m. aigner m. e. alonso e. arrondo v. vinnikov g. m

springer.com/booksellers 31Springer News 9/2009 Mathematics

M. Aigner, Freie Universität Berlin, Germany; G. M. Ziegler, Technische Universität Berlin, Germany

Proofs from THE BOOKIllustrations by: K. Hofmann

This revised and enlarged fourth edition features five new chapters, which treat classical results such as the “Fundamental Theorem of Algebra”, prob-lems about tilings, but also quite recent proofs, for example of the Kneser conjecture in graph theory. The new edition also presents further improve-ments and surprises, among them a new proof for “Hilbert’s Third Problem”.

From the reviews7 ... Inside [this book] is indeed a glimpse of math-ematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ..., but many [proofs] are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: “... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations.” I do. ... 7 AMS Notices 1999 7 ... the level is close to elementary ... the proofs are brilliant. ... 7 LMS Newsletter 1999

Features7 Revised and enlarged form 7 With five new chapters 7 Presents further improvements and surprises

ContentsPreface.- Number Theory.- Geometry.- Analysis.- Combinatorics.- Graph Theory.- About the Illus-trations.- Index.

Fields of interestMathematics, general; Number Theory; Geometry

Target groupsMathematicians and scientists of all ages and levels, students and teachers

M. E. Alonso, E. Arrondo, R. Mallavibarrena, I. Sols, Universidad Complutense de Madrid, Spain (Eds.)

Liaison, Schottky Problem and Invariant TheoryRemembering Federico Gaeta

This volume is a homage to the memory of the Spanish mathematician Federico Gaeta (1923-2007). Apart from a historical presentation of his life and interaction with the classical Italian school of algebraic geometry, the volume presents surveys and original research papers on the mathematics he studied. Specifically, it is divided into three parts: linkage theory, Schottky problem and invariant theory. On this last topic a hitherto unpublished article by Federico Gaeta is also included.

Features7 Linkage theory is revisited with a survey and several original research papers 7 There is a survey and two original research papers on Schottky problem 7 An unpublished article of Federico Gaeta is included in the book 7 A historical presentation of the interaction of Gaeta with the classical Italian school of algebraic geom-etry is also included in the book

Fields of interestAlgebraic Geometry

Target groupsAlgebraic geometers and mathematics researchers in general interested in algebraic geometry and its historical aspects

D. Alpay, V. Vinnikov, Ben Gurion University of the Negev, Beer Sheva, Israel (Eds.)

Characteristic Functions, Scattering Functions and Transfer FunctionsThe Moshe Livsic Memorial Volume

The notions of transfer function and characteristic functions proved to be fundamental in the last fifty years in operator theory and in system theory. Moshe Livsic played a central role in developing these notions, and the book contains a selection of carefully chosen refereed papers dedicated to his memory. Topics include classical operator theory, ergodic theory and stochastic processes, geometry of smooth mappings, mathematical physics, Schur analysis and system theory. The variety of topics attests well to the breadth of Moshe Livsic’s math-ematical vision and the deep impact of his work. The book will appeal to researchers in math-ematics, electrical engineering and physics.

Features7 Volume in memory of Moshe Livsic, first class mathematician who, in particular, introduced the notion of characteristic operator function and of transfer function

Field of interestOperator Theory

Target groupsResearchers in mathematics, physics and electrical engineering: particularly in linear system theory, operator theory and functional analysis

Type of publicationUndergraduate textbook

Mathematics

Due October 2009

4th ed. 2010. VIII, 275 p. 250 illus., 6 in color. Hardcover

7 € 39,95 | £34.997 * € (D) 42,75 | € (A) 43,95 | sFr 66,50ISBN 978-3-642-00855-9

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Type of publicationCommemorative publication

Mathematics

Due November 2009

2010. Approx. 300 p. (Progress in Mathematics, Volume 280) Hardcover

7 € 69,95 | £62.997 * € (D) 74,85 | € (A) 76,95 | sFr 109,00ISBN 978-3-0346-0200-6

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Type of publicationCommemorative publication

Mathematics

Due September 2009

2009. Approx. 410 p. Hardcover

7 € 129,00 | £116.007 * € (D) 138,03 | € (A) 141,90 | sFr 199,00ISBN 978-3-0346-0182-5

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www.springer.com/978-3-642-00855-9



springer.com/booksellers32 Springer News 9/2009Mathematics

H. Ammari, École Polytechnique, Palaiseau, France

Mathematical Modeling in Biomedical Imaging IElectrical and Ultrasound Tomographies, Anomaly Detection, and Brain Imaging

This volume gives an introduction to a fascinating research area to applied mathematicians. It is devoted to providing the exposition of promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.

