instance, the first two chapters deal with tions with the given coefficients. For nonlinear inte- existence, regularity and uniqueness theorems for 2008. XXVI, 292 p. 100 illus. (Springer Optimization and Its Applications, 22) gral equations with respect to possibly discontinuous minimal surfaces with partially free boundaries. Here functions having unbounded variation, existence and 978-1-4419-4570-9 ▶ 54,95 € one of the main features is the possibility of "edge- uniqueness of solutions are proved under suitable crawling" along free parts of the boundary. The third assumptions.Key features and topics:* Extensive usage chapter deals with a priori estimates for minimal of p-variation of functions* Applications to stochas- surfaces in higher dimensions and for minimizers tic processes.This work will serve as a thorough refer- of singular integrals related to the area functional. ence on its main topics for researchers and graduate In particular, far reaching Bernstein theorems are students with a background in real analysis and, for derived. The second part of the book contains what Chapter 12, in probability. one might justly call a "global theory of minimal surfaces" as envisioned by Smale. First, the Douglas prob- More on www.springer.com/978-1-4419-6949-1 lem is treated anew by using Teichmüller theory. Available Secondly, various index theorems for minimal the- 2011. XII, 671 p. 3 illus. (Springer Monographs in orems are derived, and their consequences for the Mathematics, ) space of solutions to Plateau´s problem are discussed. 978-1-4419-6949-1 ▶ 99,95 € Finally, a topological approach to minimal surfaces via Fredholm vector fields in the spirit of Smale is presented. More on www.springer.com/978-3-642-11705-3 Handbook of Combinatorial Available Optimization 2011. XVI, 584 p. (Grundlehren der mathematischen Supplement Volume B Wissenschaften, 341) This is a supplementary volume to the major three- 978-3-642-11705-3 99,95 € ▶ volume Handbook of Combinatorial Optimization- set, as well as the Supplement Volume A. It can also be regarded as a stand-alone volume which presents chapters dealing with various aspects of the subject, including optimization problems and algorithmic approaches for discrete problems. Audience This handbook is suitable for all those who use combina- J.J. Dudziak torial optimization methods to model and solve problems. Vitushkin’s Conjecture for More on www.springer.com/978-1-4419-3666-0 Removable Sets Available Vitushkin's conjecture, a special case of Painlevé's 2005. VII, 394 p. problem, states that a compact subset of the com- 978-1-4419-3666-0 ▶ 166,95 € plex plane with finite linear Hausdorff measure is U. Diwekar removable for bounded analytic functions if and only if it intersects every rectifiable curve in a set of zero Introduction to Applied arclength measure. Chapters 6-8 of this carefully writ- Optimization ten text present a major recent accomplishment of modern complex analysis, the affirmative resolution This text presents a multi-disciplined view of opti- of this conjecture. Four of the five mathematicians mization, providing students and researchers with a whose work solved Vitushkin's conjecture have won thorough examination of algorithms, methods, and the prestigious Salem Prize in analysis. Chapters 1-5 tools from diverse areas of optimization without of this book provide important background material introducing excessive theoretical detail. This second on removability, analytic capacity, Hausdorff mea- edition includes additional topics, including global sure, arclength measure, and Garabedian duality that springer.com 9 will appeal to many analysts with interests indepen- father of 39 Ph.D. students and was recently elected to gives the latest results in the theory of mixed problems dent of Vitushkin's conjecture. The fourth chapter the National Academy of Sciences. for hyperbolic operators and a list of unsolved prob- contains a proof of Denjoy's conjecture that employs More on www.springer.com/978-1-4419-2677-7 lems. Both parts cover recent research in an impor- Melnikov curvature. A brief postscript reports on tant field, which before was scattered in numerous a deep theorem of Tolsa and its relevance to going Available journals. The book will hence be of immense value to beyond Vitushkin's conjecture. Although standard 2008. XII, 432 p. (Probability and Its Applications, ) graduate students and researchers in partial differen- notation is used throughout, there is a symbol glos- 978-1-4419-2677-7 ▶ 71,95 € tial equations and theoretical physics. sary at the back of the book for the reader's conve- More on www.springer.com/978-3-642-08099-9 nience. This text can be used for a topics course or seminar in complex analysis. To understand it, the Available reader should have a firm grasp of basic real and com- 1993. VII, 241 p. 6 illus. (Encyclopaedia of Mathematical plex analysis. Sciences, 33) 978-3-642-08099-9 94,95 € More on www.springer.com/978-1-4419-6708-4 ▶ Available 2010. XII, 272 p. (Universitext, ) 978-1-4419-6708-4 ▶ 49,95 €

C. Eck, H. Garcke, P. Knabner Mathematische Modellierung Dieses Lehrbuch bietet eine lebendige und anschauliche Einführung in die mathematische Mod- ellierung von Phänomenen aus den Natur- und Inge- nieurwissenschaften. Die Leserin und der Leser lernen D. Eisenbud, D.R. Grayson, M. Stillman, B. Sturmfels mathematische Modelle zu verstehen und selbst herzuleiten und finden gleichzeitig eine Fülle von Computations in Algebraic wichtigen Beispielen für die im Mathematikstudium R. Durrett behandelten abstrakten Konzepte. Es werden Meth- Geometry with Macaulay 2 oden aus der Linearen Algebra, der Analysis und der This book presents algorithmic tools for algebraic Probability Models for DNA Theorie der gewöhnlichen und partiellen Differen- geometry and experimental applications of them. It Sequence Evolution tialgleichungen benutzt bzw. sorgfältig eingeführt. also introduces a software system in which the tools Anwendungsbeispiele aus den Bereichen elektrische have been implemented and with which the experi- How is genetic variability shaped by natural selec- Netzwerke, chemische Reaktionskinetik, Populations- ments can be carried out. Macaulay 2 is a computer tion, demographic factors, and random genetic drift? dynamik, Strömungsdynamik, Elastizitätstheorie und algebra system devoted to supporting research in To approach this question, we introduce and analyze Kristallwachstum werden ausführlich behandelt. Der algebraic geometry, commutative algebra, and their a number of probability models beginning with the Stoffumfang des Buches eignet sich für bis zu zwei applications. The reader of this book will encounter basics, and ending at the frontiers of current research. vierstündige Vorlesungen für Studierende der Mathe- Macaulay 2 in the context of concrete applications Throughout the book, the theory is developed in close matik und der Ingenieur- oder Naturwissenschaften and practical computations in algebraic geometry. connection with examples from the biology litera- ab dem vierten Semester. The expositions of the algorithmic tools presented ture that illustrate the use of these results. Along the More on www.springer.com/978-3-642-18423-9 here are designed to serve as a useful guide for those way, there are many numerical examples and graphs wishing to bring such tools to bear on their own prob- Available to illustrate the conclusions. This is the second edi- lems. These expositions will be valuable to both the tion and is twice the size of the first one. The mate- users of other programs similar to Macaulay 2 (for 2011. XIV, 513 S. (Springer-Lehrbuch, ) rial on recombination and the stepping stone model example, Singular and CoCoA) and those who are have been greatly expanded, there are many results 978-3-642-18423-9 ▶ 27,99 € not interested in explicit machine computations at form the last five years, and two new chapters on dif- all. The first part of the book is primarily concerned fusion processes develop that viewpoint. This book is with introducing Macaulay2, whereas the second part written for mathematicians and for biologists alike. Y. Egorov, M. Shubin emphasizes the mathematics. No previous knowledge of concepts from biology is More on www.springer.com/978-3-642-07592-6 assumed, and only a basic knowledge of probability, Partial Differential Equations IV Available including some familiarity with Markov chains and Microlocal Analysis and Hyperbolic Equations Poisson processes. The book has been restructured into a large number of subsections and written in a In the first part of this EMS volume Yu.V. Egorov 2002. XVI, 329 p. (Algorithms and Computation in theorem-proof style, to more clearly highlight the gives an account of microlocal analysis as a tool Mathematics, 8) main results and allow readers to find the results they for investigating partial differential equations. This 978-3-642-07592-6 ▶ 59,95 € need and to skip the proofs if they desire. Rick Dur- method has become increasingly important in the the- rett received his Ph.D. in operations research from ory of Hamiltonian systems. Egorov discusses the evo- Stanford University in 1976. He taught in the UCLA lution of singularities of a partial differential equation mathematics department before coming to Cornell in and covers topics like integral curves of Hamiltonian 1985. He is the author of eight books and 160 research systems, pseudodifferential equations and canoni- papers, most of which concern the use of probability cal transformations, subelliptic operators and Pois- models in genetics and ecology. He is the academic son brackets. The second survey written by V.Ya. Ivrii treats linear hyperbolic equations and systems. The author states necessary and sufficient conditions for C?- and L2 -well-posedness and he studies the analo- gous problem in the context of Gevrey classes. He also 10 springer.com

