A Short History of Mathematical The Ricci Flow in...

springer.com/NEWSonline 23Springer News 11/2010 Mathematics

B. Andrews, Australian National University, Canberra, ACT, Australia; C. Hopper, University of Oxford, United Kingdom

The Ricci Flow in Riemannian GeometryA Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem

This book focuses on Hamilton’s Ricci flow, begin-ning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compact-ness theorems for Riemannian manifolds, and Perelman’s noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.

Features7 A self contained presentation of the proof of the differentiable sphere theorem 7 A presenta-tion of the geometry of vector bundles in a form suitable for geometric PDE 7 A discussion of the history of the sphere theorem and of future challenges

Contents1 Introduction.- 2 Background Material.- 3 Harmonic Mappings.- 4 Evolution of the Curva-ture.- 5 Short-Time Existence.- 6 Uhlenbeck’s Trick.- 7 The Weak Maximum Principle.- 8 Regu-larity and Long-Time Existence.- 9 The Compact-ness Theorem for Riemannian Manifolds.- 10 The F-Functional and Gradient Flows.- 11 The W-Functional and Local Noncollapsing.- 12 An Algebraic Identity for Curvature Operators.- 13 The Cone Construction of Böhm and Wilking.- 14 Preserving Positive Isotropic Curvature.- 15 The Final Argument.

Fields of interestPartial Differential Equations; Differential Geom-etry; Global Analysis and Analysis on Manifolds

Target groupsResearch

S. Aniţa, V. Arnăutu, University “Al.I. Cuza” Iaşi, Romania; V. Capasso, Universita’ degli Studi di Milano, Italy

An Introduction to Optimal Control Problems in Life Sciences and EconomicsFrom Mathematical Models to Numerical Simulation with MATLAB®

Combining two important and growing areas of applied mathematics—control theory and modeling—this textbook introduces and builds on methods for simulating and tackling concrete problems in a variety of applied sciences. Emphasizing “learning by doing,” the authors focus on examples and applications to real-world problems. An elementary presentation of advanced concepts, proofs to introduce new concepts, and carefully presented MATLAB® programs guide the reader through methods in optimal control and related models. This approach not only fosters an understanding of the basic topics, but also leads the way to new, independent research. With minimal prerequisites and exercises in each chapter, An Introduction to Optimal Control Problems in Life Sciences and Economics, serves as an excellent textbook for graduate and advanced undergraduate courses in mathematics, physics, engineering, computer science, as well as biology, biotechnology, economics, and finance.

Features7 An introduction to the main tools of MATLAB, as well as programs that move from relatively simple ODE applications to more complex PDE models 7 Numerous applications to a wide range of subject areas, including HIV and insulin treat-ments, population dynamics, and stock manage-ment 7 Exploration of cutting-edge topics in later chapters designed to stimulate further research and theses projects 7 Exercises in each chapter

Fields of interestMathematical Modeling and Mathematics in Industry; Control; Systems Theory, Control

Target groupsGraduate

N. Bacaër, IRD (Institut de Recherche pour le Developpement), Bondy, France

A Short History of Mathematical Population Dynamics

As Eugene Wigner stressed, mathematics has proven unreasonably effective in the physical sciences and their technological applications. The role of mathematics in the biological, medical and social sciences has been much more modest but has recently grown thanks to the simulation capacity offered by modern computers.This book traces the history of population dynamics---a theoretical subject closely connected to genetics, ecology, epidemiology and demography---where mathematics has brought significant insights. It presents an overview of the genesis of several important themes: exponential growth, from Euler and Malthus to the Chinese one-child policy; the development of stochastic models, from Mendel’s laws and the question of extinction of family names to percolation theory for the spread of epidemics, and chaotic populations, where deter-minism and randomness intertwine. The reader of this book will see, from a different perspective, the problems that scientists face when govern-ments ask for reliable predictions to help control epidemics (AIDS, SARS, swine flu), manage renew-able resources (fishing quotas, spread of genetically modified organisms) or anticipate demographic evolutions such as aging.

Features7 Presents interesting historical background information as well as mathematical analysis of select classical mathematical models in popula-tion biology 7 Provides complementary reading for undergraduates and postgraduates studying mathematical biology 7 Details the lives of math-ematicians who have made major contributions to the field

Fields of interestHistory of Mathematical Sciences; Genetics and Population Dynamics; Mathematical Biology in General; Popular Science in Mathematics/Computer Science/Natural Science/Technology

Target groupsUpper undergraduate

Type of publicationMonograph

Due December 2010

2011. X, 276 p. 13 illus., 2 in color. (Lecture Notes in Mathematics, Number 2011) Softcover

7 approx. € 44,95 | £40.997 approx. * € (D) 48,10 | € (A) 49,45 | sFr 64,50ISBN 978-3-642-16285-5

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Type of publicationGraduate/Advanced undergraduate textbook

Due November 2010

2011. XII, 232 p. 45 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover

7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 72,00ISBN 978-0-8176-8097-8

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Due November 2010

2011. X, 158 p. 60 illus. Softcover


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www.springer.com/978-3-642-16285-5



springer.com/NEWSonline24 Springer News 11/2010Mathematics

K. Bichteler, The University of Texas, Austin, TX, USA

Integration – A Functional Approach

This book covers Lebesgue integration and its generalizations from Daniell’s point of view, modified by the use of seminorms. Integrating functions rather than measuring sets is posited as the main purpose of measure theory. From this point of view Lebesgue’s integral can be had as a rather straightforward, even simplistic, extension of Riemann’s integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewood’s observations rather than being conveyed authoritatively through definitions of (sigma)-algebras and good-cut-conditions, the latter of which are hard to justify and thus appear mysterious, even nettlesome, to the beginner. The approach taken provides the additional benefit of cutting the labor in half. The use of seminorms, ubiquitous in modern analysis, speeds things up even further. The book is intended for the reader who has some experience with proofs, a begin-ning graduate student for example. It might even be useful to the advanced mathematician who is confronted with situations – such as stochastic integration – where the set-measuring approach to integration does not work.

Features7 Complete and rapid introduction to Lebesgue integration and its generalization 7 Unusually detailed discussion of Percy Daniell’s functional analytic approach to integration 7 Comple-mented by interesting historical notes and motivations 7 Provides numerous exercises and solutions / hints for selected problems

From the contentsChapter I Review.- Chapter II Extension of the Integral.- Chapter III Measurability.- Chapter IV The Classical Banach Spaces.

Fields of interestFunctional Analysis


C. Bonnafé, CNRS, Montpellier, France

Representations of SL2(Fq)Deligne-Lusztig theory aims to study repre-sentations of finite reductive groups by means of geometric methods, and particularly l-adic cohomology. Many excellent texts present, with different goals and perspectives, this theory in the general setting. This book focuses on the smallest non-trivial example, namely the group SL2(Fq), which not only provides the simplicity required for a complete description of the theory, but also the richness needed for illustrating the most delicate aspects.The development of Deligne-Lusztig theory was inspired by Drinfeld’s example in 1974, and Representations of SL2(Fq) is based upon this example, and extends it to modular representa-tion theory. To this end, the author makes use of fundamental results of l-adic cohomology. In order to efficiently use this machinery, a precise study of the geometric properties of the action of SL2(Fq) on the Drinfeld curve is conducted, with particular attention to the construction of quotients by various finite groups.

Features7 Presents an introduction to ordinary and modular Deligne-Lusztig theory through the detailed study of an example: SL2(Fq) 7 Will serve as a complimentary text to existing titles on Deligne-Lusztig theory 7 Includes Rouquier's theorem on derived equivalences of geometric nature (with some unpublished improvements) but is simple enough to be read by graduate/Ph. D. students

From the contentsPart I Preliminaries.- Structure of SL2(Fq).- The Geometry of the Drinfeld Curve.- Part II Ordinary Characters.- Harish-Chandra Induction.- Deligne-Lusztig Induction.- The Character Table.- Part III Modular Representations.- More about Characters of G and of its Sylow Subgroups.- Unequal Char-acteristic: Generalities.- Unequal Characteristic: Equivalences of Categories.- Unequal Character-istic: Simple Modules, Decomposition Matrices.- Equal Characteristic.