Contents1 Multi-Frequency Electrical Impedance Tomography and Magnetic Resonance Electrical Impedance Tomography.- 2 Time Reversing Waves For Biomedical Applications.- 3 The Method of Small-Volume Expansions for Medical Imaging.- 4 Electric and Magnetic Activity of the Brain in Spherical and Ellipsoidal Geometry.- 5 Estimation of Velocity Fields and Propagation on Non-Euclidian Domains. Application to the Exploration of Cortical Spatiotemporal Dynamics.

Fields of interestMathematical Biology in General; Potential Theory; Ordinary Differential Equations

Target groupsResearchers and graduate students

J. Aubin, Université de Paris-Dauphine and CNRS, Paris, France

Viability Theory

This work examines viability theory and its appli-cations to control theory and differential games. The emphasis is on the construction of feedbacks and dynamical systems by myopic optimization methods. Systems of first-order partial differential inclusions, whose solutions are feedbacks, are constructed and investigated. Basic results are then extended to the case of fuzzy control problems, distributed control problems, and control systems with delays and memory. Aimed at graduate students and research math-ematicians, both pure and applied, this book offers specialists in control and nonlinear systems tools to take into account general state constraints. Viability theory also allows researchers in other disciplines – artificial intelligence, economics, game theory, theoretical biology, population genetics, cognitive sciences – to go beyond deter-ministic models by studying them in a dynamical or evolutionary perspective in an uncertain environment.

Features7 An affordable new softcover edition of a classic text 7 Wide scope makes the book an ideal refer-ence for anyone encountering problems related to viability theory in their research 7 Essentially self-contained presentation

Fields of interestSystems Theory, Control; Control, Robotics, Mechatronics; Game Theory, Economics, Social and Behav. Sciences

Target groupsGraduate students, researchers, and practitioners in pure/applied mathematics, systems/control, artificial intelligence, economics, game theory, theoretical biology, and cognitive sciences

H. Baum, A. Juhl, Humboldt-Universität Berlin, Germany

Conformal Differential Geometry

Conformal invariants (conformally invariant tensors, conformally covariant differential operators, conformal holonomy groups etc.) are of central significance in differential geometry and physics. Well-known examples of such operators are the Yamabe-, the Paneitz-, the Dirac- and the twistor operator. The aim of the seminar was to present the basic ideas and some of the recent developments around Q-curvature and conformal holonomy. The part on Q-curvature discusses its origin, its relevance in geometry, spectral theory and physics. Here the influence of ideas which have their origin in the AdS/CFT-correspondence becomes visible. The part on conformal holonomy describes recent classification results, its relation to Einstein metrics and to conformal Killing spinors, and related special geometries.

Features7 Reviews very recent developments 7 Compact introduction into an active field of research

Fields of interestDifferential Geometry

Target groupsResearchers and graduate students specialized in differential geometry, geometric analysis and mathematical physicsType of publication

Monograph

Mathematics

Due October 2009

2010. Approx. 230 p. (Lecture Notes in Mathematics / Mathematical Biosciences Subseries, Volume 1983) Softcover

7 € 69,95 | £62.997 * € (D) 74,85 | € (A) 76,95 | sFr 109,00ISBN 978-3-642-03443-5

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Type of publicationMonograph

Mathematics

Available

Originally published in the series: Systems & Control: Foundations & Applications

1st ed. 2001. 2nd printing 2009. XXVIII, 544 p. 10 illus. (Modern Birkhäuser Classics) Softcover

7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 77,50ISBN 978-0-8176-4909-8

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Type of publicationGraduate/Advanced undergraduate textbook

Mathematics

Due February 2010

2010. Approx. 100 p. (Oberwolfach Seminars, Volume 41) Softcover

7 € 19,95 | £17.997 * € (D) 21,35 | € (A) 21,95ISBN 978-3-7643-9908-5

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F. Bogomolov, Y. Tschinkel, New York University, New York, NY, USA (Eds.)

Cohomological and Geometric Approaches to Rationality ProblemsNew Perspectives

Rationality problems link algebra to geometry, and the difficulties involved depend on the transcen-dence degree of $K$ over $k$, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. Such advances has led to many interdisciplinary applications to algebraic geometry. This comprehensive book consists of surveys of research papers by leading specialists in the field and gives indications for future research in rationality problems. Topics discussed include the rationality of quotient spaces, cohomological invariants of quasi-simple Lie type groups, ratio-nality of the moduli space of curves, and rational points on algebraic varieties.