and engineers to many of the problems in dynamical cell biology. This volume was conceived of and begun by Professor Joel Keizer based on his many years of teaching and research together with his colleagues. The project was expanded and finished by his students and friends after his untimely death in 1999. Carefully selected examples are used to motivate the concepts and techniques of computational cell biology, through a progression of increasingly more complex and demanding cases. Illustrative exercises are included with every chapter, and mathematical and computational appendices are provided for reference. J. Elstrodt P. Embrechts, C. Klüppelberg, T. Mikosch This textbook will be useful for advanced undergraduate and graduate theoretical biologists, and for math- Maß- und Integrationstheorie Modelling Extremal Events ematic students and life scientists who wish to learn about modeling in cell biology. "What better tribute Dieses Lehrbuch der Maß- und Integrationstheo- for Insurance and Finance to the late Joel Keizer than to expand his unfinished rie vermittelt dem Leser ein solides Basiswissen, wie Both in insurance and in finance applications, ques- accounts of teaching and research to a splendid book. es für weite Bereiche der Mathematik unerläßlich tions involving extremal events (such as large insur- Computational Cell Biology performs much more ist, insbesondere für reelle Analysis, Funktional- ance claims, large fluctuations, in financial data, than it promises, for it also deals with considerable analysis, Wahrscheinlichkeitstheorie und mathe- stock-market shocks, risk management, ...) play an analytical material and with aspects of molecular biol- matische Statistik. Thematische Schwerpunkte sind increasingly important role. This much awaited book ogy. There's something for everybody interested in Produktmaße, Fourier-Transformation, Transforma- presents a comprehensive development of extreme how modeling leads to greater understanding in the tionsformel, Konvergenzbegriffe, absolute Stetigkeit value methodology for random walk models, time core of the biological sciences." -Lee Segel (Weizmann und Maße auf topologischen Räumen. Höhepunkte series, certain types of continuous-time stochastic Institute) sind die Herleitung des Rieszschen Darstellungssatzes processes and compound Poisson processes, all mod- mit Hilfe eines Fortsetzungsresultats von Kisy´nski els which standardly occur in applications in insur- More on www.springer.com/978-1-4419-2975-4 und der Beweis der Existenz und Eindeutigkeit des ance mathematics and mathematical finance. Both Available Haarschen Maßes. Ferner enthält das Buch einen probabilistic and statistical methods are discussed in Abschnitt über Konvergenz von Maßen und den Satz detail, with such topics as ruin theory for large claim 2002. XX, 468 p. 210 illus. (Interdisciplinary Applied von Prochorov. Der Text wird aufgelockert durch models, fluctuation theory of sums and extremes of Mathematics, 20) mathematikhistorische Ausflüge und Kurzporträts iid sequences, extremes in time series models, point 978-1-4419-2975-4 ▶ 59,95 € von Mathematikern, die zum Thema des Buches process methods, statistical estimation of tail proba- wichtige Beiträge geliefert haben. Eine Vielzahl von bilities. Besides summarising and bringing together Übungsaufgaben vertieft den Stoff.Aus den Rezensio- known results, the book also features topics that nen:„ …In diesem Buch wird die Maß- und Integra- appear for the first time in textbook form, includ- tionstheorie als ein zentrales Gebiet der Mathematik ing the theory of subexponential distributions and dargestellt, das insbesondere für die Funktional- the spectral theory of heavy-tailed time series. A typ- analysis und die Stochastik unentbehrlich ist; es hat ical chapter will introduce the new methodology in a daher zu Recht seinen Platz in der Reihe ‘Grundwis- rather intuitive (tough always mathematically correct) sen Mathematik’. Vor allem für denjenigen, der über way, stressing the understanding of new techniques Grundkenntnisse bereits verfügt, ist es eine Quelle rather than following the usual "theorem-proof" for- der Anregung und Bereicherung.“(Zentralblatt für mat. Many examples, mainly from applications in Mathematik und ihre Grenzgebiete 861 (1997), 148– insurance and finance, help to convey the usefulness 149)„ …Das Buch …zeugt von großer Lehrerfahrung of the new material. A final chapter on more extensive des Autors. Es ist flüssig geschrieben, vermittelt applications and/or related fields broadens the scope solides Grundwissen und enthält viele Beispiele further. The book can serve either as a text for a grad- A. Filler und Übungsaufgaben. Deshalb kann ich es Math- uate course on stochastics, insurance or mathemati- ematik-Studenten aller Richtungen (einschließlich cal finance, or as a basic reference source. Its reference Elementare Lineare Algebra Lehramtskandidaten) zum Gebrauch neben der Vor- quality is enhanced by a very extensive bibliography, lesung nachdrücklich empfehlen.“(Zeitschrift für annotated by various comments sections making the Linearisieren und Koordinatisieren Analysis und ihre Anwendungen 16 (1997), 493–49 book broadly and easily accessible. Das vorliegende Lehrbuch führt Sie – anknüpfend More on www.springer.com/978-3-642-17904-4 More on www.springer.com/978-3-642-08242-9 an Inhalte des Mathematikunterrichts der Sekun- darstufen I und II – auf verständliche Weise in Available Available grundlegende Inhalte und Arbeitsweisen der Lin- 1997. XVI, 648 p. 100 illus. (Stochastic Modelling and 2011. XVI, 434 S. (Springer-Lehrbuch, ) earen Algebra ein. Besonderer Wert wird auf Ver- Applied Probability, 33) anschaulichungen der behandelten mathematischen 978-3-642-17904-4 30,79 € ▶ 978-3-642-08242-9 ▶ 69,95 € Begriffe und Verfahren gelegt. Zentrale Begriffe werden anhand von Beispielen entwickelt und danach verallgemeinert, sodass Sie ausgehend von Ver- trautem Abstraktionen schrittweise vornehmen können.Rechnerische Verfahren können Sie auf C.P. Fall, E.S. Marland, J.M. Wagner, J.J. Tyson herkömmliche Weise oder mithilfe des Comput- ers nachvollziehen. Das Buch versetzt Sie in die Computational Cell Biology Lage, das freie Computeralgebrasystem Maxima This textbook provides an introduction to dynamic für Inhalte der Linearen Algebra zu nutzen. Auf der modeling in cell biology, emphasizing computational Internetseite zu diesem Buch finden Sie Lösungen approaches based on realistic molecular mechanisms. der gestellten Aufgaben, interaktive Illustratio- It is designed to introduce cell biology and neuro- nen sowie Dateien, mit denen Sie Maxima sofort science students to computational modeling, and für Berechnungen und Visualisierungen einset- applied mathematics students, theoretical biologists, zen können.Das Buch richtet sich an:Studierende springer.com 11 des Lehramts Mathematik für die Sekundarstufe matchings, covering, bipartite graphs, planar graphs I, die damit von einem "höheren Standpunkt" auf and state the graph minor theorem of Seymour and die Schulalgebra schauen,Studierende für das gym- Robertson. The book is highly illustrated and each nasiale Lehramt, die einen "sanften" Übergang chapter ends with a list of problems of varying diffi- von der Analytischen Geometrie in der Schule zu culty. Undergraduates in mathematics and computer den Vorlesungen in Linearer Algebra vollziehen science will find this book useful. möchten,Mathematiklehrkräfte der Sekundarstufe More on www.springer.com/978-1-4419-8046-5 II, die vielfältige Anregungen erhalten, um in ihrem Unterricht der Analytischen Geometrie fundamen- Available tale Ideen der Linearen Algebra lebendig werden zu lassen. 2011. XIII, 465 p. 220 illus., 20 in color. (Universitext, ) 978-1-4419-8046-5 ▶ 59,95 € More on www.springer.com/978-3-8274-2412-9 E. Friedlander, D.R. Grayson Due April 2011 Handbook of K-Theory 2011. X, 302 S. 100 Abb. (Mathematik Primar- und This handbook offers a compilation of techniques Sekundarstufe, ) and results in K-theory. These two volumes consist 978-3-8274-2412-9 ▶ approx. 21,45 € of chapters, each of which is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present pre- viously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. The overall intent of this handbook is to offer the interested reader an exposition of our current state of knowledge as well as an implicit blueprint for future research. This handbook should be especially useful for stu- L. Gawarecki, V. Mandrekar dents wishing to obtain an overview of K-theory and for mathematicians interested in pursuing challenges Stochastic Differential Equations in this rapidly expanding field. in Infinite Dimensions More on www.springer.com/978-3-540-23019-9 with Applications to Stochastic Partial F. Padberg, M. Franke Available Differential Equations Didaktik der Geometrie 2005. XXIV, 1163 p. In 2 volumes, not available separately. The systematic study of existence, uniqueness, and 978-3-540-23019-9 ▶ 109,95 € properties of solutions to stochastic differential equa- in der Grundschule tions in infinite dimensions arising from practical Das Buch zeigt angehenden Lehrern und Lehrerin- problems characterizes this volume that is intended nen Wege auf, wie in der Grundschule ein guter, for graduate students and for pure and applied mathe- substanzieller Geometrieunterricht erteilt wer- maticians, physicists, engineers, professionals working den kann. Dazu bietet es sowohl theoretisches with mathematical models of finance. Major meth- Hintergrundwissen als auch vielfältige, didak- ods include compactness, coercivity, monotonicity, tisch gut aufbereitete Anregungen zur praktischen in a variety of set-ups. The authors emphasize the Umsetzung an. Im ersten Teil werden nach einer fundamental work of Gikhman and Skorokhod on Einführung in den Geometrieunterricht mehr the- the existence and uniqueness of solutions to stochas- oretisch orientierte Grundlagen zur Entwicklung tic differential equations and present its extension to des räumlichen Vorstellungsvermögens und zum infinite dimension. They also generalize the work of Erwerb geometrischen Wissens dargestellt. Im Khasminskii on stability and stationary distributions zweiten, stärker praxisorientierten Teil des Buches of solutions. New results, applications, and exam- werden die Ausführungen anhand zentraler Inhalte ples of stochastic partial differential equations are des Geometrie-Curriculums konkretisiert. Das vor- J. Gallier included. This clear and detailed presentation gives liegende Buch will durch zahlreiche Aktivitäten the basics of the infinite dimensional version of the wie Bauen, Legen, Falten, Schneiden, Spannen Discrete Mathematics classic books of Gikhman and Skorokhod and of und Zeichnen dazu anregen, Kindern Freude an Khasminskii in one concise volume that covers the geometrischen Tätigkeiten zu vermitteln und inter- This book gives an introduction to discrete mathe- main topics in infinite dimensional stochastic PDE’s. essante geometrische Zusammenhänge und Eigen- matics for beginning undergraduates and starts with a By appropriate selection of material, the volume can schaften möglichst selbständig entdecken zu lassen. chapter on the rules of mathematical reasoning. This be adapted for a 1- or 2-semester course, and can pre- book begins with a presentation of the rules of logic More on www.springer.com/978-3-8274-1511-0 pare the reader for research in this rapidly expanding as used in mathematics where many examples of for- area. Available mal and informal proofs are given. With this logical framework firmly in place, the book describes the More on www.springer.com/978-3-642-16193-3 2006. X, 338 S. (Mathematik Primar- und major axioms of set theory and introduces the nat- Available Sekundarstufe, ) ural numbers. The rest of the book deals with func- 978-3-8274-1511-0 ▶ 19,63 € tions and relations, directed and undirected graphs 2011. XVI, 274 p. (Probability and Its Applications, ) and an introduction to combinatorics, partial orders 978-3-642-16193-3 ▶ 49,95 € and complete induction. 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dungsbeispielen aus den Ingenieurwissenschaften top research scholars in the field, using cutting-edge finden Sie zu jedem Kapitel zahlreiche Aufgaben (mit mathematical and computational techniques. Lösungen auf der Website) zum Selbstrechnen. Trotz More on www.springer.com/978-1-4419-3723-0 der verständlichen Darstellung geht die mathematische Exaktheit nicht verloren. Wenn Sie Mathematik Due April 2011 oder Informatik studieren und sehen möchten, wie 2005. IX, 292 p. 96 illus. die Mathematik in der Technik eingesetzt wird, dann 978-1-4419-3723-0 ▶ 85,95 € ist das Buch auch für Sie interessant. Hintergrundin- formationen und Beweise ergänzen die sehr umfangreiche Stoffauswahl und bieten Anknüpfungspunkte für ein Master-Studium.Stimmen zum Buch: „An diesem Buch gefällt mir, dass die Autoren sich nicht S.I. Gelfand, Y.I. Manin auf reine Rechentechnik beschränken, sondern auch weitergehende optionale Hintergrundinformationen Methods of Homological Algebra anbieten. Somit bietet dieses Buch auch jenen Natur- wissenschaftlern und Ingenieuren etwas, die nicht Homological algebra first arose as a language for nur ‚Kochrezepte‘ suchen, sondern die mathematis- describing topological prospects of geometrical chen Verfahren auch verstehen möchten.“ Prof. Dr. objects. As with every successful language it quickly Christoph Dalitz, Lehrgebiet Mathematik und Infor- expanded its coverage and semantics, and its contem- matik, Hochschule Niederrhein„Hier wird großer porary applications are many and diverse. This mod- Wert auf die Anwendung gelegt, anstatt unnötig in ern approach to homological algebra, by two leading die Tiefe zu gehen. Und genau das hat mir das Lernen writers in the field, is based on the systematic use G. Gras ungemein erleichtert." Julian Joosten, Bachelor-Stu- of the language and ideas of derived categories and dent, Hochschule Niederrhein derived functors. Relations with standard cohomol- Class Field Theory ogy theory (sheaf cohomology, spectral sequences, More on www.springer.com/978-3-8274-2761-8 From Theory to Practice etc.) are described. In most cases complete proofs are Due April 2011 Global class field theory is a major achievement of given. Basic concepts and results of homotopical alge- algebraic number theory, based on the functorial bra are also presented. The book addresses people 2011. XII, 908 S. 209 Abb. properties of the reciprocity map and the existence who want to learn a modern approach to homological 978-3-8274-2761-8 ▶ 27,99 € theorem. The author works out the consequences and algebra and to use it in their work. For the second edi- the practical use of these results by giving detailed tion the authors have made numerous corrections. studies and illustrations of classical subjects (classes, More on www.springer.com/978-3-642-07813-2 idèles, ray class fields, symbols, reciprocity laws, Available Hasse's principles, the Grunwald-Wang theorem, 2003. XX, 370 p. 3 illus. (Springer Monographs in Hilbert's towers,...). He also proves some new or less- Mathematics, ) known results (reflection theorem, structure of the abelian closure of a number field) and lays empha- 978-3-642-07813-2 79,95 € ▶ sis on the invariant (/cal T) p, of abelian p-ramifica- tion, which is related to important Galois cohomology properties and p-adic conjectures. This book, inter- mediary between the classical literature published in the sixties and the recent computational literature, gives much material in an elementary way, and is suitable for students, researchers, and all who are fasci- M.C. Golumbic, I.B. Hartman nated by this theory. In the corrected 2nd printing 2005, the author improves some mathematical and Graph Theory, Combinatorics and bibliographical details and adds a few pages about Algorithms rank computations for the general reflection theorem; Interdisciplinary Applications then he gives an arithmetical interpretation for usual class groups, and applies this to the Spiegelungssatz Graph Theory, Combinatorics and Algorithms: Inter- for quadratic fields and for the p-th cyclotomic field S. Goebbels, S. Ritter disciplinary Applications focuses on discrete mathe- regarding the Kummer--Vandiver conjecture in a matics and combinatorial algorithms interacting with probabilistic point of view. real world problems in computer science, operations Mathematik verstehen und More on www.springer.com/978-3-642-07908-5 research, applied mathematics and engineering. The anwenden – von den Grundlagen book contains eleven chapters written by experts Available bis zu Fourier-Reihen und in their respective fields, and covers a wide spec- 2003. XIV, 512 p. (Springer Monographs in Mathematics, ) trum of high-interest problems across these disci- 978-3-642-07908-5 ▶ 89,95 € Laplace-Transformation pline domains. Among the contributing authors are Gegen Angst vor Mathematik hilft Verstehen. Dieses Richard Karp of UC Berkeley and Robert Tarjan of Buch setzt nahezu keine Vorkenntnisse voraus Princeton; both are at the pinnacle of research schol- und führt schrittweise und systematisch von der arship in Graph Theory and Combinatorics. The Bruchrechnung bis zu erstaunlichen Sätzen der chapters from the contributing authors focus on "real Höheren Mathematik. Ausgehend von Problemstel- world" applications, all of which will be of consider- lungen aus Elektrotechnik und Maschinenbau werden able interest across the areas of Operations Research, Differenzial- und Integralrechnung, Vektorrechnung, Computer Science, Applied Mathematics, and Engi- Differenzialgleichungen, Fourier-Reihen, Integral- neering. These problems include Internet congestion transformationen sowie Wahrscheinlichkeitsrech- control, high-speed communication networks, multi- nung und Statistik behandelt. Dabei werden Sie vom object auctions, resource allocation, software test- Vertrauten zum Neuen geführt. Neben vielen Anwen- ing, data structures, etc. In sum, this is a book focused on major, contemporary problems, written by the springer.com 13