Fields of interestAlgebra; Algebraic Geometry; Group Theory and Generalizations


R. J. Boucherie, University of Twente, The Netherlands; N. M. Dijk, University of Amsterdam, The Netherlands (Eds.)

Queueing NetworksA Fundamental Approach

This handbook aims to highlight fundamental, methodological and computational aspects of networks of queues to provide insights and to unify results that can be applied in a more general manner. The handbook is organized into five parts: Part 1 considers exact analytical results such as of product form type. Topics include characterization of product forms by physical balance concepts and simple traffic flow equations, classes of service and queue disciplines that allow a product form, a unified description of product forms for discrete time queueing networks, insights for insensitivity, and aggregation and decomposition results that allow sub networks to be aggregated into single nodes to reduce computational burden.Part 2 looks at monotonicity and comparison results such as for computational simplification by either of two approaches: stochastic monotonicity and ordering results based on the ordering of the process generators.

Features7 Because of both the importance and the complexity of queueing networks, this branch of queueing theory continues to be a particularly hot area of research 7 Presents a series of expository chapters by leading experts in each topical area that collectively pull together the current state of the art 7 Will be a key reference for researchers, students, and practitioners involved with queueing networks

Fields of interestProbability Theory and Stochastic Processes; Operations Research/Decision Theory; Mathemat-ical Modeling and Mathematics in Industry



Due December 2010

1998. Reprint 1998. VIII, 193 p. (Modern Birkhäuser Classics) Softcover


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Due November 2010

2011. XIX, 197 p. 1 illus. (Algebra and Applications, Volume 13) Hardcover

7 € 79,95 | £72.007 * € (D) 85,55 | € (A) 87,95 | sFr 115,00ISBN 978-0-85729-156-1

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Type of publicationContributed volume

Due January 2011

2011. XXIII, 798 p. 148 illus. (International Series in Operations Research & Management Science, Volume 154) Hardcover


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S. Carl, Martin-Luther-Universität Halle-Wittenberg, Germany; S. Heikkilä, University of Oulu, Finland

Fixed Point Theory in Ordered Sets and ApplicationsFrom Differential and Integral Equations to Game Theory

This monograph provides a unified and compre-hensive treatment of an order-theoretic fixed point theory in partially ordered sets and its various useful interactions with topological structures. The material progresses systematically, by presenting the preliminaries before moving to more advanced topics. In the treatment of the applications a wide range of mathematical theories and methods from nonlinear analysis and integration theory are applied; an outline of which has been given an appendix chapter to make the book self-contained. Graduate students and researchers in nonlinear analysis, pure and applied mathematics, game theory and mathematical economics will find this book useful.

Features7 Presents a comprehensive treatment of an order-theoretic fixed point theory in partially ordered sets along with its various interactions with topological structures 7 Considers a wide range of mathematical theories and methods when dealing with applications 7 With numerous illustrations

ContentsIntroduction.- Fundamental Order-Theoretic Principles.- Multi-Valued Variational Inequali-ties.- Discontinuous Multi-Valued Elliptic Prob-lems.- Discontinutous Multi-Valued Evolutionary Problems.- Banach-Valued Ordinary Differential Equations.- Banach-Valued Integral Equations.- Game Theory.- Appendix.- List of Symbols.- Refer-ences.- Index.

Fields of interestAnalysis; Game Theory, Economics, Social and Behav. Sciences; Game Theory/Mathematical Methods


J. Cohen, A. I. Zayed, DePaul University, Chicago, IL, USA (Eds.)

Wavelets and Multiscale AnalysisTheory and Applications

Since its emergence as an important research area in the early 1980s, the topic of wavelets has under-gone tremendous development on both theoretical and applied fronts. Myriad research and survey papers and monographs have been published on the subject, documenting different areas of applications such as sound and image processing, denoising, data compression, tomography, and medical imaging. The study of wavelets remains a very active field of research, and many of its central techniques and ideas have evolved into new and promising research areas. This volume, a collection of invited contributions developed from talks at an international conference on wavelets, is divided into three parts: Part I is devoted to the mathematical theory of wavelets and features several papers on wavelet sets and the construction of wavelet bases in different settings.

Features7 Comprises work from top researchers in the field 7 Provides a comprehensive overview of fundamental concepts 7 Demonstrates state-of the-art applications to signal and image processing, denoising, tomography, and medical imaging 7 Explores new ideas in data processing 7 Valuable for a wide audience, including grad-uate students, researchers, and practitioners in mathematics, engineering, and physics

Fields of interestFourier Analysis; Signal, Image and Speech Processing; Abstract Harmonic Analysis


V. Dragović, M. Radnović, Mathematical Institute SANU, Belgrade, Serbia

Poncelet Porisms and BeyondIntegrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics

The goal of the book is to present, in a complete and comprehensive way, a few areas of math-ematics interlacing around the Poncelet porism: dynamics of integrable billiards, algebraic geom-etry of hyperelliptic Jacobians, and classical projec-tive geometry of pencils of quadrics. Most important results and ideas connected to Poncelet theorem are presented: classical as well as modern ones, together with historical overview with analysis of classical ideas, their natural gener-alizations, and natural generalizations. Special attention is paid to the realization of the Griffiths and Harris programme about Poncelet-type problems and addition theorems. This programme, formulated three decades ago, is aimed to understanding of higher-dimensional analogues of Poncelet problems and realization of synthetic approach of higher genus addition theorems. This problem is realized in a sequence of papers of the authors, published over the last 20 years. Some of those results represent key contri-butions to the development of the theory, while this book provides the complete image.

Features7 Self-contained, with an elementary introduc-tion 7 Contains a complete account of higher-dimensional generalizations of Poncelet theorem, the corresponding Cayley-type conditions, and the Poncelet-Darboux grids 7 Gives introspection into exciting interlacing of different areas of math-ematics around the Poncelet porism 7 Contains most modern results connected with the problems of Poncelet type

Fields of interestAlgebraic Geometry



Due December 2010

2011. XIV, 474 p. 20 illus. Hardcover


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Due March 2011

2011. XX, 339 p. 87 illus. (Applied and Numerical Harmonic Analysis) Hardcover


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Due November 2010

Only English language rights

2011. Approx. 290 p. (Frontiers in Mathematics) Softcover


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R. M. Dudley, Massachusetts Institute of Technology, Cambridge, MA, USA; R. Norvaiša, Institute of Mathematics and Informatics, Vilnius, Lithuania

Concrete Functional Calculus

Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions. This includes composition of two functions, and the product integral, taking a matrix- or operator-valued coefficient function into a solution of a system of linear differential equations with the given coef-ficients. For nonlinear integral equations with respect to possibly discontinuous functions having unbounded variation, existence and uniqueness of solutions are proved under suitable assump-tions.Key features and topics:* Extensive usage of p-variation of functions* Applications to stochastic processes.This work will serve as a thorough reference on its main topics for researchers and graduate students with a background in real analysis and, for Chapter 12, in probability.

Features7 Opens new possibilities to analysis of statistical functionals and gives an alternative (non-Ito) approach to stochastic calculus 7 Contains new material about the existence and smoothnesss of several nonlinear operators acting between spaces of functions having bounded p-variation 7 Will appeal to graduate students and researchers working on various aspects of calculus of non-smooth functions

ContentsPreface.- 1 Introduction and Overview.- 2 Defini-tions and Basic Properties of Extended Riemann-Stieltjes Integrals.- 3 Phi-variation and p-variation; Inequalities for Integrals.- 4 Banach Algebras.- 5 Derivatives and Analyticity in Normed Spaces.- 6 Nemytskii Operators on Some Function Spaces.- 7 Nemytskii Oerators on Lp Spaces.- 8 Two-Func-tion Composition.- 9 Product Integration.- 10 Nonlinear Differential and Integral Equations.- 11 Fourier Series.

Fields of interestFunctional Analysis; Integral Equations; Operator Theory


J. J. Dudziak, Michigan State University, East Lansing, MI, USA

Vitushkin’s Conjecture for Removable Sets

Vitushkin’s conjecture, a special case of Pain-levé’s problem, states that a compact subset of the complex plane with finite linear Hausdorff measure is removable for bounded analytic func-tions if and only if it intersects every rectifiable curve in a set of zero arc length measure. Chapters 6-8 of this carefully written text present a major recent accomplishment of modern complex analysis, the affirmative resolution of this conjec-ture. Four of the five mathematicians whose work solved Vitushkin’s conjecture have won the presti-gious Salem Prize in analysis. Chapters 1-5 of this book provide important background material on removability, analytic capacity, Hausdorff measure, arc length measure, and Garabedian duality that will appeal to many analysts with interests independent of Vitushkin’s conjecture. The fourth chapter contains a proof of Denjoy’s conjecture that employs Melnikov curvature. A brief post-script reports on a deep theorem of Tolsa and its relevance to going beyond Vitushkin’s conjecture.