Features7 Includes papers written by leading experts in the field 7 Contains a selection of articles exploring rationality problems in algebraic geom-etry 7 Gives a representative sample of problems and most recent results in algebraic geometry 7 May serve as an intense introduction for graduate students and those wishing to pursue research in algebraic geometry, more specifically, rationality problems

Fields of interestAlgebraic Geometry; Topological Groups, Lie Groups; Group Theory and Generalizations

Target groupsResearchers, mathematicians, graduate students

H. Campbell, L. Helminck, H. Kraft, D. Wehlau (Eds.)

Symmetry and SpacesIn Honor of Gerry Schwarz

This volume includes articles that are a sampling of modern day algebraic geometry with associ-ated group actions from its leading experts. There are three papers examining various aspects of modular invariant theory (Broer, Elmer and Fleis-chmann, Shank and Wehlau), and seven papers concentrating on characteristic 0 (Brion, Daigle and Freudenberg, Greb and Heinzner, Helminck, Kostant, Kraft and Wallach, Traves).

Features7 Papers written by leading experts in the field of algebraic geometry 7 Articles exploring various topics in algebraic geometry; particular focus is on characteristic 0 and modular invariant theory

From the contentsMichel Brion: Some basis results on actions of non-affine algebraic groups.- Abraham Broer: On Chevalley-Shephard-Todd’s theorem in positive characteristic.-Jonathan Elmer and Peter Fleis-chmann: On the depth of modular invariant rings for the groups $C_p×C_p$.- Daniel Daigle and Gene Freudenberg: Families of affine fibrations.- Peter Heinzner: Kählerian reduction in steps.- Aloysius Helminck: On orbit decompositions for symmetric k-varieties.- Bertram Kostant: Root systems for Levi factors and Borel-de Siebenthal theory.- Hanspeter Kraft and Nolan R Wallach: Polarizations and nullcone of representations of reductive groups.- R James Shank and David Wehlau: Decomposing symmetric powers of certain modular representations of cyclic groups.

Fields of interestAlgebraic Geometry; Commutative Rings and Algebras; Field Theory and Polynomials

Target groupsResearchers, mathematicians, and grad students interested in algebraic geometry

Ö. Ceyhan, Y. I. Manin, Max-Planck Institut, Bonn, Germany; M. Marcolli, California Institute of Technology, Pasadena, CA, USA (Eds.)

Arithmetic and Geometry Around Quantization

In recent decades, quantization has led to interesting applications in various mathematical branches. This volume, comprised of research and survey articles, discusses key topics, including symplectic and algebraic geometry, representation theory, quantum groups, the geometric Langlands program, quantum ergodicity, and non-commuta-tive geometry. A wide range of topics related to quantization are covered, giving a glimpse of the broad subject. The articles are written by distin-guished mathematicians in the field and reflect subsequent developments following the Arithmetic and Geometry around Quantization conference held in Istanbul. List of Contributors: S. Akbulut, R. Hadani, S. Arkhipov, K. Kremnizer, Ö. Ceyhan, S. Mahanta, E. Frenkel, S. Salur, K. Fukaya, G. Ben Simon, D. Gaitsgory, W. van Suijlekom, S. Gurevich.

Features7 Highlights possible new research directions 7 Includes both survey and original research articles 7 Presents the “hot topics” in and around quantization

Fields of interestGeometry; Applications of Mathematics; Algebra

Target groupsResearchers and professionals

Type of publicationContributed volume

Mathematics

Due December 2009

2010. Approx. 300 p. 10 illus. (Progress in Mathematics, Volume 282) Hardcover

7 approx. € 89,95 | £81.007 approx. * € (D) 96,25 | € (A) 98,95 | sFr 140,00ISBN 978-0-8176-4933-3

9<HTLIMH=gejddd>


Mathematics

Due December 2009

2010. Approx. 220 p. 10 illus. (Progress in Mathematics, Volume 278) Hardcover


9<HTLIMH=geihej>


Mathematics

Due December 2009

2010. XII, 388 p. 20 illus. (Progress in Mathematics, Volume 279) Hardcover


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P. Collet, École Polytechnique, Palaiseau, France; J. Eckmann, Université de Genève, Switzerland