of friends and colleagues, all top authorities in their fields of expertise and all invited plenary speakers at P.J. Haas one of two conferences in August 2008 in Hungary, both celebrating Lovász’s 60th birthday, have con- Stochastic Petri Nets tributed their latest research papers to this volume. This collection of articles offers an excellent view on Modelling, Stability, Simulation the state of combinatorics and related topics and will This book is about stochastic Petri nets (SPNs), which be of interest for experienced specialists as well as have proven to be a popular tool for modelling and young researchers. performance analysis of complex discrete-event More on www.springer.com/978-3-642-09896-3 stochastic systems. The focus is on methods for modelling a system as an SPN with general firing times Available and for studying the long-run behavior of the result- H. Gronau, H. Langmann, D. Schleicher 2008. 595 p. (Bolyai Society Mathematical Studies, 19) ing SPN model using computer simulation. Mod- 978-3-642-09896-3 ▶ 99,95 € elling techniques are illustrated in the context of 50th IMO - 50 Years of computer, manufacturing, telecommunication, and International Mathematical transportation systems. The simulation discussion centers on the theory that underlies estimation proce- Olympiads dures such as the regenerative method, the method of batch means, and spectral methods. Tying these top- In July 2009 Germany hosted the 50th International ics together are conditions on the building blocks of Mathematical Olympiad (IMO). For the very first an SPN under which the net is stable over time and time the number of participating countries exceeded specified estimation procedures are valid. In addition, 100, with 104 countries from all continents. Celebrat- the book develops techniques for comparing the mod- ing the 50th anniversary of the IMO provides an ideal elling power of different discrete-event formalisms. opportunity to look back over the past five decades These techniques provide a means for making prin- and to review its development to become a world- cipled choices between alternative modelling frame- wide event. This book is a report about the 50th IMO works and also can be used to extend stability results as well as the IMO history. A lot of data about all the and limit theorems from one framework to another. 50 IMOs are included. We list the most successful A. Gut As an overview of fundamental modelling, stability, contestants, the results of the 50 Olympiads and the convergence, and estimation issues for discrete-event 112 countries that have ever taken part. It is impres- Stopped Random Walks systems, this book will be of interest to researchers sive to see that many of the world’s leading research Limit Theorems and Applications and graduate students in Applied Mathematics, Oper- mathematicians were among the most successful IMO Classical probability theory provides information ations Research, Applied Probability, and Statistics. participants in their youth. Six of them gave presen- about random walks after a fixed number of steps. For This book also will be of interest to practitioners in tations at a special celebration: Bollobás, Gowers, applications, however, it is more natural to consider these fields, because it provides an introduction to a Lovász, Smirnov, Tao and Yoccoz. This book is aimed random walks evaluated after a random number of powerful collection of tools both for modelling and at students in the IMO age group and all those who steps. Stopped Random Walks: Limit Theorems and for simulation-based performance analysis. Peter J. have interest in this worldwide leading competition Applications shows how this theory can be used to Haas is a member of the Research Staff at the IBM for highschool students. prove limit theorems for renewal counting processes, Almaden Research Center in San Jose, California. More on www.springer.com/978-3-642-14564-3 first passage time processes, and certain two-dimen- More on www.springer.com/978-1-4419-3001-9 Available sional random walks, as well as how these results may Available 2011. VII, 241 p. 131 illus. in color. be used in a variety of applications. The present second edition offers updated content and an outlook 978-3-642-14564-3 19,95 € ▶ on further results, extensions and generalizations. A 2002. XXII, 509 p. 64 illus. (Springer Series in new chapter introduces nonlinear renewal processes Operations Research and Financial Engineering, ) and the theory of perturbed random walks, which are 978-1-4419-3001-9 ▶ 89,95 € modeled as random walks plus "noise". This self-contained research monograph is motivated by numerous examples and problems. With its concise blend of material and over 300 bibliographic references, the book provides a unified and fairly complete treatment of the area. The book may be used in the classroom as part of a course on "probability theory", "random walks" or "random walks and renewal processes", as well as for self-study. From the reviews: "The book provides a nice synthesis of a lot of useful material." --American Mathematical Society "...[a] clearly writ- M. Grötschel, G.O. Katona ten book, useful for researcher and student." --Zen- tralblatt MATH Building Bridges More on www.springer.com/978-1-4419-2773-6 D. Haftendorn Between Mathematics and Computer Science Available Discrete mathematics and theoretical computer sci- Mathematik sehen und verstehen ence are closely linked research areas with strong 2009. XIV, 263 p. (Springer Series in Operations Schlüssel zur Welt Research and Financial Engineering, ) impacts on applications and various other scien- Dieses Buch ist für Sie geschrieben. Sie zeigen Ihre 978-1-4419-2773-6 34,95 € tific disciplines. Both fields deeply cross fertilize ▶ Neugier dadurch, dass Sie es in die Hand genommen each other. One of the persons who particularly con- und umgedreht oder diesen Text angeklickt haben. tributed to building bridges between these and many Genau für Menschen wie Sie, die wissen wollen, other areas is László Lovász, a scholar whose out- wie es kommt, dass die Mathematik so universell standing scientific work has defined and shaped many die Phänomene des modernen Alltags durchzieht, research directions in the last 40 years. A number 14 springer.com ist dieses Buch geschrieben. In die folgenden The- University, in Riverside, California. Václav Zizler is men werden Sie eingeführt: Kryptografie Codierung Professorof Mathematics at the Mathematical Insti- Graphentheorie Fraktale, Chaos und Ordnung Welt tute of the Academy of Sciencesof the Czech Republic. der Funktionen Optimierung als Ziel Computer als More on www.springer.com/978-1-4419-2395-0 Werkzeuge für Mathematik Numerik Stochastik F. Hirsch, C. Profeta, B. Roynette, M. Yor Geometrie Selbstverständnis der Mathematik Das Due April 2011 Besondere an diesem Buch: Sie werden in Ihrem Peacocks and Associated Bedürfnis zu verstehen ernst genommen. Sie wer- 2008. XVIII, 342 p. (CMS Books in Mathematics, ) den schrittweise und meist durch Bilder an die tra- 978-1-4419-2395-0 ▶ 69,95 € Martingales, with Explicit genden Prinzipien herangeführt. Auf der Website Constructions zum Buch können Sie die Bilder selbst „in die Hand nehmen" und variieren. Auf Rechnungen und Umfor- We call peacock an integrable process which is mung von Formeln wird weitestgehend verzichtet, der increasing in the convex order; such a notion plays an Devise folgend: Besser Verstehen ohne zu rechnen important role in Mathematical Finance. A deep theo- als Rechnen ohne zu verstehen. „Spannend, lehrreich rem due to Kellerer states that a process is a peacock if und verständlich – Mathematik erzählt als Vermes- and only if it has the same one-dimensional marginals sung der Welt." Jürgen Neffe, Autor von "Einstein - as a martingale. Such a martingale is then said to be Eine Biografie", "Darwin - Das Abenteuer des Lebens" associated to this peacock.In this monograph, we Website zum Buch: www.mathematik-sehen-und- exhibit numerous examples of peacocks and associ- verstehen.de ated martingales with the help of different methods: construction of sheets, time reversal, time inversion, More on www.springer.com/978-3-8274-2044-2 self-decomposability, SDE, Skorokhod embeddings… Available They are developed in eight chapters, with about a hundred of exercises. H. Hege, K. Polthier 2010. X, 341 S. 310 Abb. in Farbe. More on www.springer.com/978-88-470-1907-2 978-3-8274-2044-2 ▶ 23,32 € Mathematical Visualization Due March 2011 Algorithms, Applications and Numerics 2011. 430 p. 11 illus., 6 in color. (Bocconi & Springer Series, Mathematical Visualization is a young new discipline. 2) It offers efficient visualization tools to the classi- 978-88-470-1907-2 ▶ approx. 89,95 € cal subjects of mathematics, and applies mathematical techniques to problems in computer graphics and scientific visualization. Originally, mathematical visualization started in the interdisciplinary area of differential geometry, numerical mathematics, and computer graphics. In recent years, the methods developed have found important applications, and the subject has evolved to a discipline in its own right. The current volume is the quintessence of an international workshop in September 1997in Berlin, focusing on recent developments in this emerging area. Experts P. Hajek, V. Montesinos Santalucia, J. Vanderwerff, V. Zizler present selected research work on new algorithms for visualization problems, describe the application and D.W. Hoffmann Biorthogonal Systems in Banach experiments in geometry, and develop new numeri- Spaces cal or computer graphical techniques. The sections of Grenzen der Mathematik the book contain topics on Meshes in Numerics and Eine Reise durch die Kerngebiete der The main theme of this book is the relation between Visualization, Applications in Geometry and Numer- mathematischen Logik the global structureof Banach spaces and the var- ics, Graphics Algorithms and Implementations, Geo- ious types of generalized "coordinatesystems" - or metric Visualization Techniques, and Vectorfields Ist die Mathematik frei von Widersprüchen? Gibt "bases" - they possess. This subject is not new and and Flow Visualization. The book is the second in es Wahrheiten jenseits des Beweisbaren? Lässt sich hasbeen investigated since the inception of the study a series of publications on this subject. It offers the das logische Denken mechanisieren? Ist es möglich, of Banach spaces. Inthis book, the authors systemat- reader insight to latest research and developments in unser mathematisches Wissen in eine einzige Zahl ically investigate the concepts ofMarkushevich bases, this fascinating new area. hineinzucodieren? Die moderne mathematische fundamental systems, total systems and theirvariants. Logik des zwanzigsten Jahrhunderts gibt verblüffende More on www.springer.com/978-3-642-08373-0 The material naturally splits into the case of separa- Antworten auf diese Fragen; Antworten, die die bleBanach spaces, as is treated in the first two chap- Available Mathematik in der gleichen Weise verändert haben ters, and thenonseparable case, which is covered in 1998. XX, 391 p. 187 illus., 46 in color. wie die Einstein‘sche Relativitätstheorie die Physik. Heute wissen wir, dass die Beweisbarkeit und die the remainder of the book. Thisbook contains new 978-3-642-08373-0 ▶ 119,95 € results, and a substantial portion of this materialhas Berechenbarkeit fundamentalen Grenzen unterliegen, never before appeared in book form. The book will be die wir nicht überwinden können. Diese durchdrin- of interest toboth researchers and graduate students. gen die gesamte Mathematik; sie sind integraler Topics covered in this book include: - Biorthogonal Bestandteil jener Gesetzmäßigkeiten, die diese Wis- Systems in Separable Banach Spaces- Universality and senschaft im Innersten zusammenhalten.Das vor- Szlenk Index- Weak Topologies and Renormings- liegende Buch entführt Sie auf eine Reise durch die Biorthogonal Systems in Nonseparable Spaces- Trans- Kerngebiete der mathematischen Logik. Es ist eine finite Sequence Spaces- Applications Petr Hájek is Reise voller Überraschungen, hin zu den Grenzen der Professor of Mathematics at the Mathematical Insti- Mathematik. Unter anderem werden die folgenden tute ofthe Academy of Sciences of the Czech Repub- Themen behandelt: Geschichte der mathematischen lic. Vicente Montesinos isProfessor of Mathematics Logik, formale Systeme, axiomatische Zahlentheo- at the Polytechnic University ofValencia, Spain. Jon rie und Mengenlehre, Beweistheorie, die Gödel‘schen Vanderwerff is Professor of Mathematics at LaSierra Unvollständigkeitssätze, Berechenbarkeitstheorie, springer.com 15 algorithmische Informationstheorie, Modelltheorie. the field will find the book invaluable both as a study Das Buch enthält zahlreiche zweifarbige Abbildun- material and as a desktop reference. gen und mehr als 70 Aufgaben (mit Lösungen auf der More on www.springer.com/978-3-642-07899-6 Website zum Buch). Available More on www.springer.com/978-3-8274-2559-1 2003. XIV, 772 p. (Springer Monographs in Mathematics, ) Available 978-3-642-07899-6 ▶ 119,95 € 2011. X, 409 S. 300 Abb. in Farbe. 978-3-8274-2559-1 ▶ 27,99 €

A. Iske, E. Quak, M.S. Floater Tutorials on Multiresolution in Geometric Modelling Summer School Lecture Notes Multiresolution methods in geometric modelling are concerned with the generation, representation, and manipulation of geometric objects at several levels of detail. Applications include fast visualization and K. Jänich rendering as well as coding, compression and digital transmission of 3D geometric objects. This book is Mathematik 2 W. Hundsdorfer, J.G. Verwer based on thirteen tutorials presented during the Euro- Geschrieben für Physiker Numerical Solution of Time- pean Summer School "Principles of Multiresolution in Der Inhalt dieses zweiten Bandes gliedert sich in Geometric Modelling", held at the Munich University fünf Teile zu je drei Kapiteln. Der erste Teil (Kapi- Dependent Advection-Diffusion- of Technology, Germany, during August 22-30, 2001. tel 23 - 25) ist grundlegender Art und führt von den Reaction Equations The book covers: subdivision; wavelets; scattered data Axiomen der reellen Zahlen bis zur Taylorentwick- modelling; and coding and data structures. The tuto- lung in mehreren Variablen. Der zweite Teil behan- This book describes numerical methods for partial rials are designed to be introductory in character, and delt jenen Kernbereich der Differentialrechnung in differential equations (PDEs) coupling advection, dif- include supporting exercises. Other supplementary mehreren Variablen, der ausgehend vom Umkehrsatz fusion and reaction terms, encompassing methods material and software can be downloaded from the das lokale Verhalten der nichtlinearen Abbildun- for hyperbolic, parabolic and stiff and nonstiff ordi- web site www.ma.tum.de/primus2001/. gen, die impliziten Funktionen und die Analysis nary differential equations (ODEs). The emphasis More on www.springer.com/978-3-642-07819-4 unter Nebenbedingungen und auf k-dimensionalen lies on time-dependent transport-chemistry prob- Available Flächen beschreibt. Der dritte Teil ist der klassis- lems, describing e.g. the evolution of concentrations chen und der vierte der mathematisch modernen in environmental and biological applications. Along Vektoranalysis gewidmet, der Autor vergisst aber with the common topics of stability and convergence, 2002. XI, 421 p. 172 illus., 4 in color. (Mathematics and Visualization, ) auch dabei nicht, dass seine Leser Physikstudenten much attention is paid on how to prevent spurious, 978-3-642-07819-4 ▶ 79,95 € im zweiten Semester sind. Die letzten drei Kapitel negative concentrations and oscillations, both in schließlich geben mathematische Rückendeckung für space and time. Many of the theoretical aspects are das Erlebnis der ersten physikalischen Theorievor- illustrated by numerical experiments on models from lesung, nämlich der gewöhnlich im zweiten oder drit- biology, chemistry and physics. A unified approach ten Semester gebotenen theoretischen Mechanik. Wie is followed by emphasizing the method of lines or im ersten Band helfen viele Figuren, das abstrakte semi-discretization. In this regard this book differs Verständnis durch anschauliche Vorstellungen zu substantially from more specialized textbooks which ergänzen. deal exclusively with either PDEs or ODEs. This book treats integration methods suitable for both classes of More on www.springer.com/978-3-642-16149-0 problems and thus is of interest to PDE researchers Available unfamiliar with advanced numerical ODE methods, as well as to ODE researchers unaware of the vast 2011. XII, 384 S. (Springer-Lehrbuch, ) amount of interesting results on numerical PDEs. The 978-3-642-16149-0 ▶ 27,99 € first chapter provides a self-contained introduction to the field and can be used for an undergraduate course on the numerical solution of PDEs. The remaining T. Jech four chapters are more specialized and of interest to researchers, practitioners and graduate students from Set Theory numerical mathematics, scientific computing, compu- The Third Millennium Edition, revised and tational physics and other computational sciences. expanded More on www.springer.com/978-3-642-05707-6 Set Theory has experienced a rapid development in Available recent years, with major advances in forcing, inner 2003. X, 471 p. (Springer Series in Computational models, large cardinals and descriptive set theory. Mathematics, 33) The present book covers each of these areas, giving 978-3-642-05707-6 ▶ 104,95 € the reader an understanding of the ideas involved. It can be used for introductory students and is broad and deep enough to bring the reader near the boundaries of current research. Students and researchers in 16 springer.com

ematical properties and interrelations of these non- combinatorial designs etc. This second edition is an standard theories between each other and with ZFC extended version and puts more emphasis on appli- and some variants of ZFC, foundational problems of cations to the constructive theory of finite structures. the theories, including the problem of external sets Recent progress in this field, in particular in design and the Power Set problem, and methods of their and coding theory, is described. This book will be of solution. The book is oriented towards a reader hav- great use to researchers and graduate students. ing some experience in foundations (set theory, model More on www.springer.com/978-3-642-08522-2 theory) and in nonstandard analysis. Available More on www.springer.com/978-3-642-06077-9 1999. XXVI, 454 p. (Algorithms and Combinatorics, 19) Available 978-3-642-08522-2 ▶ 119,95 € W. Kaballo 2004. XVI, 408 p. (Springer Monographs in Mathematics, ) 978-3-642-06077-9 ▶ 89,95 € Grundkurs Funktionalanalysis A. Kirillov In diesem Buch finden Sie die Grundlagen der Funk- tionalanalysis, die im ersten Drittel des 20. Jahrhun- Representation Theory and derts entwickelt wurden.Ausgehend von konkreten Noncommutative Harmonic Fragen der Analysis lernen Sie Methoden zur Unter- suchung linearer Operatoren zwischen Hilberträumen Analysis I und Banachräumen kennen und wenden diese auf Fundamental Concepts. Representations of Fourier-Reihen, lineare Integral- und Differentialgle- Virasoro and Affine Algebras ichungen und in der Quantenmechanik an.Das Buch Part I of this book is a short review of the classical part eignet sich hervorragend als Begleitlektüre zu einer of representation theory. The main chapters of rep- einführenden Vorlesung über Funktionalanalysis resentation theory are discussed: representations of und auch zum Selbststudium.Es ist sehr ausführlich finite and compact groups, finite- and infinite-dimen- und leicht verständlich geschrieben, die Konzepte sional representations of Lie groups. It is a typical und Resultate werden durch zahlreiche Beispiele und G. Kemper feature of this survey that the structure of the the- Abbildungen illustriert. Anhand vieler Übungsauf- ory is carefully exposed - the reader can easily see the gaben können Sie Ihr Verständnis des Stoffes testen, A Course in Commutative Algebra essence of the theory without being overwhelmed by anhand anderer diesen selbstständig weiterentwick- details. The final chapter is devoted to the method of eln. Lösungen finden Sie auf der Webseite zum Buch This textbook offers a thorough, modern introduc- orbits for different types of groups. Part II deals with zum Buch unter www.springer.de. An Vorkennt- tion into commutative algebra. It is intented mainly to representation of Virasoro and Kac-Moody algebra. nissen benötigen Sie nur "Analysis I", Grundlagen serve as a guide for a course of one or two semesters, The second part of the book deals with representa- der Linearen Algebra und der Topologie metrischer or for self-study. The carefully selected subject matter tions of Virasoro and Kac-Moody algebra. The wealth Räume sowie Vertrautheit mit Lebesgue-Integralen. concentrates on the concepts and results at the center of recent results on representations of infinite-dimen- Bei Bedarf können Sie viele dieser Vorkenntnisse mit- of the field. The book maintains a constant view on sional groups is presented. tels des ausführlichen Anhangs auffrischen. the natural geometric context, enabling the reader to More on www.springer.com/978-3-642-05740-3 More on www.springer.com/978-3-8274-2149-4 gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to Available Due April 2011 computational aspects. Many illustrative examples 1994. VII, 236 p. 11 illus. (Encyclopaedia of Mathematical and exercises enrich the text. 2011. XII, 348 S. 75 Abb. Sciences, 22) 978-3-8274-2149-4 ▶ 23,32 € More on www.springer.com/978-3-642-03544-9 978-3-642-05740-3 ▶ 104,95 € Available