Features7 Presents a complete proof of a major recent accomplishment of modern complex analysis, the affirmative resolution of Vitushkin's conjecture 7 Includes Melnikov and Verdera's proof of Denjoy's conjecture 7 Reports on a deep theorem of Tolsa and its relevance to going beyond Vitushkin's conjecture 7 Contains important background material on removability, analytic capacity, Hausdorff measure, arclength measure, and Garabedian duality

From the contentsPreface.- 1 Removable Sets and Analytic Capacity.- 2 Removable Sets and Hausdorff Measure.- 3 Garabedian Duality for Hole-Punch Domains.- 4 Melnikov and Verdera’s Solution to the Denjoy Conjecture.- 5 Some Measure Theory.- 6 A Solution to Vitushkin’s Conjecture Modulo Two Difficult Results.

Fields of interestSeveral Complex Variables and Analytic Spaces


J. Duistermaat, University of Utrecht, The Netherlands

Fourier Integral Operators

This volume is a useful introduction to the subject of Fourier Integral Operators and is based on the author’s classic set of notes. Covering a range of topics from Hörmander’s exposition of the theory, Duistermaat approaches the subject from symplectic geometry and includes application to hyperbolic equations (= equations of wave type) and oscillatory asymptotic solutions which may have caustics. This text is suitable for mathematicians and (theoretical) physicists with an interest in (linear) partial differential equations, especially in wave propagation, rep. WKB-methods. Familiarity with analysis (distributions and Fourier transformation) and differential geometry is useful. Additionally, this book is designed for a one-semester introduc-tory course on Fourier integral operators aimed at a broad audience.

Features7 Based on author’s original lecture notes 7 Covers a broad range of topicsUseful for both practitioners and students 7 Applications put theory in context

From the contentsPreface.- 0. Introduction.- 1. Preliminaries.- 1.1 Distribution densities on manifolds.- 1.2 The method of stationary phase.- 1.3 The wave front set of a distribution.- 2. Local Theory of Fourier Integrals.- 2.1 Symbols.- 2.2 Distributions defined by oscillatory integrals.- 2.3 Oscillatory integrals with nondegenerate phase functions.- 2.4 Fourier integral operators (local theory).- 2.5 Pseudodifferential operators in Rn.- 3. Symplectic Differential Geometry.- 3.1 Vector fields.- 3.2 Differential forms.- 3.3 The canonical 1- and 2-form T* (X).- 3.4 Symplectic vector spaces.

Fields of interestFourier Analysis; Integral Equations; Operator Theory



Due December 2010

2011. XII, 672 p. 3 illus. (Springer Monographs in Mathematics) Hardcover


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Available

2010. XII, 272 p. (Universitext) Softcover

7 € 49,95 | £29.997 * € (D) 53,45 | € (A) 54,95 | sFr 72,00ISBN 978-1-4419-6708-4

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Due December 2010

2011. XII, 142 p. 9 illus. (Modern Birkhäuser Classics) Softcover


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R. H. Enns, Simon Fraser University, Burnaby, BC, Canada

It’s a Nonlinear World

Drawing examples from mathematics, physics, chemistry, biology, engineering, economics, medi-cine, politics, and sports, this book illustrates how nonlinear dynamics plays a vital role in our world. Examples cover a wide range from the spread and possible control of communicable diseases, to the lack of predictability in long-range weather fore-casting, to competition between political groups and nations. After an introductory chapter that explores what it means to be nonlinear, the book covers the mathematical concepts such as limit cycles, frac-tals, chaos, bifurcations, and solitons, that will be applied throughout the book. Numerous computer simulations and exercises allow students to explore topics in greater depth using the Maple computer algebra system. The mathematical level of the text assumes prior exposure to ordinary differential equations and familiarity with the wave and diffu-sion equations. No prior knowledge of Maple is assumed, and all Maple examples are included on a CD.

Features7 Explores in each chapter nonlinear phenomena drawn from a unique discipline within the physical and social sciences, engineering, and medicine

ContentsPreface.- Part I. World of Mathematics.- 1. World of Nonlinear Systems.- 2. World of Nonlinear ODEs.- 3. World of Nonlinear Maps.- 4. World of Solitons.- Part II. Our Nonlinear World.- 5. World of Motion.- 6. World of Sports.- 7. World of Elec-tromagnetism.- 8. World of Weather Prediction.- 9. World of Chemistry.- 10. World of Disease.- 11. World of War.- Bibliography.- Index.

Fields of interestApplications of Mathematics; Simulation and Modeling; Ordinary Differential Equations

Target groupsLower undergraduate

A. Etheridge, University of Oxford, UK

Some Mathematical Models from Population GeneticsÉcole d’Été de Probabilités de Saint-Flour XXXIX-2009

This work reflects sixteen hours of lectures deliv-ered by the author at the 2009 St Flour summer school in probability. It provides a rapid introduc-tion to a range of mathematical models that have their origins in theoretical population genetics. The models fall into two classes: forwards in time models for the evolution of frequencies of different genetic types in a population; and backwards in time (coalescent) models that trace out the genealogical relationships between individuals in a sample from the population. Some, like the classical Wright-Fisher model, date right back to the origins of the subject. Others, like the multiple merger coalescents or the spatial Lambda-Fleming-Viot process are much more recent. All share a rich mathematical structure. Biological terms are explained, the models are carefully motivated and tools for their study are presented systematically.

Features7 First volume aimed at mathematicians to cover a wide range of models from population genetics 7 Provides the biological motivation for models without using too much `jargon' 7 Provides the mathematical and biological background needed by a mathematician to read research papers in theoretical population genetics

Fields of interestGenetics and Population Dynamics; Mathematical Biology in General; Mathematical Modeling and Mathematics in Industry


H. M. Farkas, S. Zemel, The Hebrew University, Jerusalem, Israel

Generalizations of Thomae’s Formula for Zn Curves

Previous publications on the generalization of the Thomae formulae to Zn curves have emphasized the theory’s implications in mathematical physics and depended heavily on applied mathematical techniques. This book redevelops these previous results demonstrating how they can be derived directly from the basic properties of theta functions as functions on compact Riemann surfaces. “Generalizations of Thomae’s Formula for Zn Curves” includes several refocused proofs developed in a generalized context that is more accessible to researchers in related mathematical fields such as algebraic geometry, complex analysis, and number theory. This book is intended for mathematicians with an interest in complex analysis, algebraic geometry or number theory as well as physicists studying conformal field theory.

Features7 The first monograph to study generalizations of the Thomae Formulae to Zn curves 7 Provides an introduction to the basic principles of compact Riemann surfaces, theta functions, algebraic curves, and branch points 7 Examples support the theory and reveal the broad applicability of this theory to numerous other disciplines including conformal field theory, low dimensional topology, the theory of special functions

Contents1. Riemann Surfaces.- 2. Zn Curves.- 3. Examples of Thomae Formulae.- 4. Thomae Formulae for Nonsingular Zn Curves.- 5. Thomae Formulae for Singular Zn Curves.-6. Some More Singular Zn Curves.-Appendix A. Constructions and General-izations for the Nonsingular and Singular Cases.-Appendix B. The Construction and Basepoint Change Formulae for the Symmetric Equation Case.-References.-List of Symbols.

Fields of interestAlgebraic Geometry; Functions of a Complex Variable; Several Complex Variables and Analytic Spaces


Type of publicationUndergraduate textbook

Due October 2010

2011. XII, 382 p. 145 illus., 8 in color. (Springer Undergraduate Texts in Mathematics and Technology) Hardcover

7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 72,00ISBN 978-0-387-75338-6

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Due January 2011

2011. VIII, 114 p. (Lecture Notes in Mathematics / Ecole d’Eté Probabilit.Saint-Flour, Volume 2012) Softcover


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Due December 2010

2011. XVIII, 354 p. (Developments in Mathematics, Volume 21) Hardcover


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L. Gawarecki, Kettering University, Flint, MI, USA; V. Mandrekar, Michigan State University, East Lansing, MI, USA

Stochastic Differential Equations in Infinite Dimensionswith Applications to Stochastic Partial Differential Equations

The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance. Major methods include compactness, coercivity, monotonicity, in a variety of set-ups. The authors emphasize the fundamental work of Gikhman and Skorokhod on the existence and uniqueness of solutions to stochastic differential equations and present its extension to infinite dimension. They also generalize the work of Khas-minskii on stability and stationary distributions of solutions. New results, applications, and examples of stochastic partial differential equations are included.

Features7 Most comprehensive coverage of the modern techniques used for solving problems in infinite dimensional stochastic differential equations 7 Presents major methods, including compact-ness, coercivity, monotonicity, in different set-ups 7 Provides a broad range of new results and applications

From the contentsPreface.- Part I: Stochastic Differential Equations in Infinite Dimensions.- 1.Partial Differential Equations as Equations in Infinite.- 2.Stochastic Calculus.- 3.Stochastic Differential Equations.- 4.Solutions by Variational Method.