Iterated Maps on the Interval as Dynamical Systems

From the reviews7 This book is a thorough and readable introduc-tion to some aspects of the theory of one-dimen-sional dynamical systems…The kneading calculus of Milnor – Thurston receives its most accessible treatment to date in print…This is an important and beautiful exposition, both as an orientation for the reader unfamiliar with this theory and as a prelude to studying in greater depth some of the hard papers on the subject 7 Mathematical Reviews – Review of the original hardcover edition7 This book provides a good survey of recent developments in the study of the dynamics of smooth self-maps on the interval. It…deals with a subject whose literature often appears in physics journals. This literature suffers in general from a failure to distinguish between mathematical theorems and ‘facts’ determined empirically, usually by computer experiment. It is a difficult task to consider both of these types of information and carefully maintain the distinction (an absolute necessity from the point of view of a mathematician). The work under review seems to do a good job of this…On the whole this work is a good one meeting a need to survey recent results in this active and important area of math-ematics. 7 Zentralblatt MATH – Review of the original hardcover edition

Features7 An affordable new softcover edition of a classic text 7 Comprehensive introductory overview of continuous maps and dynamical systems

Fields of interestDynamical Systems and Ergodic Theory; Mathematical Methods in Physics

Target groupsGraduate students, researchers, and practitioners in mathematics and physics

A. Dembo, Stanford University, Stanford, CA, USA; O. Zeitouni, Weizmann Institute of Science, Rehovot, Israel and University of Minnesota, M. N. USA

Large Deviations Techniques and Applications

Large deviation estimates have proved to be the crucial tool required to handle many questions in statistics, engineering, statistial mechanics, and applied probability. Amir Dembo and Ofer Zeitouni, two of the leading researchers in the field, provide an introduction to the theory of large deviations and applications at a level suitable for graduate students. The mathematics is rigorous and the applications come from a wide range of areas, including electrical engineering and DNA sequences. The second edition, printed in 1998, included new material on concentration inequalities and the metric and weak convergence approaches to large deviations. General statements and applica-tions were sharpened, new exercises added, and the bibliography updated. The present soft cover edition is a corrected printing of the 1998 edition.

Features7 Written by two of the leading researchers in the field 7 Applications come from a wide range of areas, including electrical engineering and DNA sequencing 7 This second edition includes three new sections which reflect current developments in the field, particularly with regard to applica-tions 7 New exercises have been added and the bibliography has been updated

From the contentsLDP for Finite Dimensional Space.- Applications - The Finite Dimensional Case.- General Prin-ciples.- Sample Path Large Deviations.- The LDP for Abstract Empirical Measures.- Applications of Empirical Measures LDP.

Fields of interestSystems Theory, Control; Probability Theory and Stochastic Processes

Target groupsGraduate students and researchers

M. Djoric, University of Belgrade, Serbia; M. Okumura, Saitama University, Japan

CR Submanifolds of Complex Projective Space

This book covers the necessary topics for learning the basic properties of complex manifolds, offering an easy, friendly, and accessible introduction into the subject while aptly guiding the reader to topics of current research and to more advanced publica-tions. The first half of the book provides an introduc-tion to complex differential geometry and the properties of complex manifolds. The second half describes the properties of hypersurfaces of various complex spaces and CR submanifolds, with particular emphasis on CR submanifolds of maximal CR dimension.

Features7 Presents many recent developments and results in the study of CR submanifolds not previously published 7 Provides a self-contained introduc-tion to complex differential geometry 7 Provides relevant techniques, results, application, and insight into the motivations and ideas behind the theory

Fields of interestDifferential Geometry; Global Analysis and Analysis on Manifolds; Several Complex Variables and Analytic Spaces

Target groupsAdvanced undergraduates, graduate students and researchers in differential geometry


Mathematics

Due October 2009

Originally published in the series: Progress in Physics

Reprint of the 1st ed. 1980. 2nd printing 1990. 2009. XII, 248 p. 67 illus. (Modern Birkhäuser Classics) Softcover

7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 77,50ISBN 978-0-8176-4926-5

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Mathematics

Due October 2009

2nd ed. 1998. Corr. 2nd printing 2010. XVI, 420 p. (Stochastic Modelling and Applied Probability, Volume 38) Softcover

7 € 39,95 | £35.997 * € (D) 42,75 | € (A) 43,95 | sFr 62,00ISBN 978-3-642-03310-0

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Mathematics

Due November 2009

2010. XVI, 176 p. (Developments in Mathematics, Volume 19) Hardcover

7 € 69,95 | £62.997 * € (D) 74,85 | € (A) 76,95 | sFr 109,00ISBN 978-1-4419-0433-1

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T. Eisner, Universität Tübingen, Germany

Stability of Operators and Operator Semigroups

The asymptotic behaviour, in particular “stability” in some sense, is studied systematically for discrete and for continuous linear dynamical systems on Banach spaces. Of particular concern is conver-gence to an equilibrium with respect to various topologies. Parallels and differences between the discrete and the continuous situation are empha-sised.