2011. XI, 246 p. (Graduate Texts in Mathematics, 256) 978-3-642-03544-9 ▶ 49,95 €

P.E. Kloeden, E. Platen V. Kanovei, M. Reeken Nonstandard Analysis, Numerical Solution of Stochastic Axiomatically Differential Equations A. Kerber The book is devoted to nonstandard set theories that The numerical analysis of stochastic differential equations differs significantly from that of ordinary serve as foundational basis for nonstandard mathe- Applied Finite Group Actions matics. Several popular and some less known non- differential equations due to peculiarities of stochas- standard theories are considered, including internal The topic of this book is finite group actions and their tic calculus. This book provides an introduction to set theory IST, Hrbacek set theory HST, and others. use in order to approach finite unlabeled structures by stochastic calculus and stochastic differential equa- The book presents the basic structure of the set uni- defining them as orbits of finite groups of sets. Well- tions, in both theory and applications, emphasising verse of these theories and methods to effectively known examples are graphs, linear codes, chemical the numerical methods needed to solve such equa- develop "applied" nonstandard analysis, metamath- isomers, spin configurations, isomorphism classes of tions. It assumes of the reader an undergraduate back- springer.com 17 ground in mathematical methods typical of engineers orously developing computer algebra, and narrowly on the bijection between these eta products and lattice and physicists, though many chapters begin with interpreted as the study of algebraic objects defined simplices. a descriptive summary. The book is also accessible by generators and their relations. The author shows More on www.springer.com/978-3-642-16151-3 to others who only require numerical recipes. The how objects like words, graphs and automata provide stochastic Taylor expansion provides the basis for valuable information in asymptotic studies. The main Available the discrete time numerical methods for differential methods emply the notions of Gröbner bases, gen- 2011. X, 480 p. (Springer Monographs in Mathematics, ) equations. The book presents many new results on erating functions, growth and those of homological 978-3-642-16151-3 ▶ 89,95 € high-order methods for strong sample path approx- algebra. Treated are also problems of relationships imations and for weak functional approximations, between different series, such as Hilbert, Poincare including implicit, predictor-corrector, extra-polation and Poincare-Betti series. Hyperbolic and quantum and variance-reduction methods. Besides serving as a groups are also discussed. The reader does not need basic text on such methods, the book offers the reader much of background material for he can find defi- ready access to a large number of potential research nitions and simple properties of the defined notions problems in a field that is just beginning to expand introduced along the way. "Non-Associative Struc- rapidly and is widely applicable. To help the reader to tures" by E.N.Kuz'min and I.P.Shestakov surveys the develop an intuitive understanding of the underlying modern state of the theory of non-associative struc- mathematics and hand-on numerical skills, exercises tures that are nearly associative. Jordan, alternative, and over 100 PC-Exercises are included. Malcev, and quasigroup algebras are discussed as well More on www.springer.com/978-3-642-08107-1 as applications of these structures in various areas of mathematics and primarily their relationship with Available the associative algebras. Quasigroups and loops are 1992. XXXVI, 636 p. (Stochastic Modelling and Applied treated too. The survey is self-contained and com- H. Kütting, F. Padberg, M.J. Sauer Probability, 23) plete with references to proofs in the literature. The 978-3-642-08107-1 ▶ 79,95 € book will be of great interest to graduate students and Elementare Stochastik researchers in mathematics, computer science and theoretical physics. Mathematische Grundlagen und didaktische Konzepte More on www.springer.com/978-3-642-08124-8 Praxisnah und gut lesbar geschrieben, vermittelt Available dieses Werk einen Einblick in die Wissenschaft, die 1995. VII, 287 p. 5 illus. (Encyclopaedia of Mathematical sich mit Zufallserscheinungen befasst. Der Leser Sciences, 57) lernt die „Mathematik des Zufalls“ kennen und 978-3-642-08124-8 ▶ 94,95 € verstehen. In der vorliegenden überarbeiteten und durch Aufnahme von zwei Kapiteln zur Statistik erweiterten dritten Auflage werden gründlich u. a. folgende zentrale Themen behandelt:Deskriptive Statistik: Historische Entwicklung, Erhebung und Aufbereitung von Daten (Lage- und Streu- ungsparameter), Lineare Regression und Kor- relationGenese der Wahrscheinlichkeitstheorie S. Kobayashi mit ihren faszinierenden Beispielen aus dem 17. JahrhundertAxiomatischer Aufbau der Wahrschein- Hyperbolic Complex Space lichkeitstheorie im 20. JahrhundertGrundbegriffe In the three decades since the introduction of the der KombinatorikSimulation von Zufallsex- Kobayashi distance, the subject of hyperbolic com- perimentenDiskrete ZufallsvariableAllgemeine plex spaces and holomorphic mappings has grown WahrscheinlichkeitsräumeStetige Verteilungsfunk- tionenInduktive Statistik: Schätztheorie, Testtheorie to be a big industry. This book gives a comprehen- G. Köhler sive and systematic account on the Carathéodory and (ein- und zweiseitige Tests, Gütefunktionen), Konfi- Kobayashi distances, hyperbolic complex spaces and Eta Products and Theta Series denzintervalleBesonderer Wert wird auf das Model- holomorphic mappings with geometric methods. A lieren gelegt, d. h. auf die Kompetenz, Sachverhalte very complete list of references should be useful for Identities der Alltagswirklichkeit in mathematische Modelle zu prospective researchers in this area. übertragen.Beispiele und Übungsaufgaben – für das This monograph deals with products of Dedekind's Verstehen von Mathematik von eminenter Bedeutung More on www.springer.com/978-3-642-08339-6 eta function, with Hecke theta series on quadratic – nehmen in diesem Buch einen breiten Raum ein. Available number fields, and with Eisenstein series. The author Im Anhang sind Lösungen angegeben.Das Buch wen- brings to the public the large number of identities 1998. XIII, 472 p. 8 illus. (Grundlehren der mathematischen det sich an Lehramts-Studierende, die Mathematik als Wissenschaften, 318) that have been discovered over the past 20 years, the eines ihrer Fächer haben, an Studierende in den Bach- majority of which have not been published elsewhere. 978-3-642-08339-6 ▶ 89,95 € elor- und Masterstudiengängen und an Lehrende mit The book will be of interest to graduate students and dem Fach Mathematik. scholars in the field of number theory and, in partic- More on www.springer.com/978-3-8274-2759-5 ular, modular forms. It is not an introductory text in A. Kostrikin, I. Shafarevich this field. Nevertheless, some theoretical background Due April 2011 material is presented that is important for under- Algebra VI standing the examples in Part II. In Part I relevant 2011. VIII, 418 S. 104 Abb. (Mathematik Primar- und Combinatorial and Asymptotic Methods of definitions and essential theorems -- such as a com- Sekundarstufe, ) Algebra. Nonassociative Structures plete proof of the structure theorems for coprime 978-3-8274-2759-5 ▶ 23,32 € residue class groups in quadratic number fields that This book contains two contributions: "Combina- are not easily accessible in the literature -- are pro- torial and Asymptotic Methods in Algebra" by V.A. vided. Another example is a thorough description Ufnarovskij is a survey of various combinatorial of an algorithm for listing all eta products of given methods in infinite-dimensional algebras, widely weight and level, together with proofs of some results interpreted to contain homological algebra and vig- 18 springer.com

Chemie der Elemente ist nun Inhalt eines eigenen, vierten Bandes. More on www.springer.com/978-3-642-17522-0 Due April 2011 H.P. Langtangen A Primer on Scientific 2011. XIV, 306 S. 139 Abb. (Springer-Lehrbuch, ) 978-3-642-17522-0 27,99 € Programming with Python ▶ The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example- and problem-oriented, where the applications are R.S. Liptser, A.N. Shiryaev taken from mathematics, numerical calculus, statistics, physics, biology, and finance. The book teaches Statistics of Random Processes "Matlab-style" and procedural programming as well I. General Theory as object-oriented programming. High school math- The subject of these two volumes is non-linear fil- ematics is a required background, and it is advanta- tering (prediction and smoothing) theory and its geous to study classical and numerical one-variable application to the problem of optimal estimation, calculus in parallel with reading this book. Besides control with incomplete data, information theory, and learning how to program computers, the reader will sequential testing of hypothesis. The required mathe- also learn how to solve mathematical problems, aris- Z. Li matical background is presented in the first volume: ing in various branches of science and engineering, the theory of martingales, stochastic differential equa- with the aid of numerical methods and programming. Measure-Valued Branching tions, the absolute continuity of probability measures By blending programming, mathematics and scien- for diffusion and Ito processes, elements of stochastic tific applications, the book lays a solid foundation for Markov Processes calculus for counting processes. The book is not only practicing computational science. Measure-valued branching processes arise as high addressed to mathematicians but should also serve More on www.springer.com/978-3-642-18365-2 density limits of branching particle systems. The the interests of other scientists who apply probabilis- Due April 2011 Dawson-Watanabe superprocess is a special class of tic and statistical methods in their work. The theory of those. The author constructs superprocesses with martingales presented in the book has an independent 2011. XXIX, 701 p. 50 illus. in color. (Texts in Borel right underlying motions and general branching interest in connection with problems from financial Computational Science and Engineering, 6) mechanisms and shows the existence of their Borel mathematics. In the second edition, the authors have 978-3-642-18365-2 ▶ 49,95 € right realizations. He then uses transformations to made numerous corrections, updating every chapter, derive the existence and regularity of several differ- adding two new subsections devoted to the Kalman ent forms of the superprocesses. This treatment sim- filter under wrong initial conditions, as well as a new plifies the constructions and gives useful perspectives. chapter devoted to asymptotically optimal filtering Martingale problems of superprocesses are discussed under diffusion approximation. Moreover, in each under Feller type assumptions. The most important chapter a comment is added about the progress of feature of the book is the systematic treatment of recent years. immigration superprocesses and generalized Orn- More on www.springer.com/978-3-642-08366-2 stein--Uhlenbeck processes based on skew convolu- Available tion semigroups. The volume addresses researchers in measure-valued processes, branching processes, 2001. XV, 427 p. (Stochastic Modelling and Applied stochastic analysis, biological and genetic models, and Probability, 5) graduate students in probability theory and stochastic 978-3-642-08366-2 ▶ 79,95 € processes. More on www.springer.com/978-3-642-15003-6 H.P. Latscha, H.A. Klein, M. Mutz Available

Allgemeine Chemie 2011. X, 350 p. (Probability and Its Applications, ) Chemie-Basiswissen I 978-3-642-15003-6 ▶ 59,95 € C. Maclachlan, A.W. Reid Der erste Band der Reihe Chemie-Basiswissen vermittelt in seiner neuen Auflage die allgemeinen The Arithmetic of Hyperbolic 3- Grundlagen der Chemie für Bachelor-Studiengänge mit Chemie als Haupt- oder Nebenfach sowie für Manifolds Studierende des höheren Lehramtes. Als Grundla- For the past 25 years, the Geometrization Program of gen-Repetitorium ist er auch für den Master-Studi- Thurston has been a driving force for research in 3- engang Chemie geeignet. Die Autoren präsentieren manifold topology. This has inspired a surge of activ- den Stoff in kurzer und übersichtlicher Form und ity investigating hyperbolic 3-manifolds (and Kleinian mit einem lernfreundlichen Layout. Das didaktis- groups), as these manifolds form the largest and least che Konzept und die am Curriculum orientierte well-understood class of compact 3-manifolds. Famil- Stoffauswahl haben die Vorauflagen so erfolgreich iar and new tools from diverse areas of mathematics gemacht. Mit der 10. Auflage dieses Bandes sind die have been utilized in these investigations, from topol- Inhalte noch besser auf die Bedürfnisse der ange- ogy, geometry, analysis, group theory, and from the sprochenen Studierenden zugeschnitten. Die für point of view of this book, algebra and number the- das Hauptfach Chemie darüber hinaus erforderliche ory. This book is aimed at readers already familiar with the basics of hyperbolic 3-manifolds or Kleinian groups, and it is intended to introduce them to the springer.com 19 interesting connections with number theory and the mization methods for tackling the ‘linear ordering tools that will be required to pursue them. While problem’ (LOP). Whereas important applications there are a number of texts which cover the topologi- in business, engineering and economics lie beyond cal, geometric and analytical aspects of hyperbolic 3- the reach of methodologies that have been the focus manifolds, this book is unique in that it deals exclu- A. Martinez of academic research for three decades, the fresh sively with the arithmetic aspects, which are not cov- approaches set out in this volume provide practical ered in other texts. Colin Maclachlan is a Reader in An Introduction to Semiclassical solutions to the LOP. The focus on the LOP does not the Department of Mathematical Sciences at the Uni- limit the monograph’s scope and applicability, how- versity of Aberdeen in Scotland where he has served and Microlocal Analysis ever. The exact and heuristic techniques outlined in since 1968. He is a former President of the Edinburgh This book presents most of the techniques used in these pages can be put to use in any number of com- Mathematical Society. Alan Reid is a Professor in the microlocal treatment of semiclassical problems binatorial optimization problems. While the authors the Department of Mathematics at The University coming from quantum physics. Both the standard C? employ the LOP to illustrate cutting-edge optimiza- of Texas at Austin. He is a former Royal Society Uni- pseudodifferential calculus and the analytic microlo- tion technologies, the book is also a tutorial on how versity Research Fellow, Alfred P. Sloan Fellow and cal analysis are developed, in a context which remains to design effective and successful implementations of winner of the Sir Edmund Whittaker Prize from The intentionally global so that only the relevant diffi- exact and heuristic procedures alike. The information Edinburgh Mathematical Society. Both authors have culties of the theory are encountered. The original- in these pages provides readers with a toolkit that can published extensively in the general area of discrete ity lies in the fact that the main features of analytic be employed in a variety of settings. As a result, the groups, hyperbolic manifolds and low-dimensional microlocal analysis are derived from a single and ele- book will be of great interest to researchers and prac- topology. mentary a priori estimate.Various exercises illustrate titioners in a number of fields, including computer More on www.springer.com/978-1-4419-3122-1 the chief results of each chapter while introducing the science, mathematics, operations research, manage- reader to further developments of the theory. Appli- ment science, industrial engineering, and economics. Due April 2011 cations to the study of the Schrödinger operator are It is also suitable for use as a textbook on issues of also discussed, to further the understanding of new practical optimization in a masters course, or as a 2003. XIII, 463 p. 57 illus. (Graduate Texts in reference book for engineering optimization algo- Mathematics, 219) notions or general results by replacing them in the context of quantum mechanics. This book is aimed rithms. The authors have sought to make the book 978-1-4419-3122-1 59,95 € ▶ at non-specialists of the subject and the only required accessible to as wide an audience as possible by pro- prerequisite is a basic knowledge of the theory of viding the reader with basic definitions and concepts distributions.André Martinez is currently Professor in optimization. In addition, the numerous tutorials of Mathematics at the University of Bologna, Italy, aid speedy assimilation, while the coverage given to after having moved from France where he was Profes- the next generation of Flash software prepares readers sor at Paris-Nord University. He has published many for future developments. research articles in semiclassical quantum mechan- More on www.springer.com/978-3-642-16728-7 ics, in particular related to the Born-Oppenheimer Available approximation, phase-space tunneling, scattering theory and resonances. 2011. XII, 171 p. 38 illus., 12 in color. (Applied Mathematical Sciences, 175) More on www.springer.com/978-1-4419-2961-7 978-3-642-16728-7 ▶ 79,95 € Due April 2011