Fields of interestProbability Theory and Stochastic Processes; Partial Differential Equations; Quantitative Finance


Y. E. Gliklikh, Voronezh State University, Russia

Global and Stochastic Analysis with Applications to Mathematical Physics

Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important direc-tions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems.This book develops methods of Global Analysis and Stochastic Analysis such that their combina-tion allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation.Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of math-ematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions on linear spaces and manifolds.

Features7 Covers branches of mathematics previously absent in monograph form 7 Combines methods of Global and Stochastic Analysis, enabling a more or less common treatment for areas of mathemat-ical physics traditionally considered as divergent 7 Includes substantial background material on manifolds and stochastic analysis, in addition to new work on set-valued mappings and applications of Nelson's mean derivatives

From the contentsPart I Global Analysis.- Manifolds and Related Objects.- Connections.- Ordinary Differential Equations.- Elements of the Theory of Set-Valued Mappings.- Analysis on Groups of Diffeomor-phisms.- Part II Stochastic Analysis.

Fields of interestGlobal Analysis and Analysis on Manifolds; Prob-ability Theory and Stochastic Processes; Math-ematical Methods in Physics


B. Goodwine, University of Notre Dame, South Bend, IN, USA

Engineering Differential EquationsTheory and Applications

This book is a comprehensive treatment of engineering undergraduate differential equa-tions as well as linear vibrations and feedback control. While this material has traditionally been separated into different courses in undergraduate engineering curricula. This text provides a stream-lined and efficient treatment of material normally covered in three courses. Ultimately, engineering students study mathe-matics in order to be able to solve problems within the engineering realm. Engineering Differen-tial Equations: Theory and Applications guides students to approach the mathematical theory with much greater interest and enthusiasm by teaching the theory together with applications. Addition-ally, it includes an abundance of detailed examples. Appendices include numerous C and FORTRAN example programs. This book is intended for engineering undergrad-uate students, particularly aerospace and mechan-ical engineers and students in other disciplines concerned with mechanical systems analysis and control. Prerequisites include basic and advanced calculus with an introduction to linear algebra.

Features7 Utilizes an abundance of examples 7 Stream-lines three courses into one two semester course 7 Guides students to approach the mathematical subjects with much greater interest

From the contentsPreface.- Introduction and Preliminaries.- First-Order Ordinary Differential Equations.- Second-Order Linear Constant-Coefficient Ordinary Differential Equations.- Single Degree of Freedom Vibrations.- Variable-Coefficient Linear Ordinary Differential Equations.

Fields of interestOrdinary Differential Equations; Appl.Math-ematics/Computational Methods of Engineering; Applications of Mathematics



Due December 2010

2011. XVI, 274 p. (Probability and Its Applications) Hardcover


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Due November 2010

2011. X, 452 p. 5 illus. (Theoretical and Mathematical Physics) Hardcover

7 € 89,95 | £81.007 * € (D) 96,25 | € (A) 98,95 | sFr 129,00ISBN 978-0-85729-162-2

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Due January 2011

2011. XVI, 748 p. 313 illus. Hardcover


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D. F. Griffiths, University of Dundee, UK; D. J. Higham, University of Strathclyde, Glasgow, UK

Numerical Methods for Ordinary Differential EquationsInitial Value Problems

Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject. It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture’ sized pieces, motivated and illustrated by numerous theoretical and computational examples. Over 200 exercises are provided and these are starred according to their degree of difficulty. Solu-tions to all exercises are available to authorized instructors. The book covers key foundation topics: Taylor series methods, Runge – Kutta methods, Linear multistep methods, Convergence, Stability and a range of modern themes: Adaptive stepsize selection, Long term dynamics, Modified equa-tions, Geometric integration, Stochastic differential equations The prerequisite of a basic university-level calculus class is assumed, although appro-priate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com

Features7 Focuses on the analysis of numerical methods without losing sight of the practical nature of the subject 7 Covers topics traditionally treated in a first course, but also highlights new and emerging themes 7 Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples

Fields of interestNumerical Analysis; Numeric Computing


A. W. Grootendorst, Delft University, The Netherlands; J. Aarts, Delft University of Technology, The Netherlands; M. Bakker, Centrum Wiskunde & Informatica, Amsterdam, The Netherlands; R. Erné, Leiden, The Netherlands (Eds.)

Jan de Witt’s Elementa Curvarum LinearumLiber Secundus

Following on from the 2000 edition of Jan De Witt’s Elementa Curvarum Linearum, Liber Primus, this book provides the accompanying translation of the second volume of Elementa Curvarum Linearum (Foundations of Curved Lines). One of the first books to be published on Analytic Geometry, it was originally written in Latin by the Dutch statesman and mathematician Jan de Witt, soon after Descartes’ invention of the subject. Born in 1625, Jan de Witt served with distinction as Grand Pensionary of Holland for much of his adult life. In mathematics, he is best known for his work in actuarial mathematics as well as extensive contributions to analytic geometry. Elementa Curvarum Linearum, Liber Secondus moves forward from the construction of the familiar conic sections covered in the Liber Primus, with a discussion of problems connected with their classification; given an equation, it covers how one can recover the standard form, and additionally how one can find the equation’s geometric properties.

Features7 Annotation explaining finer points of the translation 7 Etensive commentary on the math-ematics 7 Makes the work of Jan de Witt acces-sible to a broad group of today’s mathematicians

ContentsPreliminary pages.- Introduction.- Summary.- Latin text and translation.- Annotations.- Appendix.

Fields of interestHistory of Mathematical Sciences; Geometry


C. Heil, Georgia Institute of Technology, Atlanta, GA, USA

A Basis Theory PrimerExpanded Edition

The classical subject of bases in Banach spaces has taken on a new life in the modern development of applied harmonic analysis. This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and their use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses. The self-contained presentation with clear proofs is accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications. No other text develops the ties between classical basis theory and its modern uses in applied harmonic analysis.

Features7 Unique book in the literature 7 A good text to learn from, with detailed explanations of abstract material that are usually explained with the remark "clearly..." in other texts 7 Covers abstract material with a high degree of relevance to a wide variety of modern topics 7 For a broad audience of graduate students, pure and applied mathemati-cians as well as engineers 7 Exercises at the end of each chapter

Fields of interestAbstract Harmonic Analysis; Appl.Mathematics/Computational Methods of Engineering; Func-tional Analysis



Due December 2010

2011. XIV, 268 p. 69 illus. (Springer Undergraduate Mathematics Series) Softcover

7 € 39,95 | £19.997 * € (D) 42,75 | € (A) 43,95 | sFr 57,50ISBN 978-0-85729-147-9

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Due October 2010

2010. X, 318 p. 111 illus. (Sources and Studies in the History of Mathematics and Physical Sciences) Hardcover

7 € 89,95 | £81.007 * € (D) 96,25 | € (A) 98,95 | sFr 129,00ISBN 978-0-85729-141-7

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Due November 2010

2011. XXVI, 536 p. 42 illus. (Applied and Numerical Harmonic Analysis) Hardcover

7 € 64,95 | £58.997 * € (D) 69,50 | € (A) 71,45 | sFr 93,50ISBN 978-0-8176-4686-8

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J. Herzog, Universität Duisburg-Essen, Essen, Germany; T. Hibi, Osaka University, Toyonaka, Osaka, Japan

Monomial Ideals

This book demonstrates current trends in research on combinatorial and computational commutative algebra with a primary emphasis on topics related to monomial ideals. Providing a useful and quick introduction to areas of research spanning these fields, Monomial Ideals is split into three parts. Part I offers a quick introduction to the modern theory of Gröbner bases as well as the detailed study of generic initial ideals. Part II supplies Hilbert functions and resolutions and some of the combinatorics related to monomial ideals including the Kruskal—Katona theorem and algebraic aspects of Alexander duality. Part III discusses combinato-rial applications of monomial ideals, providing a valuable overview of some of the central trends in algebraic combinatorics. Main subjects include edge ideals of finite graphs, powers of ideals, algebraic shifting theory and an introduction to discrete polymatroids. Theory is complemented by a number of examples and exercises throughout, bringing the reader to a deeper understanding of concepts explored within the text.

Features7 Theory is complemented by a number of examples and exercises throughout, bringing the reader to a deeper understanding of concepts explored within the text 7 Provides a quick and useful introduction to research spanning the fields of combinatorial and computational commutative algebra, with a special focus on monomial ideals

From the contentsPart I Gröbner bases: Monomial Ideals.- A short introduction to Gröbner bases.- Monomial orders and weights.- Generic initial ideals.- The exterior algebra.- Part II: Hilbert functions and resolutions.- Hilbert functions and the theorems of Macaulay and Kruskal-Katona.- Resolutions of monomial ideals and the Eliahou-Kervaire formula.- Alexander duality and resolutions.