2002. VIII, 190 p. (Universitext, ) S. Mardesic 978-1-4419-2961-7 ▶ 59,95 € Strong Shape and Homology Shape theory is an extension of homotopy theory from the realm of CW-complexes to arbitrary spaces. Besides applications in topology, it has interesting applications in various other areas of mathematics, especially in dynamical systems and C*-algebras. Strong shape is a refinement of ordinary shape with distinct advantages over the latter. Strong homology generalizes Steenrod homology and is an invariant of strong shape. The book gives a detailed account based V. Maz'ya on approximation of spaces by polyhedra (ANRs) using the technique of inverse systems. It is intended Sobolev Spaces for researchers and graduate students. Special care is with Applications to Elliptic Partial Differential devoted to motivation and bibliographic notes. R. Martí, G. Reinelt Equations More on www.springer.com/978-3-642-08546-8 The Linear Ordering Problem Sobolev spaces play an outstanding role in modern Available Exact and Heuristic Methods in Combinatorial analysis, in particular, in the theory of partial differential equations and its applications in mathematical 2000. XII, 489 p. (Springer Monographs in Mathematics, ) Optimization physics. They form an indispensable tool in approxi- 978-3-642-08546-8 95,95 € ▶ Complex optimization problems abound in the real mation theory, spectral theory, differential geometry world. In the face of these challenges, established etc. The theory of these spaces is of interest in itself methods often fall short of providing solutions. being a beautiful domain of mathematics. The present However, ‘exact’ and ‘heuristic’ techniques are dra- volume includes basics on Sobolev spaces, approx- matically enhancing our ability to solve significant imation and extension theorems, embedding and practical problems in the world of optimization. They compactness theorems, their relations with isoperi- are changing the landscape in the field, broaden- metric and isocapacitary inequalities, capacities with ing the frontiers of the possible, and allowing us to applications to spectral theory of elliptic differen- engage effectively with a whole new range of chal- tial operators as well as pointwise inequalities for lenges. This monograph sets out state-of-the-art opti- derivatives. The selection of topics is mainly influ- 20 springer.com enced by the author’s involvement in their study, a the volume rewarding." -The Mathematical Gazette considerable part of the text is a report on his work (2001) in the field. Part of this volume #rst appeared in Ger- More on www.springer.com/978-1-4419-7891-2 man as three booklets of Teubner-Texte zur Mathe- matik (1979,1980). In the Springer volume “Sobolev Available Spaces”, published in English in 1985, the material was expanded and revised. The present 2nd edition is 2011. XXVIII, 448 p. (Interdisciplinary Applied enhanced by many recent results and it includes new Mathematics, 11) applications to linear and nonlinear partial differential 978-1-4419-7891-2 ▶ 89,95 € equations. New historical comments, five new chapters and a signi#cantly augmented list of references aim to create a broader and modern view of the area. F. Modler, M. Kreh More on www.springer.com/978-3-642-15563-5 Available Tutorium Analysis 2 und Lineare 2011. XXVIII, 866 p. (Grundlehren der mathematischen Wissenschaften, 342) Algebra 2 978-3-642-15563-5 ▶ 129,95 € Mathematik von Studenten für Studenten erklärt und kommentiert Nach dem großen Erfolg von Tutorium Analysis 1 und Lineare Algebra 1 erscheint nun ein Fortset- zungsband der beiden Autoren, mit dem sie den Zweitsemestern und allen, die Analysis 2 und Lin- F. Modler, M. Kreh eare Algebra 2 oder verwandte Vorlesungen hören müssen, wieder unterstützend unter die Arme Tutorium Analysis 1 und Lineare greifen. Das Konzept bleibt das Altbewährte: Es Algebra 1 gibt wieder einen mathematischen Teil, in dem die Definitionen, Sätze und Beweise stehen, und einen Mathematik von Studenten für Studenten erklärenden Teil, in dem die schwierigen Definitio- erklärt und kommentiert nen und Sätze auf gewohnt lockere und lustige Art Dieses Buch soll Ihnen als Mathematik-Erstsemester und Weise mit vielen Beispielen und Abbildungen mit den Einstieg und Umstieg von der Schulmathematik Leben gefüllt werden. Über 150 Beispiele und ca. 70 J.M. McCarthy, G.S. Soh in die Hochschulmathematik erleichtern und Ihnen Abbildungen erleichtern hierbei das Verständnis und somit helfen, viele der üblichen Erstsemester-Fehler bieten dem Leser zweierlei: einerseits einen Blick für Geometric Design of Linkages zu vermeiden. Denn aller Anfang ist schwer, und mathematisch exakte Definitionen und den mathematisch präzisen Satz und Beweis und andererseits Hil- This book is an introduction to the mathematical die Autoren wollen versuchen, Ihnen den Anfang fen und Anschauungen, die ebenso wichtig sind, um theory of design for articulated mechanical systems so leicht wie möglich zu machen und Ihnen helfen, den Stoff zu verstehen. known as linkages. The focus is on sizing mechani- Schwierigkeiten zu überstehen, die im ersten Semester cal constraints that guide the movement of a work- ganz normal sind. Das Buch ist anders als alle More on www.springer.com/978-3-8274-2630-7 anderen, denn es wurde von Studenten geschrieben, piece, or end effector, of the system. The function Available of the device is prescribed as a set of positions to be die Erfahrung als Tutor, Übungsleiter und Korrek- toren haben. Dadurch wissen die Autoren zum einen, reachable by the end effector; and the mechanical 2011. X, 313 S. 73 Abb. welche Themen schwer verständlich sind und beson- constraints are formed by joints that limit relative 978-3-8274-2630-7 ▶ 18,64 € movement. The goal is to find all the devices that ders ausführlich behandelt werden müssen, und zum can achieve a specific task. Formulated in this way anderen kennen sie häufige Fehler und können auf the design problem is purely geometric in character. diese hinweisen. In dem Buch gibt es einen math- Robot manipulators, walking machines, and mechan- ematischen Teil, den der Student für Prüfungen ical hands are examples of articulated mechanical sys- beherrschen muss. Bei Fragen oder Problemen kann tems that rely on simple mechanical constraints to er dann in dem Kommentarteil nachschauen und provide a complex workspace for the end effector.This dort ausführliche Erklärungen, Hilfen und Beispiele new edition includes research results of the past der Autoren finden. So verfügt der Leser über zweier- P. Moral decade on the synthesis of multiloop planar and lei: einerseits über die mathematisch exakte Defini- spherical linkages, and the use of homotopy methods tion oder den mathematisch präzisen Satz und Beweis Feynman-Kac Formulae and Clifford algebras in the synthesis of spatial serial und anderseits über Hilfen und Anschauungen, die Genealogical and Interacting Particle Systems ebenso wichtig sind, um den Stoff zu verstehen. Unter chains. One new chapter on the synthesis of spatial with Applications serial chains introduces the linear product decompo- www.mathestudium-tutor.de können Sie Fragen zum sition of polynomial systems and polynomial contin- Buch stellen. This book contains a systematic and self-contained treatment of Feynman-Kac path mea- uation solutions. The second new chapter introduces More on www.springer.com/978-3-8274-2345-0 sures, their genealogical and interacting particle the Clifford algebra formulation of the kinematics Available equations of serial chain robots. Examples are used interpretations,and their applications to a variety of throughout to demonstrate the theory. Review of First problems arising in statistical physics, biology, and 2010. XI, 363 S. 45 Abb. advanced engineering sciences. Topics include spec- Edition: "...I found the author had provided an excel- 978-3-8274-2345-0 ▶ 18,64 € lent text that enabled me to come to terms with the tral analysis of Feynman-Kac-Schrödinger opera- subject. Readers with an interest in the area will find tors, Dirichlet problems with boundary conditions, finance, molecular analysis, rare events and directed polymers simulation, genetic algorithms, Metropo- lis-Hastings type models, as well as filtering problems and hidden Markov chains. This text takes readers in a clear and progressive format from simple to recent and advanced topics in pure and applied probability springer.com 21 such as contraction and annealed properties of non cal concepts from fibre spaces (Chap.2), CW-com- linear semi-groups, functional entropy inequalities, plexes, homology and homotopy, through bordism empirical process convergence, increasing propaga- theory and K-theory to the Adams-Novikov spectral tions of chaos, central limit,and Berry Esseen type sequence (Chap.3), and in Chapter 4 an exhaustive theorems as well as large deviations principles for (but necessarily concentrated) survey of the theory of strong topologies on path-distribution spaces. Topics manifolds. An appendix sketching the recent impres- also include a body of powerful branching and inter- sive developments in the theory of knots and links acting particle methods and worked out illustrations and low-dimensional topology generally, brings the of the key aspect of the theory. With practical and survey right up to the present. This work represents easy to use references as well as deeper and modern the flagship, as it were, in whose wake follow more mathematics studies, the book will be of use to engi- detailed surveys of the various subfields, by various neers and researchers in pure and applied mathemat- authors. J. Neukirch ics, statistics, physics, biology, and operation research More on www.springer.com/978-3-642-05735-9 who have a background in probability and Markov chain theory. Pierre Del Moral is a research fellow in Algebraic Number Theory Available mathematics at the C.N.R.S. (Centre National de la 1996. VI, 320 p. 78 illus. (Encyclopaedia of Mathematical "The present book has as its aim to resolve a discrep- Recherche Scientifique) at the Laboratoire de Statis- Sciences, 12) ancy in the textbook literature and ... to provide a tique et Probabilités of Paul Sabatier University in 978-3-642-05735-9 104,95 € comprehensive introduction to algebraic number the- ▶ Toulouse. He received his Ph.D. in signal processing ory which is largely based on the modern, unifying at the LAAS-CNRS (Laboratoire d'Analyse et Archi- conception of (one-dimensional) arithmetic algebraic tecture des Systèmes) of Toulouse. He is one of the geometry. ... Despite this exacting program, the book principal designers of the modern and recently devel- remains an introduction to algebraic number theory oping theory on particle methods in filtering theory. for the beginner... The author discusses the classical He served as a research engineer in the company Ste- concepts from the viewpoint of Arakelov theory.... ria-Digilog from 1992 to 1995 and he has been a vis- The treatment of class field theory is ... particularly A. Okubo, S.A. Levin iting professor at Purdue University and Princeton rich in illustrating complements, hints for further University. He is a former associate editor of the jour- study, and concrete examples.... The concluding chap- nal Stochastic Analysis and Applications. Diffusion and Ecological ter VII on zeta-functions and L-series is another out- More on www.springer.com/978-1-4419-1902-1 standing advantage of the present textbook.... The Problems: Modern Perspectives Due April 2011 book is, without any doubt, the most up-to-date, sys- This substantially expanded and updated version of 2004. XVIII, 555 p. 15 illus. (Probability and Its Applications, ) tematic, and theoretically comprehensive textbook the classic 1980 book by the late Akira Okubo traces on algebraic number field theory available." W. Klein- 978-1-4419-1902-1 ▶ 73,95 € the developments that have flowed from the original ert in Z.blatt f. Math., 1992 "The author's enthusiasm work, building on detailed notes he left for revision. for this topic is rarely as evident for the reader as in The first edition was a comprehensive treatment of this book. - A good book, a beautiful book." F. Lorenz the use of diffusion models in ecology that integrated in Jber. DMV 1995 "The present work is written in a rigorous mathematical theory and substantive appli- very careful and masterly fashion. It does not show cations. Enormous in scope, covering a wide variety of the pains that it must have caused even an expert like topics and including models of spread, critical patch Neukirch. It undoubtedly is liable to become a classic; size, and grouping, it has remained one of the most the more so as recent developments have been taken popular books in mathematical biology and has stim- into account which will not be outdated quickly. Not ulated extensive research in the two decades since its only must it be missing from the library of no number publication. In this volume, friends and disciples of theorist, but it can simply be recommended to every Okubo incorporate a wide range of results from their mathematician who wants to get an idea of modern own fields that build upon the framework he first arithmetic." J. Schoissengeier in Montatshefte Mathe- established. matik 1994 More on www.springer.com/978-1-4419-3151-1 More on www.springer.com/978-3-642-08473-7 W. Narkiewicz Available Available Elementary and Analytic Theory 1999. XVII, 571 p. 16 illus. (Grundlehren der mathematischen 2001. XX, 467 p. 134 illus. (Interdisciplinary Applied of Algebraic Numbers Wissenschaften, 322) Mathematics, 14) 978-3-642-08473-7 ▶ 109,95 € 978-1-4419-3151-1 ▶ 73,95 € This book gives an exposition of the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. The follow- S. Novikov, S. Novikov ing topics are treated: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ide- Topology I les and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic General Survey fields, and factorization problems. Each chapter ends This book constitutes nothing less than an up-to-date with exercises and a short review of the relevant lit- survey of the whole field of topology (with the excep- erature up to 2003. The bibliography has over 3400 tion of "general (set-theoretic) topology"), or, in the items. words of Novikov himself, of what was termed at the More on www.springer.com/978-3-642-06010-6 end of the 19th century "Analysis Situs", and subse- quently diversified into the various subfields of com- Available binatorial, algebraic, differential, homotopic, and 2004. XI, 708 p. (Springer Monographs in Mathematics, ) geometric topology. The book gives an overview of 978-3-642-06010-6 ▶ 119,95 € these subfields, beginning with the elements and proceeding right up to the present frontiers of research. Thus one finds here the whole range of topologi- 22 springer.com

uate students in differential geometry, algebra and strategienSehr differenzierte Analyse des halb- theoretical physics. schriftlichen RechnensViele konkrete Hinweise More on www.springer.com/978-3-642-08120-0 zum entdeckenden Lernen und beziehungsre- ichen ÜbenVorstellung vielfältiger Zugangswege Available zum schriftlichen RechnenDiagnose von Lern- 1994. V, 248 p. 1 illus. (Encyclopaedia of Mathematical schwierigkeiten, Analyse von Fehlerstrategien, Sciences, 41) konstruktiven Umgang mit Fehlern sowie durch 978-3-642-08120-0 ▶ 104,95 € Hinweise zur FörderarbeitVielfältige Anregun- gen zum überschlagenden und kontrollierenden RechnenGründliche Darstellung zum Einsatz von A. Onishchik, E. Vinberg Taschenrechnern und Computern in der Grund- schule Einbeziehung von rund 130 sorgfältig aus- A. Olivieri, E. Pitacco Lie Groups and Lie Algebras II gesuchten, überzeugenden Aufgabenbeispielen aus neuesten Schulbüchern – erstmalig in FarbeDas Introduction to Insurance Discrete Subgroups of Lie Groups and Buch wendet sich an Studierende für das Lehramt Cohomologies of Lie Groups and Lie Algebras Mathematics im Primarbereich, an Lehramtsanwärterinnen und The first part of this book on Discrete Subgroups of Lehramtsanwärter mit Mathematik als Fach sowie an Technical and Financial Features of Risk Lie Groups is written by E.B. Vinberg, V.V. Gorbat- Lehrkräfte, die nach neuen Ideen für ihren täglichen Transfers sevich, and O.V. Shvartsman. Various types of dis- Unterricht suchen. The book aims at presenting technical and financial crete subgroups of Lie groups arise in the theory of More on www.springer.com/978-3-8274-1996-5 functions of complex variables, arithmetic, geome- features of life insurance, non-life insurance, pen- Due April 2011 sion plans. The book has been planned assuming try, and crystallography. Since the foundation of their general theory in the 50-60s of this century, consid- non-actuarial readers as its “natural” target, namely 2011. X, 374 S. 150 Abb. in Farbe. (Mathematik erable and in many respects exhaustive results were - advanced undergraduate and graduate students in Primar- und Sekundarstufe, ) Economics, Business and Finance; - professionals and obtained. This development is reflected in this sur- 978-3-8274-1996-5 ▶ 23,32 € technicians operating in Insurance and pension areas, vey. Both semisimple and general Lie groups are con- whose job may regard investments, risk analysis, sidered. Part II on Cohomologies of Lie Groups and financial reporting, etc, and hence implies a commu- Algebras is written by B.L. Feigin and D. B.Fuchs. It nication with actuarial professionals and managers. contains different definitions of cohomologies of Lie Given the assumed target, the book focuses on techni- groups and (both finite-dimensional and some infi- cal and financial aspects of insurance, however avoid- nite-dimensional) Lie algebras, the main methods of ing the use of complex mathematical tools. In this their calculation, and the results of these calculations. sense, the book can be placed at some “midpoint” of The book can be useful as a reference and research the existing literature, part of which adopts more for- guide to graduate students and researchers in differ- mal approaches to insurance problems implying the ent areas of mathematics and theoretical physics. use of non-elementary mathematics, whereas another More on www.springer.com/978-3-642-08071-5 part addresses practical questions totally avoiding Available even simple mathematical tools (which, in our opin- ion, can conversely provide effective tools for present- 2000. VII, 223 p. 3 illus. (Encyclopaedia of Mathematical ing technical and financial features of the insurance Sciences, 21) P.J. Papajorgji, P.M. Pardalos business). 978-3-642-08071-5 ▶ 104,95 € More on www.springer.com/978-3-642-16028-8 Advances in Modeling Available Agricultural Systems This book presents an up-to-date review of advances 2011. XV, 475 p. 180 illus. in the mathematical modeling of agricultural sys- 978-3-642-16028-8 ▶ 59,95 € tems. It covers a broad spectrum of problems and applications based on internet and communications technology, as well as methodological approaches A. Onishchik, E. Vinberg based on the integration of different simulation and data management tools. Using real-world cases, each Lie Groups and Lie Algebras III chapter presents a detailed solution of a problem in a Structure of Lie Groups and Lie Algebras particular field. This book demonstrates that regard- less of the nature of the problem and the application The book contains a comprehensive account of the domain, modeling is a central and important activ- structure and classification of Lie groups and finite- F. Padberg, C. Benz ity in the process of developing agricultural systems. dimensional Lie algebras (including semisimple, solv- Researchers and graduate students in the fields of able, and of general type). In particular, a modern Didaktik der Arithmetik agriculture and environmental studies will benefit approach to the description of automorphisms and für Lehrerausbildung und Lehrerfortbildung from this book. It will also serve as an excellent refer- gradings of semisimple Lie algebras is given. A spe- ence for managers, team leaders, developers and mod- cial chapter is devoted to models of the exceptional Die neuesten Lehrpläne und Bildungsstandards haben elers of agricultural and environmental systems and Lie algebras. The book contains many tables and will in jüngster Zeit zu substanziellen Veränderungen researchers in the applied computation field. serve as a reference. At the same time many results are im Arithmetikunterricht geführt. Auf diese sowie accompanied by short proofs. Onishchik and Vinberg auf weitere wünschenswerte Veränderungen bere- More on www.springer.com/978-1-4419-4525-9 are internationally known specialists in their field and iten wir in dieser stark überarbeiteten Neuauflage Available well-known for their monograph "Lie Groups and der bewährten Didaktik der Arithmetik gründlich 2009. X, 522 p. 172 illus. (Springer Optimization and Its Algebraic Groups" (Springer-Verlag 1990). This Ency- vor durch: Vielseitige Grundlegung tragfähiger Applications, 25) clopaedia volume will be immensely useful to grad- ZahlvorstellungenBreite Thematisierung von Vorken- 978-1-4419-4525-9 ▶ 86,95 € ntnissen und informellen LösungsstrategienBetonung flexibler mündlicher und halbschriftlicher Rechen- springer.com 23

ment of epilepsy and other brain disorders, * treatment of head-and-neck, prostate, and other cancers using conventional conformal and intensity-modu- lated radiation therapy as well as proton therapy, * treatment selection for breast cancer based on new P. Pedregal classification schemes, * optimization for the genome project, *optimal timing of organ transplants. This Introduction to Optimization handbook is an invaluable resource for graduate students and academic researchers in biomedical engi- This undergraduate textbook introduces students neering, computer science, operations research, and of science and engineering to the fascinating field of medicine. Practioners as well will be able to adapt the optimization. It is a unique book that brings together different approaches to their needs. the subfields of mathematical programming, variational calculus, and optimization in a single refer- P.M. Pardalos, V.A. Yatsenko More on www.springer.com/978-1-4419-3532-8 ence. As a primer on optimization, its main goal is to Optimization and Control of Due April 2011 provide a succinct and accessible introduction to lin- 2009. XIII, 442 p. 129 illus. (Springer Optimization and Its ear programming, nonlinear programming, numer- Bilinear Systems Applications, 26) ical optimization algorithms, variational problems, Theory, Algorithms, and Applications 978-1-4419-3532-8 ▶ 99,95 € dynamic programming, and optimal control. Prereq- uisites have been kept to a minimum, although a basic The purpose of this book is to acquaint the reader knowledge of calculus, linear algebra, and differential with the developments in bilinear systems theory and equations is assumed. There are numerous examples, its applications. Bilinear systems can be used to rep- illustrations, and exercises throughout the text, mak- resent a wide range of physical, chemical, biological, ing it an ideal book for self-study. Applied mathemati- and social systems, as well as manufacturing pro- cians, physicists, engineers, and scientists will find this cesses, which cannot be effectively modeled under the introduction to optimization extremely useful. assumption of linearity. This book provides a unified More on www.springer.com/978-1-4419-2334-9 approach for the identification and control of nonlinear complex objects that can be transformed into Due April 2011 bilinear systems, with a focus on the control of open physical processes functioning in a non-equilibrium 2004. 248 p. 38 illus. (Texts in Applied Mathematics, mode. The material is intended for graduate students, 46) researchers, and specialists engaged in the fields of 978-1-4419-2334-9 ▶ 66,95 € quantum and molecular computing, control of physical processes, biophysics, superconducting levitation, G. Peccati, M.S. Taqqu physical information science, mathematics, and engineering. Wiener Chaos: Moments, More on www.springer.com/978-1-4419-4468-9 Cumulants and Diagrams Available A survey with Computer Implementation 2008. XXVI, 374 p. 40 illus. (Springer Optimization and Its The concept of Wiener chaos generalizes to an infi- Applications, 11) nite-dimensional setting the properties of orthogonal 978-1-4419-4468-9 ▶ 62,95 € polynomials associated with probability distributions on the real line. It plays a crucial role in modern probability theory, with applications ranging from Malli- avin calculus to stochastic differential equations and from probabilistic approximations to mathematical finance. This book is concerned with combinatorial M.M. Peixoto, A.A. Pinto, D.A. Rand structures arising from the study of chaotic random variables related to infinitely divisible random mea- Dynamics, Games and Science I sures. The combinatorial structures involved are those DYNA 2008, in Honor of Maurício Peixoto of partitions of finite sets, over which Möbius func- and David Rand, University of Minho, Braga, tions and related inversion formulae are defined. This combinatorial standpoint (which is originally due to Portugal, September 8-12, 2008 Rota and Wallstrom) provides an ideal framework Dynamics, Games and Science I and II are a selec- for diagrams, which are graphical devices used to tion of surveys and research articles written by leading compute moments and cumulants of random vari- researchers in mathematics. The majority of the con- P.M. Pardalos, H.E. Romeijn ables. Several applications are described, in particular, tributions are on dynamical systems and game theory, recent limit theorems for chaotic random variables. focusing either on fundamental and theoretical devel- Handbook of Optimization in An Appendix presents a computer implementation in opments or on applications to modeling in biology, Medicine MATHEMATICA for many of the formulae. ecomonics, engineering, finances and psychology. The More on www.springer.com/978-88-470-1678-1 papers are based on talks given at the International Handbook of Optimization in Medicine is devoted to Conference DYNA 2008, held in honor of Mauricio examining the dramatic increase in the application Available Peixoto and David Rand at the University of Braga, of effective optimization techniques to the delivery 2011. 200 p. 30 illus. (Bocconi & Springer Series, 1) Portugal, on September 8-12, 2008. The aim of the- of health care. The articles, written by experts from 978-88-470-1678-1 ▶ 79,95 € se volumes is to present cutting-edge research in these the areas of optimization (operations research), com- areas to encourage graduate students and researchers puter science, and medicine, focus on models and algorithms that have led to more efficient and sophisticated treatments of patients. Topics covered include: * optimization in medical imaging, * classification and data mining with medical applications, * treat- 24 springer.com in mathematics and other fields to develop them fur- cal Engineering and Computer Science, UC Berkeley, problems and their solutions provide the reader with ther. USA http://dm.tzi.de/research/contextual-computing/ an opportunity to sharpen their skills and to apply More on www.springer.com/978-3-642-11455-7 More on www.springer.com/978-3-642-17395-0 the theory. This framework guides the reader to an easy comprehension of some of the jewels of num- Available Available ber theory The book is self-contained and rigorously 2011. XXXI, 809 p. (Springer Proceedings in Mathematics, 1) 2011. XII, 178 p. 4 illus. in color. (Cognitive Technologies, ) presented. Various aspects will be of interest to grad- 978-3-642-11455-7 ▶ 159,95 € 978-3-642-17395-0 ▶ 79,95 € uate and undergraduate students in number theory, advanced high school students and the teachers who train them for mathematics competitions, as well as to scholars who will enjoy learning more about number theory. Michael Th. Rassias has received several awards in mathematical problem solving competitions including two gold medals at the Pan-Hellenic Mathematical Competitions of 2002 and 2003 held in Athens, a silver medal at the Balkan Mathematical Olympiad of 2002 held in Targu Mures, Romania and a silver medal at the 44th International Mathematical Olympiad of 2003 held in Tokyo, Japan. More on www.springer.com/978-1-4419-0494-2 Available

R. Porzel A. Prestel, C.N. Delzell 2011. XV, 324 p. 3 illus. Contextual Computing Positive Polynomials 978-1-4419-0494-2 ▶ 49,95 € Models and Applications From Hilbert's 17th Problem to Real Algebra Recent advances in the fields of knowledge represen- Positivity is one of the most basic mathematical con- tation, reasoning and human-computer interaction cepts. In many areas of mathematics (like analysis, have paved the way for a novel approach to treating real algebraic geometry, functional analysis, etc.) it and handling context. The field of research presented shows up as positivity of a polynomial on a certain in this book addresses the problem of contextual com- subset of R^n which itself is often given by polyno- puting in artificial intelligence based on the state of mial inequalities. The main objective of the book is the art in knowledge representation and human-com- to give useful characterizations of such polynomi- puter interaction. The author puts forward a knowl- als. It takes as starting point Hilbert's 17th Problem edge-based approach for employing high-level context from 1900 and explains how E. Artin's solution of that in order to solve some persistent and challenging problem eventually led to the development of real problems in the chosen showcase domain of natu- algebra towards the end of the 20th century. Beyond ral language understanding. Specifically, the prob- basic knowledge in algebra, only valuation theory as lems addressed concern the handling of noise due to explained in the appendix is needed. Thus the mono- K. Reiss, G. Stroth speech recognition errors, semantic ambiguities, and graph can also serve as the basis for a 2-semester the notorious problem of underspecification. Conse- course in real algebra. Endliche Strukturen quently the book examines the individual contribu- More on www.springer.com/978-3-642-07445-5 tions of contextual composing for different types of In diesem Band stehen Probleme im Mittelpunkt, context. Therefore, contextual information stemming Available die sich zunächst einfach anhören, dann aber eine from the domain at hand, prior discourse, and the 2001. VIII, 268 p. (Springer Monographs in Mathematics, ) anspruchsvollere mathematische Bearbeitung verlan- specific user and real world situation are considered 978-3-642-07445-5 ▶ 79,95 € gen. Sie kommen aus unterschiedlichen Bereichen, and integrated in a formal model that is applied and doch ist ihnen gemeinsam, dass sie sich auf eine evaluated employing different multimodal mobile dia- endliche Anzahl von Elementen beziehen. Hierfür log systems. This book is intended to meet the needs werden mathematische Modelle betrachtet und of readers from at least three fields – AI and computer immer wieder die gleichen Fragen gestellt: Hat ein science; computational linguistics; and natural lan- bestimmtes Problem überhaupt eine Lösung? Kann guage processing – as well as some computationally man alle Lösungen systematisch bestimmen? Gibt oriented linguists, making it a valuable resource for es dabei einen wirklich effizienten Weg? Das Buch scientists, researchers, lecturers, language processing konzentriert sich in fünf Kapiteln auf die grundle- practitioners and professionals as well as postgradu- genden algebraischen Strukturen Gruppe, Ring und ates and some undergraduates in the aforementioned Körper sowie auf Einblicke in die Galoistheorie, die fields. “The book addresses a problem of great and Codierungstheorie und die Graphentheorie. Am increasing technical and practical importance – the Beispiel endlicher Strukturen wird jeweils aufgezeigt, role of context in natural language processing (NLP). welche Theorien die Mathematik zur Verfügung stellt, It considers the role of context in three important wenn konkrete Fragestellungen wie das Abzählen von Mustern, die Codierung von Nachrichten oder tasks: Automatic Speech Recognition, Semantic Inter- M.T. Rassias pretation, and Pragmatic Interpretation. Overall, the das Aufstellen von Tourenplänen bearbeitet werden book represents a novel and insightful investigation Problem-Solving and Selected sollen. into the potential of contextual information process- More on www.springer.com/978-3-642-17181-9 ing in NLP.” Jerome A Feldman, Professor of Electri- Topics in Number Theory Available In the Spirit of the Mathematical Olympiads This book is designed to introduce some of the most 2011. X, 325 S. (Mathematik für das Lehramt, ) important theorems and results from number the- 978-3-642-17181-9 ▶ 23,32 € ory while testing the reader’s understanding through carefully selected Olympiad-caliber problems. These springer.com 25