Fields of interestCommutative Rings and Algebras


G. Högnäs, Åbo Akademi University, Finland; A. Mukherjea, University of Texas – Pan American, Edinburg, TX, USA

Probability Measures on SemigroupsConvolution Products, Random Walks and Random Matrices

This second edition presents up-to-date material on the theory of weak convergance of convolution products of probability measures in semigroups, the theory of random walks on semigroups, and their applications to products of random matrices. In addition, this unique work examines the essentials of abstract semigroup theory and its application to concrete semigroups of matrices. This substantially revised text includes exercises at various levels at the end of each section and includes the best available proofs on the most important theorems used in a book, making it suitable for a one semester course on semigroups. In addition, it could also be used as a main text or supplementary material for courses focusing on probability on algebraic structures or weak convergence. This book is ideally suited to graduate students in mathematics, and students in other fields, such as engineering and the sciences with an interest in probability. Students in statistics using advanced probability will also find this book useful.

Features7 Presents up-to-date material 7 Examines abstract semigroup theory and its application to concrete semigroups of matrices 7 Includes exercises at various levelsIncludes the best avail-able proofs on the most important theorems used in a book

ContentsSemigroups.- Probability Measures on Topological Semigroups.- Random Walks on Semigroups.- Random Matrices.- Index.

Fields of interestProbability Theory and Stochastic Processes; Probability and Statistics in Computer Science; Topological Groups, Lie Groups


M. Holtz, Universität Bonn

Sparse Grid Quadrature in High Dimensions with Applications in Finance and Insurance

This book deals with the numerical analysis and efficient numerical treatment of high-dimensional integrals using sparse grids and other dimension-wise integration techniques with applications to finance and insurance. The book focuses on providing insights into the interplay between coor-dinate transformations, effective dimensions and the convergence behaviour of sparse grid methods. The techniques, derivations and algorithms are illustrated by many examples, figures and code segments. Numerical experiments with applica-tions from finance and insurance show that the approaches presented in this book can be faster and more accurate than (quasi-) Monte Carlo methods, even for integrands with hundreds of dimensions.

Fields of interestComputational Mathematics and Numerical Analysis; Quantitative Finance



Available

2011. XVI, 305 p. 5 illus. (Graduate Texts in Mathematics, Volume 260) Hardcover

7 € 59,95 | £53.997 * € (D) 64,15 | € (A) 65,95 | sFr 86,00ISBN 978-0-85729-105-9

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Due November 2010

2nd ed. 2011. XIV, 461 p. (Probability and Its Applications) Hardcover


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Due November 2010

2011. VIII, 182 p. (Lecture Notes in Computational Science and Engineering, Volume 77) Hardcover


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W. Huang, University of Kansas, Lawrence, KA, USA; R. D. Russell, Simon Fraser University, Burnaby, BC, Canada

Adaptive Moving Mesh Methods

Moving mesh methods are an effective, mesh-adaptation-based approach for the numerical solution of mathematical models of physical phenomena. Currently there exist three main strategies for mesh adaptation, namely, to use mesh subdivision, local high order approximation (sometimes combined with mesh subdivision), and mesh movement. The latter type of adaptive mesh method has been less well studied, both computationally and theoretically. This book is about adaptive mesh generation and moving mesh methods for the numerical solution of time-dependent partial differential equations. It presents a general framework and theory for adaptive mesh generation and gives a comprehen-sive treatment of moving mesh methods and their basic components, along with their application for a number of nontrivial physical problems. Many explicit examples with computed figures illustrate the various methods and the effects of parameter choices for those methods. The partial differen-tial equations considered are mainly parabolic (diffusion-dominated, rather than convection-dominated). The extensive bibliography provides an invaluable guide to the literature in this field. Each chapter contains useful exercises. Graduate students, researchers and practitioners working in this area will benefit from this book.

Features7 First ever comprehensive treatment of moving mesh methods for solving time-dependent Partial Differential Equations 7 General error analysis for adaptive mesh generation using equidistribu-tion and alignment is covered 7 Numerous numerical examples and several Matlab codes are included

Fields of interestNumerical Analysis; Computational Mathematics and Numerical Analysis; Partial Differential Equa-tions


K. Iohara, Université Claude Bernard Lyon, Villeurbanne, France; Y. Koga, University of Fukui, Japan

Representation Theory of the Virasoro Algebra

The Virasoro algebra is an infinite dimensional Lie algebra that plays an increasingly important role in mathematics and theoretical physics. This book describes some fundamental facts about the representation theory of the Virasoro algebra in a self-contained manner. Topics include the structure of Verma modules and Fock modules, the classification of (unitarizable) Harish-Chandra modules, tilting equivalence, and the rational vertex operator algebras associated to the so-called minimal series representations.Covering a wide range of material, this book has three appendices which provide background information required for some of the chapters. The authors organize fundamental results in a unified way and refine existing proofs. For instance in chapter three, a generalization of Jantzen filtration is reformulated in an algebraic manner, and geometric interpreta-tion is provided. Statements, widely believed to be true, are collated, and results which are known but not verified are proven, such as the corrected structure theorem of Fock modules in chapter eight.This book will be of interest to a wide range of mathematicians and physicists from the level of graduate students to researchers.

Features7 Brings much of the existing literature under one roof 7 Fundamental results are organized in a unified manner 7 A number of existing proofs are refined 7 Corrects a number of errors that have spread throughout the literature

From the contentsPreliminary.- Classification of Harish-Chandra Modules.- The Jantzen Filtration.- Determinant Formulae.- Verma Modules I: Preliminaries.- Verma Modules II: Structure Theorem.- A Duality among Verma Modules.- Fock Modules.

Fields of interestAlgebra; Non-associative Rings and Algebras; Theoretical, Mathematical and Computational Physics


G. Kaiser, Center for Signals & Waves, Austin, TX, USA

A Friendly Guide to Wavelets

This volume is designed as a textbook for an introductory course on wavelet analysis and time-frequency analysis aimed at graduate students or advanced undergraduates in science and engineering. It can also be used as a self-study or reference book by practicing researchers in signal analysis and related areas. Since the expected audience is not presumed to have a high level of mathematical background, much of the needed analytical machinery is developed from the begin-ning. The only prerequisites for the first eight chap-ters are matrix theory, Fourier series, and Fourier integral transforms. Each of these chapters ends with a set of straightforward exercises designed to drive home the concepts just covered, and the many graphics should further facilitate absorption.

Features7 Considered one of the best textbooks on this topic for mathematicians and physicists interested in wavelet analysis 7 Covers all the fundamental concepts of wavelets in an elegant, straightfor-ward way 7 Has a number of unique features, which makes the book particularly valuable for newcomers to the field

From the contentsPreface.- Suggestions to the Reader.- Symbols, Conventions, and Transforms.- Part I: Basic Wavelet Analysis. Preliminaries: Background and Notation.- Windowed Fourier Transforms.- Continuous Wavelet Transforms.- Generalized Frames: Key to Analysis and Synthesis.- Discrete Time-Frequency Analysis and Sampling.- Discrete Time-Scale Analysis.- Multiresolution Analysis.- Daubechies’ Orthonormal Wavelet Bases.- Part II: Physical Wavelets.- Introduction to Wavelet Electromagnetics.

Fields of interestApplications of Mathematics; Signal, Image and Speech Processing; Mathematical Methods in Physics



Due November 2010

2011. XVIII, 470 p. 121 illus., 7 in color. (Applied Mathematical Sciences, Volume 174) Hardcover


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Due November 2010

2011. XVI, 476 p. 15 illus. (Springer Monographs in Mathematics) Hardcover

7 € 89,95 | £81.007 * € (D) 96,25 | € (A) 98,95 | sFr 129,00ISBN 978-0-85729-159-2

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Due November 2010

2011. XVIII, 300 p. 33 illus. (Modern Birkhäuser Classics) Softcover


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K. Aomoto

Theory of Hypergeometric Functions

This book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. Starting from an integrand which is a product of powers of poly-nomials, integrals are explained, in an open affine space, as a pair of twisted de Rham cohomology and its dual over the coefficients of local system. It is shown that hypergeometric integrals gener-ally satisfy holonomic system of linear differen-tial equations with respect to the coefficients of polynomials and also satisfy holonomic system of linear difference equations with respect to the exponents. These are basically deduced from Grothendieck-Deligne’s rational de Rham cohomology on the one hand, and by multidimen-sional extension of Birkhoff ’s classical theory on analytic difference equations on the other.

Features7 Reader will understand clearly multidimen-sional hypergeometric function as a natural extension of the classical one from viewpoint of integrals 7 A quick introduction to rational de Rham cohomology due to A.Grothendieck and P.Deligne and also to holonomic differential equa-tions (or Gauss-Manin connection) and difference equations associated with hypergeometric func-tions 7 Application of hypergeometric functions to several analytic or geometric problems

Contents1 Introduction: the Euler-Gauss Hypergeometric Function.- 2 Representation of Complex Integrals and Twisted de Rham Cohomologies.- 3 Hyper-geometric functions over Grassmannians.- 4 Holonomic Difference Equations and Asymptotic Expansion References Index.

Fields of interestGeometry; Functional Analysis

Target groupsProfessional/practitioner

G. Köhler, Universität Würzburg

Eta Products and Theta Series Identities

This monograph deals with products of Dedekind’s eta function, with Hecke theta series on quadratic number fields, and with Eisenstein series. The author brings to the public the large number of identities that have been discovered over the past 20 years, the majority of which have not been published elsewhere. The book will be of interest to graduate students and scholars in the field of number theory and, in particular, modular forms. It is not an introductory text in this field. Never-theless, some theoretical background material is presented that is important for understanding the examples in Part II of the book.

Features7 This monograph brings to the public the large number of identities which were found during the past 20 years 7 The majority of these identities is new and has not been published elsewhere 7 Presents more than hundred examples for the coincidence of theta series of weight 1 on three distinct quadratic fields

ContentsFrom the contents Introduction.- Part I: Theoret-ical background.- 1. Dedekind’s eta function and modular forms.- 2. Eta products.- 3. Eta products and lattice points in simplices.- 4. An algorithm for listing lattice points in a simplex.- 5. Theta series with Hecke character.- 6. Groups of coprime residues in quadratic fields.- Part II: Examples.- 7. Ideal numbers for quadratic fields.- 8 Eta products of weight .- 9. Level 1: The full modular group.- 10. The prime level N = 2.- 11. The prime level N = 3.- 12. Prime levels N = p ≥ 5.- 13. Level N = 4.- 14. Levels N = p2 with primes p ≥ 3. - 15 Levels N = p3 and p4 for primes p.- 16. Levels N = pq with primes 3 ≤ p q.- 17. Weight 1 for levels N = 2p with primes p ≥ 5.- 18. Level N = 6. - 19. Weight 1 for prime power levels p5 and p6. - 20. Levels p2q for distinct primes p = 2 and q. - 21. Levels 4p for the primes p = 23 and 19.

Fields of interestNumber Theory; Algebraic Topology


A. Leitsch, Technische Universitaet Wien, Austria; M. Baaz, Vienna University of Technology, Vienna, Austria

Methods of Cut-Elimination

This book is on methods of cut-elimination. It contains a thorough and rigorous analysis of reductive cut-elimination methods and an in-depth presentation of the recent method CERES developed by the authors. The book contains a detailed complexity analysis and comparison of CERES and of reductive methods. Finally several applications of CERES are presented: to interpola-tion, fast cut-elimination, generalization of proofs and to the analysis of mathematical proofs. Finally an extension of CERES to nonclassical logics is presented, in particular to finitely-valued logics and to Goedel logic.

Features7 First book on methods of cut-elimination 7 Combines techniques and results from proof theory and automated deduction 7 Thereby the book provides a completely new view on proof theoretic methods and their applications 7 This specific feature makes the book interesting for researchers and graduate students in proof theory and computational logic

Contents1 Preface.- 2 Introduction.- 3 Preliminaries. - 4 Complexity of Cut-Elimination.- 5 Reduction and Elimination.- 6 Cut-Elimination by Resolu-tion.- 7 Extensions of CERES.- 8 Applications of CERES.- 9 CERES in Nonclassical Logics. - 10 Related Research.

Fields of interestMathematical Logic and Foundations; Mathemat-ical Logic and Formal Languages



Due January 2011

2011. V, 315 p. 30 illus. With online files/update. (Springer Monographs in Mathematics) Hardcover

7 € 89,95 | £81.007 * € (D) 96,25 | € (A) 98,95 | sFr 129,00ISBN 978-4-431-53912-4

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Due December 2010

2011. X, 480 p. (Springer Monographs in Mathematics) Hardcover


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Due January 2011

2011. Approx. 295 p. (Trends in Logic, Volume 34) Hardcover


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Z. Li, Beijing Normal University, China

Measure-Valued Branching Markov Processes

Measure-valued branching processes arise as high density limits of branching particle systems. The Dawson-Watanabe superprocess is a special class of those. The author constructs superprocesses with Borel right underlying motions and general branching mechanisms and shows the existence of their Borel right realizations. He then uses trans-formations to derive the existence and regularity of several different forms of the superprocesses. This treatment simplifies the constructions and gives useful perspectives. Martingale problems of superprocesses are discussed under Feller type assumptions. The most important feature of the book is the systematic treatment of immigra-tion superprocesses and generalized Ornstein--Uhlenbeck processes based on skew convolution semigroups. The volume addresses researchers in measure-valued processes, branching processes, stochastic analysis, biological and genetic models, and graduate students in probability theory and stochastic processes.

Features7 For the first time a book in this research area 7 Gives treatments of the basic regularities of Dawson-Watanabe superprocesses with general branching mechanisms and spatial motions 7 Studies immigration superprocesses and gener-alized Ornstein-Uhlenbeck processes 7 Designed as a study text for graduates

ContentsPreface.- 1. Random Measures on Metric Spaces.- 2. Measure-valued Branching Processes.- 3. One-dimensional Branching Processes.- 4. Branching Particle Systems.- 5. Basic Regularities of Super-processes.- 6. Constructions by Transformations.- 7. Martingale Problems of Superprocesses. - 8. Entrance Laws and Excursion Laws. - 9. Structures of Independent Immigration. - 10. State-dependent Immigration Structures. - 11. Generalized Ornstein-Uhlenbeck Processes.

Field of interestProbability Theory and Stochastic Processes


J. M. McCarthy, G. S. Soh, University of California, Irvine, CA, USA

Geometric Design of Linkages

This book is an introduction to the mathematical theory of design for articulated mechanical systems known as linkages. The focus is on sizing mechanical constraints that guide the movement of a work piece, or end-effector, of the system. The function of the device is prescribed as a set of positions to be reachable by the end-effector; and the mechanical constraints are formed by joints that limit relative movement. The goal is to find all the devices that can achieve a specific task. Formulated in this way the design problem is purely geometric in character. Robot manipula-tors, walking machines, and mechanical hands are examples of articulated mechanical systems that rely on simple mechanical constraints to provide a complex workspace for the end- effector. The prin-ciples presented in this book form the foundation for a design theory for these devices. The emphasis, however, is on articulated systems with fewer degrees of freedom than that of the typical robotic system, and therefore, less complexity.

Features7 Only book that brings together the kinematic synthesis theory of planar, spherical and spatial kinematic chains 7 This mathematical theory forms the foundation for numerical methods for dimensional synthesis of the articulated skeletons of modern machine, manipulator and robotic systems

From the contentsIntroduction.- Analysis of Planar Linkages.- Graphical Synthesis in the Plane.- Planar Kine-matics.- Algebraic Synthesis of Planar.- Multiloop Planar Linkages.- Analysis of Spherical Linkages.- Spherical Kinematics.- Algebraic Synthesis of Spherical Chains.- Multiloop Spherical.- Analysis of Spatial Chains.- Spatial Kinematics.- Algebraic Synthesis of Spatial.- Synthesis of Spatial Chains with Reachable Surface.

Fields of interestSystems Theory, Control; Robotics and Automa-tion; Control


I. Moerdijk, Utrecht University, The Netherlands; B. Toën, Toulouse University, France

Simplicial Methods for Operads and Algebraic Geometry

This book is an introduction to two new topics in homotopy theory: Dendroidal Sets (by Ieke Moerdijk) and Derived Algebraic Geometry (by Bertrand Toën). The category of dendroidal sets is an extension of that of simplicial sets, based on rooted trees instead of linear orders, suitable as a model category for higher topological structures. Derived algebraic geometry deals with functors from simplicial commutative rings to simplicial sets subject to a homotopical descent condition. The material in the book is an enhanced version of lecture notes from courses given within a special year on Homotopy Theory and Higher Categories at the CRM in Barcelona.