zweiter, grundlegend überarbeiteter und aktualisierter Auflage. Paulo Ribenboim ist emeritierter Professor der kanadischen Queen's University, Fellow der Royal Society of Canada und Träger des George Pólya- M. Renardy, R.C. Rogers Preises der Mathematical Association of America. Er ist Autor von 13 Büchern und über 150 Forschungsar- An Introduction to Partial tikeln. Differential Equations More on www.springer.com/978-3-642-18078-1 Available Partial differential equations (PDEs) are fundamental to the modeling of natural phenomena, arising 2011. XXVII, 364 S. 380 Abb. (Springer-Lehrbuch, ) in every field of science. Consequently, the desire 978-3-642-18078-1 27,99 € to understand the solutions of these equations has ▶ S. Roman always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as Field Theory complex function theory, functional analysis, and This book presents the basic theory of fields, starting algebraic topology. Like algebra, topology, and ratio- more or less from the beginning. It is suitable for a nal mechanics, PDEs are a core area of mathematics. graduate course in field theory, or independent study. This book aims to provide the background necessary The reader is expected to have taken an undergrad- to initiate work on a Ph.D. thesis in PDEs for begin- uate course in abstract algebra, not so much for the ning graduate students. Prerequisites include a truly material it contains but in order to gain a certain level advanced calculus course and basic complex variables. of mathematical maturity. For this new edition, the Lebesgue integration is needed only in chapter 10, author has rewritten the text based on his experiences and the necessary tools from functional analysis are teaching from the first edition. There are new exer- developed within the coarse. The book can be used to cises, a new chapter on Galois theory from an his- teach a variety of different courses. This new edition torical perspective, and additional topics sprinkled features new problems throughout, and the problems throughout the text, including a proof of the Fun- J. Richter-Gebert have been rearranged in each section from simplest to damental Theorem of Algebra, a discussion of casus most difficult. New examples have also been added. Perspectives on Projective irreducibilis, Berlekamp's algorithm for factoring The material on Sobolev spaces has been rearranged polynomials over Zp and natural and accessory irra- and expanded. A new section on nonlinear variational Geometry tionalities. From the reviews of the first edition: The problems with "Young-measure" solutions appears. A Guided Tour Through Real and Complex book is written in a clear and explanatory style...the The reference section has also been expanded. Geometry book is recommended for a graduate course in field More on www.springer.com/978-1-4419-1820-8 theory as well as for independent study. - T. Albu, Projective geometry is one of the most fundamen- Available Mathematical Reviews ...[the author] does an excel- tal and at the same time most beautiful branches of lent job of stressing the key ideas. This book should geometry. It can be considered the common foun- 2004. XIV, 434 p. 21 illus. (Texts in Applied not only work well as a textbook for a beginning grad- dation of many other geometric disciplines like Mathematics, 13) uate course in field theory, but also for a student who Euclidean geometry, hyperbolic and elliptic geometry 978-1-4419-1820-8 ▶ 73,95 € wishes to take a field theory course as independent or even relativistic space-time geometry. This book study. - J.N.Mordeson, Zentralblatt offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains More on www.springer.com/978-1-4419-2095-9 how metric concepts may be best understood in pro- Due April 2011 jective terms. One of the major themes that appears throughout this book is the beauty of the interplay- 2006. XII, 335 p. 18 illus. (Graduate Texts in between geometry, algebra and combinatorics. This Mathematics, 158) book can especially be used as a guide that explains 978-1-4419-2095-9 ▶ 49,95 € how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations. P. Ribenboim More on www.springer.com/978-3-642-17285-4 Die Welt der Primzahlen Available Geheimnisse und Rekorde 2011. XXII, 571 p. 380 illus., 250 in color. Die Welt der Primzahlen - in faszinierender Weise 978-3-642-17285-4 ▶ 64,95 € werden die wesentlichen Ergebnisse über die elementaren Bausteine der natürlichen Zahlen vorgestellt. Grundlegende Sätze und die wichtigsten J. Saranen, G. Vainikko offenen Fragen und ungelösten Probleme werden von einer wohl einmaligen Sammlung von Rekorden Periodic Integral and über Primzahlen begleitet. Ein umfangreiches Liter- Pseudodifferential Equations with aturverzeichnis ergänzt das Buch zu einer wichtigen Quelle für jeden Leser, der sich für die Zahlenthe- Numerical Approximation orie und insbesondere für Primzahlen interessiert. Classical boundary integral equations arising In der englischen Originalfassung fast schon ein from the potential theory and acoustics (Laplace Klassiker, erscheint die deutsche Ausgabe jetzt in 26 springer.com and Helmholtz equations) are derived. Using the control, the material gives the student the opportunity parametrization of the boundary these equations take to see the connections between different fields and a form of periodic pseudodifferential equations. A the underlying ideas that unify them. This text will general theory of periodic pseudodifferential equa- benefit students in applied mathematics, economics, tions and methods of solving are developed, includ- engineering, and related fields. Prerequisites include a ing trigonometric Galerkin and collocation methods, course in calculus and elementary probability theory. their fully discrete versions with fast solvers, quadra- No knowledge of measure theory is assumed. ture and spline based methods. The theory of periodic More on www.springer.com/978-1-4419-4569-3 pseudodifferential operators is presented in details, with preliminaries (Fredholm operators, periodic dis- Due April 2011 tributions, periodic Sobolev spaces) and full proofs. 2009. X, 222 p. This self-contained monograph can be used as a text- S. Schwarze book by graduate/postgraduate students. It also con- 978-1-4419-4569-3 ▶ 46,95 € tains a lot of carefully chosen exercises. Path Player Games More on www.springer.com/978-3-642-07538-4 Analysis and Applications Available A path player game is a new innovative type of game 2002. XI, 452 p. (Springer Monographs in Mathematics, ) which considers network flow problems from the 978-3-642-07538-4 ▶ 99,95 € viewpoint of network owners. This strategy enables modeling real-world problems and has many practical applications. Key features: * Presents a rigorous exposition of the theoretical foundations of the concept of a path player game; * Suggests 18 practical open problems for future research in such areas as traffic planning, computation of equilibria, and optimization; * Examines potentials for games on polyhedra as well as integer versions of generalized Nash equilibria. Written clearly, with well-presented mathematics, this J. Serre book is intended for graduate students, mathematicians, engineers, and computer scientists. Local Algebra More on www.springer.com/978-1-4419-4606-5 This is an English translation of the now classic Available "Algèbre Locale - Multiplicités" originally published 2009. X, 168 p. (Springer Optimization and Its Applications, by Springer as LNM 11, in several editions since 1965. O. Scherzer 24) It gives a short account of the main theorems of com- 978-1-4419-4606-5 ▶ 42,95 € mutative algebra, with emphasis on modules, homo- Handbook of Mathematical logical methods and intersection multiplicities ("Tor- Methods in Imaging formula"). Many modifications to the original French text have been made by the author for this English The Handbook of Mathematical Methods in Imag- edition: they make the text easier to read, without ing provides a comprehensive treatment of the math- changing its intended informal character. ematical techniques used in imaging science. The material is grouped into two central themes, namely, More on www.springer.com/978-3-642-08590-1 Inverse Problems (Algorithmic Reconstruction) and Available Signal and Image Processing. Each section within the 2000. XIII, 129 p. (Springer Monographs in Mathematics, ) themes covers applications (modeling), mathemat- 978-3-642-08590-1 ▶ 49,95 € ics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through con- nected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied A. Seierstad mathematics. Engineers and computer scientists working in imaging will also find this handbook use- Stochastic Control in Discrete and ful. Continuous Time More on www.springer.com/978-0-387-92921-7 This book provides a comprehensive introduction Available to stochastic control problems in discrete and con- 2011. XVIII, 1607 p. 150 illus. Print + eReference. tinuous time. The material is presented logically, 978-0-387-92921-7 ▶ 624,00 € beginning with the discrete-time case before proceed- J.R. Shackell ing to the stochastic continuous-time models. Cen- tral themes are dynamic programming in discrete Symbolic Asymptotics time and HJB-equations in continuous time. Top- Symbolic asymptotics has recently undergone con- ics covered include stochastic maximum principles siderable theoretical development, especially in areas for discrete time and continuous time, even for prob- where power series are no longer an appropriate tool. lems with terminal conditions. Numerous illustrative Implementation is beginning to follow. The present examples and exercises, with solutions at the end of book, written by one of the leading specialists in the the book, are included to enhance the understanding area, is currently the only one to treat this part of of the reader. By interlinking many fields in stochastic symbolic asymptotics. It contains a good deal of inter- springer.com 27 esting material in a new, developing field of math- only prerequisite being a basic course in algebraic in the sense that proofs proceed step-by-step from ematics at the intersection of algebra, analysis and number theory. elementary first principals without further appeal computing, presented in a lively and readable way. More on www.springer.com/978-1-4419-2478-0 to outside results. Several chapters have new hereto- The associated areas of zero equivalence and Hardy fore unpublished research results. On the other hand, fields are also covered. The book is intended to be Available certain groups of chapters would make good gradu- accessible to anyone with a good general background ate courses. All but one chapter provide exercises for in mathematics, but it nonetheless gets right to the 2007. VIII, 152 p. (Springer Monographs in either use in such a course, or to elicit new research cutting edge of active research. Some results appear Mathematics, ) directions. 978-1-4419-2478-0 ▶ 46,95 € here for the first time, while others have hitherto only More on www.springer.com/978-3-642-15626-7 been given in preprints. Due to its clear presentation, this book is interesting for a broad audience of mathe- Available maticians and theoretical computer scientists. M. Shubin 2011. XXII, 676 p. (Universitext, ) More on www.springer.com/978-3-642-05925-4 Partial Differential Equations VII 978-3-642-15626-7 ▶ 69,95 € Available Spectral Theory of Differential Operators 2004. XII, 243 p. 1 illus. (Algorithms and Computation in Mathematics, 12) This EMS volume contains a survey of the princi- 978-3-642-05925-4 ▶ 79,95 € ples and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finite-dimensional spaces. The basic notions and theorems are first reviewed and followed by a comprehensive presentation of a variety of advanced approaches such as the factorization method, the variational techniques, the approximate spectral projec- tion method, and the probabilistic method, to name a few. Special attention is devoted to the spectral properties of Schrödinger and Dirac operators and of other operators as well. In addition, a special section of Sunada's recent solution of Kac's celebrated problem F. Skof of whether or not "one can hear the shape of a drum" is included. Giuseppe Peano between More on www.springer.com/978-3-642-08116-3 Mathematics and Logic Available G. Shimura Proceeding of the International Conference 1994. V, 272 p. (Encyclopaedia of Mathematical Sciences, 64) in honour of Giuseppe Peano on the 150th Elementary Dirichlet Series and 978-3-642-08116-3 ▶ 104,95 € anniversary of his birth and the centennial of the Modular Forms Formulario Mathematico Torino (Italy) October 2-3, 2008 The main topics of the book are the critical values of Dirichlet L-functions and Hecke L-functions of an This book contains the papers developing out the imaginary quadratic field, and various problems on presentations given at the International Conference elliptic modular forms. As to the values of Dirich- organized by the Torino Academy of Sciences and let L-functions, all previous papers and books reiter- the Department of Mathematics Giuseppe Peano of ate a single old result with a single old method. After the Torino University to celebrate the 150th anniver- a review of elementary Fourier analysis, the author sary of G. Peano's birth - one of the greatest figures in presents completely new results with new methods, modern mathematics and logic and the most impor- though old results will also be proved. No advanced tant mathematical logician in Italy - a century after knowledge of number theory is required up to this the publication of Formulario Mathematico, a great point. As applications, new formulas for the second attempt to systematise Mathematics in symbolic form. factor of the class number of a cyclotomic field will be More on www.springer.com/978-88-470-1835-8 given. The second half of the book assumes familiarity E.E. Shult Available with basic knowledge of modular forms. However, all definitions and facts are clearly stated, and precise ref- Points and Lines 2011. X, 190 p. 8 illus. erences are given. The notion of nearly holomorphic Characterizing the Classical Geometries 978-88-470-1835-8 ▶ 89,95 € modular forms is introduced and applied to the deter- mination of the critical values of Hecke L-functions The classical geometries of points and lines include of an imaginary quadratic field. Other notable fea- not only the projective and polar spaces, but simi- tures of the book are: (1) some new results on classical lar truncations of geometries naturally arising from Eisenstein series; (2) the discussion of isomorphism the groups of Lie type. Virtually all of these geome- classes of elliptic curves with complex multiplication tries (or homomorphic images of them) are charac- in connection with their zeta function and periods; (3) terized in this book by simple local axioms on points a new class of holomorphic differential operators that and lines. Simple point-line characterizations of Lie send modular forms to those of a different weight. incidence geometries allow one to recognize Lie inci- The book will be of interest to graduate students and dence geometries and their automorphism groups. researchers who are interested in special values of L- These tools could be useful in shortening the enor- functions, class number formulae, arithmetic prop- mously lengthy classification of finite simple groups. erties of modular forms (especially their values), and Similarly, recognizing ruled manifolds by axioms on the arithmetic properties of Dirichlet series. It treats light trajectories offers a way for a physicist to rec- in detail, from an elementary viewpoint, the simplest ognize the action of a Lie group in a context where cases of a fundamental area of ongoing research, the it is not clear what Hamiltonians or Casimir operators are involved. The presentation is self-contained 28 springer.com

nigfaltigkeiten (u.a. den Differentialformenkalkül, Vektorfelder und ihre Flüsse, den Satz von Stokes und die de Rham-Kohomologie). Die notwendigen Hilfsmittel aus der Multilinearen Algebra und über Vektorbündel werden bereitgestellt. Außerdem werden Lie-Gruppen, Zusammenhänge und der Satz von Frobenius, (pseudo-) Riemannsche Mannig- faltigkeiten, Grundbegriffe der Algebraischen Topolo- gie, Funktionentheorie und Riemannsche Flächen sowie die Funktionalanalysis einschließlich der Oper- atorentheorie behandelt. Zahlreiche Beispiele und J. Stillwell Aufgaben begleiten den Text. A. Soifer Naive Lie Theory More on www.springer.com/978-3-8274-2767-0 The Colorado Mathematical Available In this new textbook, acclaimed author John Stillwell Olympiad and Further presents a lucid introduction to Lie theory suitable 2000. 868 S. Explorations for junior and senior level undergraduates. In order 978-3-8274-2767-0 ▶ 37,34 € From the Mountains of Colorado to the Peaks of to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, Mathematics and quaternion spaces. These symmetry groups may This book presents the 20-year account of the Col- be represented by matrices, which allows them to be orado Mathematical Olympiad — its dreams and studied by elementary methods from calculus and lin- rewards, hard work and conflict. It features more than ear algebra. This naive approach to Lie theory is orig- just original wonderful problems and their ingenious inally due to von Neumann, and it is now possible to solutions; it tells a compelling story involving the lives streamline it by using standard results of undergradu- of those who have been part of the Olympiad. The ate mathematics. To compensate for the limitations of reader will meet Olympians and follow their paths as the naive approach, end of chapter discussions intro- professionals. In the vast field of competition books, duce important results beyond those proved in the this book is unique, for it builds bridges between book, as part of an informal sketch of Lie theory and Olympiads and “real” mathematics by demonstrat- its history. John Stillwell is Professor of Mathematics ing through 20 “Further Explorations,” the trains at the University of San Francisco. He is the author of of mathematical thought, showing how a solved several highly regarded books published by Springer, A. Sznitman Olympiad problem gives birth to deeper problems including The Four Pillars of Geometry (2005), Ele- and leads to the forefront of mathematical research ments of Number Theory (2003), Mathematics and Its Brownian Motion, Obstacles and full of striking results and open problems.Like Gauss, History (Second Edition, 2002), Numbers and Geom- Alexander Soifer would not hesitate to inject Eureka! etry (1998) and Elements of Algebra (1994). Random Media at the right moment. Like van der Waerden, he can More on www.springer.com/978-0-387-78214-0 This book is aimed at graduate students and transform a dispassionate exercise in logic into a com- researchers. It provides an account for the non-spe- pelling account of sudden insights and ultimate tri- Available cialist of the circle of ideas, results and techniques, umph. — Cecil Rousseau Chair, USA Mathematical which grew out in the study of Brownian motion Olympiad Committee ... this book is not so much 2008. XIII, 218 p. 25 illus. (Undergraduate Texts in and random obstacles. This subject has a rich phe- mathematical literature as it is literature built around Mathematics, ) nomenology which exhibits certain paradigms, mathematics… with the Further Explorations sec- 978-0-387-78214-0 ▶ 40,95 € emblematic of the theory of random media. It also tions, anyone so inclined could spend a lifetime on Special offer valid until July 31, 2011 22,95 € brings into play diverse mathematical techniques such the mathematics sprouting from this volume. —Peter as stochastic processes, functional analysis, poten- D. Johnson, Jr., Auburn University I finished reading tial theory, first passage percolation. In a first part, the book in one sitting – I just could not put it down. the book presents, in a concrete manner, background Professor Soifer has indebted us all by first making material related to the Feynman-Kac formula, poten- the effort to organize the Colorado Mathematical tial theory, and eigenvalue estimates. In a second Olympiads, and then making the additional effort to part, it discusses recent developments including the tell us about it in such an engaging and useful way. method of enlargement of obstacles, Lyapunov coeffi- —Branko Grünbaum, University of Washington A cients, and the pinning effect. The book also includes delightful feature of the book is that in the second part an overview of known results and connections with more related problems are discussed. Some of them other areas of random media. are still unsolved. —Paul Erd#s The book is a gold mine of brilliant reasoning with special emphasis on More on www.springer.com/978-3-642-08420-1 the power and beauty of coloring proofs. Strongly rec- Available ommended to both serious and recreational mathe- U. Storch, H. Wiebe 1998. XVI, 353 p. 45 illus. (Springer Monographs in maticians on all levels of expertise. —Martin Gardner Mathematics, ) More on www.springer.com/978-0-387-75471-0 Lehrbuch der Mathematik, Band 4 978-3-642-08420-1 ▶ 79,95 € Due April 2011 Analysis auf Mannigfaltigkeiten - Funktionentheorie - Funktionalanalysis 2011. XXX, 405 p. 185 illus., 18 in color. Die "Analysis auf Mannigfaltigkeiten" ist der 978-0-387-75471-0 ▶ 49,95 € abschließende Band eines vierbändigen Lehrbuchs der Mathematik für Mathematiker, Physiker und Informatiker über den Lehrstoff bis zum mathematischen Vorexamen und darüber hinaus. Der Band enthält die Grundlagen der Differential- und Integralrechnung auf reellen und komplexen Man- springer.com 29

obtained in and around the theory of spherical varieties. More on www.springer.com/978-3-642-18398-0 Available 2011. XXI, 253 p. 16 illus. (Encyclopaedia of Mathematical Sciences, 138) 978-3-642-18398-0 ▶ 89,95 €