Features7 The material is not available elsewhere, except in the original research articles 7 The material is presented by the best experts, in fact the inventors themselves 7 The exposition has maintained the directness of the original lectures

From the contentsPart I: Lectures on Dendroidal Sets 1. Operads 2. Trees as operads 3. Dendroidal sets 4. Tensor product of dendroidal sets 5. A Reedy model structure on dendroidal spaces 6. The Boardman-Vogt resolution and homotopy coherent nerve 7. Inner Kan complexes and normal dendroidal sets 8. Model structures on dendroidal sets Part II: Simplicial Presheaves and Derived Algebraic Geometry 1. Motivation and objectives 2. Simpli-cial presheaves as stacks 3. Algebraic stacks 4. Simplicial commutative algebras 5. Derived stacks and derived algebraic stacks.

Fields of interestCategory Theory, Homological Algebra; Algebraic Topology



Due November 2010

2011. X, 350 p. (Probability and Its Applications) Hardcover


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Due December 2010

2nd Ed. 2011. X, 464 p. (Interdisciplinary Applied Mathematics, Volume 11) Hardcover


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Due February 2011

2011. 200 p. (Advanced Courses in Mathematics – CRM Barcelona) Softcover


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J. Murín, Slovak University of Technology in Bratislava, Slovakia; V. Kompiš, Academy of Armed Forces, Slovakia; V. Kutiš, Slovak University of Technology, Bratislava, Slovakia (Eds.)

Computational Modelling and Advanced Simulations

This book contains selected, extended papers presented in the thematic ECCOMAS conference on Computational Modelling and Advanced Simu-lations (CMAS2009) held in Bratislava, Slovakia, in June 30 – July 3, 2009. Modelling and simulation of engineering prob-lems play a very important role in the classic and new composite material sciences, and in design and computational prototyping of modern and advanced technologic parts and systems. According to this, the existing numerical methods have been improved and new numerical methods have been established for modelling and simula-tion of more and more complex and complicated engineering problems. The present book should contribute to the effort to make the modelling and simulation more effective and accurate.

Features7 Newest results on the area of computational modeling and simulations of the selected engi-neering problems 7 State of the art papers 7 World leading expert contributions

From the contentsIntroduction; 1. Nonlinear Dynamic Analysis of Partially Supported Beam-Columns on Nonlinear Elastic Foundation Including Shear Deformation Effect, by E.J. Sapountzakis, A.E. Kampitsis; 2. Mechanics of viscoelastic plates made of FGMs, by H. Altenbach, V.A. Eremeyev; 3. Indirect Trefftz method for solving Cauchy problem of linear piezoelectricity, by G. Dziatkiewicz, P. Fedeliński; 4. New Phenomenological Model for Solid Foams, by V. Goga; 5. The Effect of an Interphase on Micro-Crack Behaviour in Polymer Composites, by P. Hutař, L. Náhlík, Z. Majer, Z. Knésl;

Fields of interestComputational Science and Engineering; Mate-rials Science, general; Theoretical and Applied Mechanics


K. Neeb, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany; A. Pianzola, University of Alberta, Edmonton, AB, Canada (Eds.)

Developments and Trends in Infinite-Dimensional Lie Theory

This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Part (A) is mainly concerned with the structure and representation theory of infinite-dimensional Lie algebras and contains articles on the structure of direct-limit Lie algebras, extended affine Lie algebras and loop algebras, as well as representa-tions of loop algebras and Kac–Moody superalge-bras. The articles in Part (B) examine connections between infinite-dimensional Lie theory and geometry. The topics range from infinite-dimensional groups acting on fiber bundles, corresponding characteristic classes and gerbes, to Jordan-theoretic geometries and new results on direct-limit groups.

Features7 Invited papers written by distinguished researchers 7 Expository essays focus on recent developments and trends in infinite-dimensional Lie theory 7 Discusses new methods, structures, and representations of infinite-dimensional Lie groups

Fields of interestTopological Groups, Lie Groups; Group Theory and Generalizations; Algebra


A. Olivieri, Università di Parma, Italy; E. Pitacco, Università di Trieste, Italy

Introduction to Insurance MathematicsTechnical and Financial Features of Risk Transfers

The book aims at presenting technical and financial features of life insurance, non-life insur-ance, pension plans. The book has been planned assuming non-actuarial readers as its “natural” target, namely advanced undergraduate and grad-uate students in Economics, Business and Finance; professionals and technicians operating in Insur-ance and pension areas, whose job may regard investments, risk analysis, financial reporting, etc, and hence implies a communication with actuarial professionals and managers. Given the assumed target, the book focuses on technical and financial aspects of insurance, however avoiding the use of complex mathematical tools. In this sense, the book can be placed at some “midpoint” of the existing literature, part of which adopts more formal approaches to insurance problems implying the use of non-elementary mathematics, whereas another part addresses practical questions totally avoiding even simple mathematical tools (which, in our opinion, can conversely provide effective tools for presenting technical and financial features of the insurance business).

Features7 Wide range of topics dealt with (life insur-ance, non-life insurance, and pensions included) 7 Careful attention to practical issues A “less mathematical and formal” perspective, if compared to other textbooks

From the contentsRisks and insurance.- Managing a portfolio of risks.- Life insurance: modelling the lifetime.- Life insurance: pricing.- Life insurance: reserving.- Reserves and profits in a life insurance portfolio.

Fields of interestGame Theory, Economics, Social and Behav. Sciences; Finance /Banking; Statistics for Business/Economics/Mathematical Finance/Insurance



Due January 2011

2011. 400 p. (Computational Methods in Applied Sciences, Volume 24) Hardcover

7 € 189,95 | £171.007 * € (D) 203,25 | € (A) 208,94 | sFr 272,50ISBN 978-94-007-0316-2

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Due November 2010

2011. VIII, 492 p. 9 illus. (Progress in Mathematics, Volume 288) Hardcover

7 € 109,95 | £99.007 * € (D) 117,65 | € (A) 120,95 | sFr 158,00ISBN 978-0-8176-4740-7

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Due December 2010

2011. 475 p. 180 illus. Softcover


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I. Peeva, Cornell University, Ithaca, NY, USA

Graded Syzygies

The study of free resolutions is a core and beau-tiful area in Commutative Algebra. The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions. Many examples are given in order to illustrate ideas and key concepts. A valuable feature of the book is the inclusion of open problems and conjectures; these provide a glimpse of exciting, and often challenging, research directions in the field. Three types of problems are presented: Conjectures, Problems, and Open-Ended Prob-lems. The latter do not describe specific problems but point to interesting directions for exploration. The first part of the monograph contains basic background material on graded free resolutions. Further coverage of topics includes syzygies over a polynomial ring, resolutions over quotient rings, lex ideals and Hilbert functions, compression, resolutions of monomial ideals, and syzygies of toric ideals. With a clear and self-contained exposi-tion this text is intended for advanced graduate students and postdoctorates; it will be also of interest to senior mathematicians.

Features7 Focuses on the graded aspect of syzygies, while most of the standard texts in commutative algebra mainly consider local rings 7 Provides a substan-tial amount of open problems and conjectures 7 A wealth of examples- Contains basic back-ground material on free resolutions making the text accessible to beginners

ContentsGraded Free Resolutions.- Hilbert Functions.- Monomial Resolutions.- Syzygies of Toric Ideals.

Fields of interestCommutative Rings and Algebras


S. Roch, Technische Universität Darmstadt, Germany; P. A. Santos, Centro de Mathemàtica Aplicada, Lisboa, Portugal; B. Silbermann, Technische Universität Chemnitz, Germany

Non-commutative Gelfand TheoriesA Tool-kit for Operator Theorists and Numerical Analysts

Written as a hybrid between a research mono-graph and a textbook the first half of this book is concerned with basic concepts for the study of Banach algebras that, in a sense, are not too far from being commutative. Essentially, the algebra under consideration either has a sufficiently large center or is subject to a higher order commutator property (an algebra with a so-called polynomial identity or in short: Pl-algebra). In the second half of the book, a number of selected examples are used to demonstrate how this theory can be successfully applied to problems in operator theory and numerical analysis. Distinguished by the consequent use of local principles (non-commutative Gelfand theories), PI-algebras, Mellin techniques and limit operator techniques, each one of the applications presented in chapters 4, 5 and 6 forms a theory that is up to modern standards and interesting in its own right. Written in a way that can be worked through by the reader with fundamental knowledge of analysis, functional analysis and algebra, this book will be accessible to 4th year students of mathematics or physics whilst also being of interest to researchers in the areas of operator theory, numerical analysis, and the general theory of Banach algebras.

Features7 Provides an overview of the theoretical developments of the last thirty years in addition to a number of concrete applications in operator theory and numerical analysis 7 Focuses on non-C*-algebras 7 Contains new results not yet published 7 Written in a way that it can be worked through by a reader with fundamental knowledge of analysis, functional analysis and algebra

Fields of interestFunctional Analysis; Numerical Analysis; Integral Equations


L. Rodino, University of Torino, Italy; M. W. Wong, H. Zhu, York University, Toronto, ON, Canada (Eds.)

Pseudo-Differential Operators: Analysis, Applications and Computations

This volume consists of eighteen peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held at Imperial College London on July 13-18, 2009. Featured in this volume are the analysis, applications and computations of pseudo-differen-tial operators in mathematics, physics and signal analysis. This volume is a useful complement to the volumes “Advances in Pseudo-Differential Opera-tors”, “Pseudo-Differential Operators and Related Topics”, “Modern Trends in Pseudo-Differential Operators”, “New Developments in Pseudo-Differential Operators” and “Pseudo-Differential Operators: Complex Analysis and Partial Differ-ential Equations” published in the same series in, respectively, 2004, 2006, 2007, 2009 and 2010.

Features7 Most new developments in pseudo-differential operators are represented 7 Numerical computa-tions of pseudo-differential operators and discrete analogs of pseudo-differential operators are featured 7 Diversity of topics related to pseudo-differential operators is presented

From the contentsAdaptive Wavelet Computations for Inverses of Pseudo-Differential Operators.- Spectral Theory of Pseudo-Differential Operators on S1.- A Charac-terization of Compact Pseudo-Differential Opera-tors on S1.- Melin Operator with Asymptotics on Manifolds with Corners.- The Iterative Structure of the Corner Calculus.- Elliptic Equations and Boundary Value Problems in Non-Smooth Domains.- Calculus of Pseudo-Differential Opera-tors and a Local Index of Dirac Operators.

Fields of interestPartial Differential Equations; Operator Theory; Geometry



Due November 2010

2011. X, 302 p. 23 illus. (Algebra and Applications, Volume 14) Hardcover

7 € 89,95 | £81.007 * € (D) 96,25 | € (A) 98,95 | sFr 129,00ISBN 978-0-85729-176-9

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Due November 2010

2011. VI, 392 p. 14 illus., 2 in color. (Universitext) Softcover


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Due January 2011

2011. 350 p. Hardcover


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S. A. Sauter, University of Zurich, Switzerland; C. Schwab, ETH Zurich, Switzerland

Boundary Element Methods

This work presents a thorough treatment of boundary element methods (BEM) for solving elliptic integral equations. The book is self-contained, the prerequisites on elliptic partial differential and integral equations being presented in Chapters 2 and 3. The main focus is on the development, analysis, and implementation of Galerkin boundary element methods, which is one of the most flexible and robust numerical discretization methods for integral equations. For the efficient realization of the Galerkin BEM, it is essential to replace time-consuming steps in the numerical solution process with fast algorithms. In Chapters 5-9 these methods are developed, analyzed, and formulated in an algorithmic way.

Features7 Self-contained presentation of Variational Boundary 7 Integral Equation Formulations of second order elliptic problems 7 Complete and self-contained numerical analysis of advanced Galerkin Boundary Element Methods 7 Guided exposition from mathematical preliminaries to research literature

ContentsPreface.- Introduction.- Elliptic Differential Equations.- Elliptic Boundary Integral Equations.- Boundary Element Methods.- Generating the Matrix Coefficients.- Solution of Linear Systems of Equations.- Cluster Methods.- Parametric Surface Approximation.- A Posteriori Error Estimation.- Bibliography.- Index of Symbols.- Index.

Fields of interestComputational Mathematics and Numerical Analysis


S. Shirali, H. L. Vasudeva, Panjab University, Chandigarh, India

Multivariable Analysis

This book provides a rigorous treatment of multivariable differential and integral calculus. Implicit function theorem and the inverse function theorem based on total derivatives is explained along with the results and the connec-tion to solving systems of equations. There is an extensive treatment of extrema, including constrained extrema and Lagrange multipliers, covering both first order necessary conditions and second order sufficient conditions. The mate-rial on Riemann integration in n dimensions, being delicate by its very nature, is discussed in detail. Differential forms and the general Stokes’ Theorem are expounded in the last chapter. With a focus on clarity rather than brevity, this text gives clear motivation, definitions and examples with transparent proofs. Much of the material included is published for the first time in textbook form, for example Schwarz’ Theorem in Chapter 2 and double sequences and sufficient conditions for constrained extrema in Chapter 4. A wide selec-tion of problems, ranging from simple to more challenging, are included with carefully formed solutions. Ideal as a classroom text or a self study resource for students, this book will appeal to higher level undergraduates in Mathematics.

Features7 Contains a number of examples as well as section-by section problems, ranging from simple to complex 7 Problems illustrate the application of concepts introduced as well as further developments 7 Extensive hints and solutions are provided 7 Full chapter on extrema, including examples when the Lagrange method appears to "fail"

ContentsPreliminaries.- Functions between Euclidean Spaces.- Differentiation.- Inverse and Implicit Function Theorems.- Extrema.- Riemann Integra-tion in Euclidean Space.- The General Stokes Theorem.- Solutions.

Field of interestReal Functions


A. Tveito, H. P. Langtangen, Simula Research Laboratory, Lysaker, Norway; B. F. Nielsen, Norwegian University of Life Sciences, Ås, Norway; X. Cai, Simula Research Laboratory, Lysaker, Norway

Elements of Scientific Computing

Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disci-plines. This book is a gentle introduction to such computational methods where the techniques are explained through examples. It is our goal to teach principles and ideas that carry over from field to field. You will learn basic methods and how to implement them. In order to gain the most from this text, you will need prior knowledge of calculus, basic linear algebra and elementary programming.

Features7 A very gentle introduction 7 Learn to master basic methods by examples 7 Includes a chapter on scientific software

ContentsComputing Integrals.- Differential Equations: The First Steps.- Systems of Ordinary Differential Equations.- Nonlinear Algebraic Equations.- The Method of Least Squares.- About Scientific Software.- The Diffusion Equation.- Analysis of the Diffusion Equation.- Parameter Estimation and Inverse Problems. – A Glimpse of Parallel Computing.- Index.

Fields of interestComputational Mathematics and Numerical Analysis; Computational Science and Engineering; Numerical and Computational Physics

Target groupsLower undergraduate


Due November 2010

2011. 500 p. (Springer Series in Computational Mathematics, Volume 39) Hardcover


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Due December 2010

2011. V, 393 p. 18 illus. Softcover


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Available

2011. XII, 460 p. (Texts in Computational Science and Engineering, Volume 7) Hardcover

7 € 59,95 | £53.997 * € (D) 64,15 | € (A) 65,95 | sFr 86,00ISBN 978-3-642-11298-0

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A. F. Verbeure, Institute for Theoretical Physics, K.U.Leuven, Belgium

Many-Body Boson SystemsHalf a Century Later

This book offers a modern way of dealing with the problems of equilibrium states of Bose systems. Starting with the variation principle of statis-tical mechanics and the energy-entropy balance principle as equilibrium criteria, results for general boson systems and models are explicitly derived using simple functional analytic calculus.Bridging the gap between general theoretical physics and the phenomenological research in the field of Bose systems, this book provides an insight into the fascinating quantum world of bosons. Key topics include the occurrence of BEC and its intimate structural relation with the phenomena of spon-taneous symmetry breaking and off-diagonal long range order; the condensate equation; the issue concerning the choice of boundary conditions; solvable versus non-solvable boson models; the set of quasi-free boson states; the role of dissipa-tive perturbations; and the surprising but general relation between general quantum fluctuations and boson systems.Only some knowledge of quantum mechanics and undergraduate algebra and analysis is assumed. This textbook brings students and researchers smoothly from general concepts to vivid applications.

Features7 Presents tools needed to analyze qualitatively and quantitatively different models 7 Bridges the gap between mathematics and physics 7 With a focus on boson systems, ideas developed in the book lead to new ways of looking at existing prob-lems; new technologies for solving old problems and new applications for new exact results

ContentsIntroduction.- Bose systems.- Equilibrium States.- Bose Einstein Condensation (BEC).- Bose System Dynamics.- Quantum Fluctuations and Bosoniza-tion.- Appendix.

Fields of interestFunctional Analysis; Operator Theory; Theoretical, Mathematical and Computational Physics



Due November 2010

2011. X, 185 p. (Theoretical and Mathematical Physics) Hardcover

7 € 69,95 | £62.997 * € (D) 74,85 | € (A) 76,95 | sFr 100,50ISBN 978-0-85729-108-0

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