K. Taira S. Vasishth, M. Broe Semigroups, Boundary Value The Foundations of Statistics: A Problems and Markov Processes Simulation-based Approach The purpose of this book is to provide a careful and Statistics and hypothesis testing are routinely used accessible account along modern lines of the subject in areas (such as linguistics) that are traditionally which the title deals, as well as to discuss problems not mathematically intensive. In such fields, when of current interest in the field. More precisely this faced with experimental data, many students and book is devoted to the functional-analytic approach researchers tend to rely on commercial packages to a class of degenerate boundary value problems for to carry out statistical data analysis, often without R.S. Varga second-order elliptic integro-differential operators understanding the logic of the statistical tests they which includes as particular cases the Dirichlet and Geršgorin and His Circles rely on. As a consequence, results are often misin- Robin problems. This class of boundary value prob- terpreted, and users have difficulty in flexibly apply- lems provides a new example of analytic semigroups. This book studies the original results, and their exten- ing techniques relevant to their own research — they As an application, we construct a strong Markov pro- sions, of the Russian mathematician, S.A. Geršgorin, use whatever they happen to have learned. A sim- cess corresponding to such a diffusion phenomenon who wrote a seminal paper in 1931, on how to easily ple solution is to teach the fundamental ideas of sta- that a Markovian particle moves both by jumps and obtain estimates of all n eigenvalues (characteristic tistical hypothesis testing without using too much continuously in the state space until it dies at the time values) of any given n-by-n complex matrix. Since the mathematics. This book provides a non-mathemat- when it reaches the set where the particle is definitely publication of this paper, there has been many newer ical, simulation-based introduction to basic statisti- absorbed. results spawned by his paper, and this book will be the cal concepts and encourages readers to try out the simulations themselves using the source code and More on www.springer.com/978-3-642-07371-7 first which is devoted solely to this resulting area. As such, it will include the latest research results, such as data provided (the freely available programming lan- Available Brauer ovals of Cassini and Brualdi lemniscates, and guage R is used throughout). Since the code presented 2004. XI, 337 p. (Springer Monographs in Mathematics, ) their comparisons. This book is dedicated to the late in the text almost always requires the use of previ- 978-3-642-07371-7 ▶ 84,95 € Olga Taussky-Todd and her husband, John Todd. It ously introduced programming constructs, diligent was Olga who brought to light Geršgorin's paper and students also acquire basic programming abilities in its significance to the mathematical world. The level R. The book is intended for advanced undergraduate and graduate students in any discipline, although D. Timashev of this book requires only a modest background in linear algebra and analysis, and is therefore compre- the focus is on linguistics, psychology, and cognitive Homogeneous Spaces and hensible to upper-level and graduate level students in science. It is designed for self-instruction, but it can mathematics. also be used as a textbook for a first course on statis- Equivariant Embeddings tics. Earlier versions of the book have been used in More on www.springer.com/978-3-540-21100-6 undergraduate and graduate courses in Europe and Homogeneous spaces of linear algebraic groups lie Available the US. ”Vasishth and Broe have written an attrac- at the crossroads of algebraic geometry, theory of 2004. X, 226 p. 1 illus. in color. (Springer Series in tive introduction to the foundations of statistics. It is algebraic groups, classical projective and enumera- Computational Mathematics, 36) concise, surprisingly comprehensive, self-contained tive geometry, harmonic analysis, and representation 978-3-540-21100-6 ▶ 79,95 € and yet quite accessible. Highly recommended.” theory. By standard reasons of algebraic geometry, Harald Baayen, Professor of Linguistics, University in order to solve various problems on a homoge- of Alberta, Canada ”By using the text students not neous space, it is natural and helpful to compactify it only learn to do the specific things outlined in the while keeping track of the group action, i.e., to con- book, they also gain a skill set that empowers them to sider equivariant completions or, more generally, explore new areas that lie beyond the book’s cover- open embeddings of a given homogeneous space. age.” Colin Phillips, Professor of Linguistics, Univer- Such equivariant embeddings are the subject of this sity of Maryland, USA book. We focus on the classification of equivariant embeddings in terms of certain data of "combinato- More on www.springer.com/978-3-642-16312-8 rial" nature (the Luna-Vust theory) and description of Available various geometric and representation-theoretic properties of these varieties based on these data. The class 2011. XVI, 178 p. 25 illus. of spherical varieties, intensively studied during the 978-3-642-16312-8 ▶ 39,95 € last three decades, is of special interest in the scope of this book. Spherical varieties include many classical examples, such as Grassmannians, flag varieties, and varieties of quadrics, as well as well-known toric varieties. We have attempted to cover most of the important issues, including the recent substantial progress 30 springer.com

E. Vinberg the same time simplified proofs of zero estimates (due to P. Philippon) on linear algebraic groups. Geometry More on www.springer.com/978-3-642-08608-3 Volume 2: Spaces of Constant Curvature Available This book contains a systematic and comprehensive 2000. XXIII, 633 p. (Grundlehren der mathematischen exposition of Lobachevskian geometry and the the- Wissenschaften, 326) ory of discrete groups of motions in Euclidean space 978-3-642-08608-3 ▶ 109,95 € and Lobachevsky space. The authors give a very clear account of their subject describing it from the view- points of elementary geometry, Riemannian geometry and group theory. The result is a book which has no Z. Wang, G.J. Klir rival in the literature. Part I contains the classification of motions in spaces of constant curvature and non- traditional topics like the theory of acute-angled poly- Generalized Measure Theory hedra and methods for computing volumes of non- This comprehensive text examines the relatively new Euclidean polyhedra. Part II includes the theory of mathematical area of generalized measure theory. cristallographic, Fuchsian, and Kleinian groups and This area expands classical measure theory by aban- an exposition of Thurston's theory of deformations. doning the requirement of additivity and replacing The greater part of the book is accessible to first-year it with various weaker requirements. Each of these students in mathematics. At the same time the book weaker requirements characterizes a class of non- includes very recent results which will be of interest to additive measures. This results in new concepts and researchers in this field. G. Walz, F. Zeilfelder, T. Rießinger methods that allow us to deal with many problems More on www.springer.com/978-3-642-08086-9 in a more realistic way. For example, it allows us to Brückenkurs Mathematik work with imprecise probabilities. The exposition Available für Studieneinsteiger aller Disziplinen of generalized measure theory unfolds systemati- 1993. IX, 254 p. 87 illus. (Encyclopaedia of Mathematical cally. It begins with preliminaries and new concepts, Sciences, 29) Dieses Buch erspart Ihnen die Einstiegsprobleme followed by a detailed treatment of important new 978-3-642-08086-9 ▶ 104,95 € in die Mathematik, indem es Ihnen auf unterhalt- results regarding various types of nonadditive mea- same Weise eine Brücke baut, die Sie sanft über alle sures and the associated integration theory. The latter Untiefen hinweg ins Innere der Hochschulmathe- involves several types of integrals: Sugeno integrals, matik hineingeleitet. Die Brücke beginnt auf der einen Choquet integrals, pan-integrals, and lower and upper Seite beim einfachen Zahlenrechnen, wie es Ihnen integrals. All of the topics are motivated by numerous vermutlich in der Mittelstufe schon begegnet ist, und examples, culminating in a final chapter on applica- führt Sie hinüber bis zu den Grundlagen von Lin- tions of generalized measure theory. Some key fea- earer Algebra, Differenzialrechnung und Wahrschein- tures of the book include: many exercises at the end lichkeitsrechnung, die die Hauptinhalte Ihrer ersten of each chapter along with relevant historical and bib- Semester darstellen werden. Diesen Inhalten wer- liographical notes, an extensive bibliography, and den Sie dort immer gegenüberstehen, und bei deren name and subject indices. The work is suitable for a Behandlung können Sie dann beruhigt sagen: "Kenn' classroom setting at the graduate level in courses or ich schon!" Den Autoren ist es gelungen, ein Mathe- seminars in applied mathematics, computer science, matik-Buch für Studierende aller Fachrichtungen und engineering, and some areas of science. A sound back- die berufliche Weiterbildung zu schreiben, das man ground in mathematical analysis is required. Since the von vorne bis hinten einfach lesen kann, ohne im For- book contains many original results by the authors, it M. Waldschmidt malismus oder in humorloser Trockenheit verloren will also appeal to researchers working in the emerg- zu gehen, das einem nach dem Lesen aber dennoch ing area of generalized measure theory. About the Diophantine Approximation on das nötige Wissen und die fachliche Sicherheit ver- Authors: Zhenyuan Wang is currently a Professor Linear Algebraic Groups mittelt hat.Zu jedem Kapitel finden sich Übungsauf- in the Department of Mathematics of University of gaben, mit deren Hilfe die vermittelten Inhalte Nebraska at Omaha. His research interests have been Transcendence Properties of the Exponential eingeübt und vertieft werden können.Neu in die 3. in the areas of nonadditive measures, nonlinear inte- Function in Several Variables Auflage aufgenommen ist eine Formelsammlung zum grals, probability and statistics, and data mining. He Herausnehmen. Stimmen zur 1. Auflage „Endlich ein The theory of transcendental numbers is closely has published one book and many papers in these ansprechender, gelungener Vorbereitungskurs, der related to the study of diophantine approximation. areas. George J. Klir is currently a Distinguished Pro- die elementaren, aber wesentlichen Grundkonzepte This book deals with values of the usual exponen- fessor of Systems Science at Binghamton University genau passend herausstellt.“ Priv.-Doz. Dr. Frank tial function e^z. A central open problem is the con- (SUNY at Binghamton). He has published 29 books Hettlich, Universität Karlsruhe „Leicht zu lesendes jecture on algebraic independence of logarithms of and well over 300 papers in a wide range of areas. His und erarbeitendes Werk, das durch seine unter- algebraic numbers. This book includes proofs of current research interests are primarily in the areas of haltsame Art sehr überzeugt.“ Prof. Dr. Sax Kreutz, the main basic results (theorems of Hermite-Linde- fuzzy systems, soft computing, and generalized infor- Hochschule für Angewandte Wissenschaften, Ham- mann, Gelfond-Schneider, 6 exponentials theorem), mation theory. burg an introduction to height functions with a discussion More on www.springer.com/978-1-4419-4576-1 of Lehmer's problem, several proofs of Baker's the- More on www.springer.com/978-3-8274-2763-2 Available orem as well as explicit measures of linear indepen- Available dence of logarithms. An original feature is that proofs 2009. XVI, 384 p. 25 illus. (IFSR International Series on make systematic use of Laurent's interpolation deter- 2011. VIII, 392 S. 60 Abb. Systems Science and Engineering, 25) minants. The most general result is the so-called The- 978-3-8274-2763-2 ▶ 25,19 € orem of the Linear Subgroup, an effective version of 978-1-4419-4576-1 ▶ 62,95 € which is also included. It yields new results of simulta- neous approximation and of algebraic independence. 2 chapters written by D. Roy provide complete and at springer.com 31

prehensive risk management tools increasingly important.This book adresses the needs of both researchers and practitioners. It combines a rigorous overview of the mathematics of financial markets with an insight into the practical application of these mod- Y. Zhu, X. Wu, I. Chern els to the risk and portfolio management of interest rate derivatives. It may also serve as a valuable text- Derivative Securities and book for graduate and PhD students in mathematics who want to get some knowledge about financial Difference Methods markets.The first part of the book is an exposition of This book is devoted to determining the prices of advanced stochastic calculus. It defines the theoretical financial derivatives using a partial differential equa- framework for the pricing and hedging of contingent tion approach. In the first part the authors describe M. Wohlgemuth, M. Wohlgemuth claims with a special focus on interest rate markets. the formulation of the problems (including related The second part is a mathematically biased mar- free-boundary problems) and derive the closed form Mathematisch für Anfänger ket-oriented description of the most famous interest solutions if they have been found. The second part Die beliebtesten Beiträge von Matroids rate models and a variety of interest rate derivatives. It discusses how to obtain their numerical solutions effi- Matheplanet covers a selection of short and long-term oriented risk ciently for both European-style and American-style measures as well as their application to the risk man- derivatives and for both stock options and interest Dies ist kein Lehrbuch! Dieses Buch ist ein agement of interest rate portfolios. Interesting and rate derivatives. The numerical methods discussed Schatzkästlein mit erklärenden und motivieren- comprehensive case studies based on real market data are finite-difference methods. The book also discusses den Beiträgen, die genau zu den Vorlesungen are provided to illustrate the theoretical concepts and how to determine the coefficients in the partial dif- im ersten Jahr des Mathe-Studiums passen. Als to illuminate their practical usefulness. ferential equations. The aim of the book is to provide Mathematik-Interessierter wirst du das Buch readers who have some code writing experience for gerne zur Hand nehmen, egal welchen Studien- More on www.springer.com/978-3-642-08708-0 engineering computations with the skills to develop gang du belegst. Die Autoren geben dir durch- Available efficient derivative-pricing codes. The book includes dachte und gezielte Hilfestellung bei vielen üblichen 2002. XV, 341 p. (Springer Finance, ) exercises throughout and will appeal to students and Anfängerschwierigkeiten. Sie machen anschaulich 978-3-642-08708-0 ▶ 79,95 € researchers in quantitative finance as well as practi- und anwendbar, was in der Vorlesung immer zu kurz tioners in the financial industry and code developers. kommt. Und sie wissen genau, wo Probleme liegen können, denn sie waren selbst Anfänger und erin- More on www.springer.com/978-1-4419-1925-0 M. Zelikin nern sich gut daran. Dieses Buch spricht mit dir, wie Due April 2011 ein fortgeschrittener Student, der dir die Dinge gut 2004. XVIII, 518 p. 92 illus. (Springer Finance, ) erklären kann: "Mathematisch für Anfänger!". Alle Control Theory and Optimization I 978-1-4419-1925-0 80,95 € Artikel wurden zuerst für die Internet-Seite 'Matroids Homogeneous Spaces and the Riccati Equation ▶ Matheplanet' geschrieben und sind für diese Ausgabe in the Calculus of Variations noch einmal sorgfältig durchgesehen und inhaltlich This book is devoted to geometric methods in the und didaktisch verbessert worden. Wenn du dich theory of differential equations with quadratic right- auf deinem Weg durch die Mathematik von diesem hand sides (Riccati-type equations), which are closely Buch begleiten lässt, wirst du die Tipps und Tricks related to the calculus of variations and optimal con- der Beweistechniken, Linearen Algebra und Analysis trol theory. Connections of the calculus of varia- nicht verpassen. Unser Ziel ist, dass du am Ende sagen tions and the Riccati equation with the geometry of wirst: Ja, ich habe es verstanden, ich hatte Erfolg, und Lagrange-Grassmann manifolds and classical Car- ich habe Spaß daran gefunden! tan-Siegel homogeneity domains in a space of sev- More on www.springer.com/978-3-8274-2285-9 eral complex variables are considered. In the study of Available the minimization problem for a multiple integral, a quadratic partial differential equation that is an ana- 2009. XIV, 316 S. 49 Abb. logue of the Riccati equation in the calculus of vara- 978-3-8274-2285-9 ▶ 18,64 € tiations is studied. This book is based on lectures E. Çinlar given by the author ower a period of several years in the Department of Mechanics and Mathematics Probability and Stochastics of Moscow State University. The book is addressed to undergraduate and graduate students, scientific This text is an introduction to the modern theory researchers and all specialists interested in the prob- and applications of probability and stochastics. The lems of geometry, the calculus of variations, and dif- style and coverage is geared towards the theory of ferential equations. stochastic processes, but with some attention to the applications. In many instances the gist of the prob- More on www.springer.com/978-3-642-08603-8 lem is introduced in practical, everyday language Available and then is made precise in mathematical form. The 2000. X, 283 p. (Encyclopaedia of Mathematical Sciences, 86) first four chapters are on probability theory: mea- 978-3-642-08603-8 ▶ 114,95 € sure and integration, probability spaces, conditional expectations, and the classical limit theorems. There follows chapters on martingales, Poisson random measures, Levy Processes, Brownian motion, and R. Zagst Markov Processes.Special attention is paid to Pois- son random measures and their roles in regulating Interest-Rate Management the excursions of Brownian motion and the jumps The complexity of new financial products as well as of Levy and Markov processes. Each chapter has a the ever-increasing importance of derivative secu- large number of varied examples and exercises. The rities for financial risk and portfolio management book is based on the author’s lecture notes in courses have made mathematical pricing models and com- offered over the years at Princeton University. These courses attracted graduate students from engineer- 32 springer.com ing, economics, physics, computer sciences, and mathematics. Erhan Çinlar has received many awards for excellence in teaching, including the President’s Award for Distinguished Teaching at Princeton Uni- versity. His research interests include theories of Markov processes, point processes, stochastic calculus, and stochastic flows. The book is full of insights and observations that only a lifetime researcher in probability can have, all told in a lucid yet precise style. More on www.springer.com/978-0-387-87858-4 Available

2011. XIII, 557 p. (Graduate Texts in Mathematics, 261) 978-0-387-87858-4 ▶ 59,95 €