Features7 Joint treatment of discrete and continuous systems 7 Careful investigation of the behavior with respect to different topologies on infinite dimensional spaces

Fields of interestOperator Theory; Dynamical Systems and Ergodic Theory; Systems Theory, Control

Target groupsGraduate students and researches in functional analysis and operator theory

K. D. Elworthy, University of Warwick, Coventry, UK; Y. LeJan, Université Paris-Sud, Orsay, France; X. Li, University of Warwick, Coventry, UK

The Geometry of Filtering

The geometry which is the topic of this book is that determined by a map of one space N onto another, M, mapping a diffusion process, or operator, on N to one on M. Filtering theory is the science of obtaining or estimating information about a system from partial and possibly flawed observations of it. The system itself may be random, and the flaws in the observations can be caused by additional noise. In this volume the randomness and noises will be of Gaussian white noise type so that the system can be modelled by a diffusion process; that is it evolves continuously in time in a Markovian way, the future evolution depending only on the present situation.

Features7 Develops a calculus for diffusion processes independently of any representation by stochastic differential equations 7 Shows that the geometry arises naturally and gives insight even in classical situations on Rn 7 Extends some of the theory of Riemannian submersions to semi-Riemannian contexts 7 Includes filtering of such infinite dimensional systems as stochastic flows

Fields of interestGlobal Analysis and Analysis on Manifolds; Differential Geometry; Probability Theory and Stochastic Processes

Target groupsResearchers in stochastic analysis, and related areas, graduate students wishing to specialise in these areas or to gain a broad knowledge of funda-mental mathematics, some interest from geometric analysts interested in semi-Riemannian geometry and from global analysts, and researchers in oper-ator theory or mathematical statistics, theoretical workers in applied topics using filtering, such as pollution control

T. Feeman, Villanova University, Villanova, PA, USA

A Beginner’s Guide to the Mathematics of Medical Imaging

This text explores medical imaging, one of the most significant areas of recent mathematical applications, in a concise manner accessible to undergraduate students. The author emphasizes the mathematical aspects of medical imaging, including not only the theoretical background, but also the role of approximation methods and the computer implementation of the inversion algorithms. In twenty-first century health care, CAT scans, ultrasounds, and MRIs are commonplace. Signifi-cant computational advances, along with the devel-opment, design, and improvement of the machines themselves, can only occur in conjunction with a proper understanding of the mathematics. This book is inherently interdisciplinary in nature, and therefore is appropriate for students of engineering, physics, and computer science, in addition to mathematics. A working knowledge of multivariable calculus, as well some basic knowl-edge of differential equations and basic linear algebra and matrix methods, are mathematical prerequisites.

Features7 Offers consice treatment of mathematics for undergraduates solely within the context of medical imaging 7 Inherently interdisciplinary between students of mathematics, physics, computer science, and biomedical engineering 7 Covers current medical imaging development and improvement regarding CAT scans, ultra-sounds, MRIs, and more

Fields of interestFunctional Analysis; Imaging / Radiology; Integral Transforms, Operational Calculus

Target groupsUndergraduate students in mathematics and interdisciplinary fields of engineering, computer science, biomedical research and physics


Mathematics

Due February 2010

2010. Approx. 200 p. (Operator Theory, Volume 203) Hardcover

7 € 79,95 | £72.007 * € (D) 85,55 | € (A) 87,95 | sFr 129,00ISBN 978-3-0346-0194-8

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Mathematics

Due February 2010

2010. Approx. 170 p. (Frontiers in Mathematics) Softcover

7 € 29,95 | £26.997 * € (D) 32,05 | € (A) 32,95 | sFr 49,90ISBN 978-3-0346-0175-7

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Mathematics

Due February 2010

2010. XII, 168 p. 50 illus. (Springer Undergraduate Texts in Mathematics and Technology ) Hardcover


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V. A. Fomichov, State University - Higher School of Economics, Moscow, Russia

Semantics-Oriented Natural Language ProcessingMathematical Models and Algorithms

This book examines key issues in designing seman-tics-oriented natural language processing systems. A broad conceptual framework for describing structured meanings of NL-texts is obtained by defining a new class of formal languages called standard knowledge languages (SK-languages) using a system theoretical approach. Readers will gain knowledge of these languages and will learn a way of building semantic representations using them. With extensive use of examples and illustrations to clarify complex material and demonstrate practical applications, generous historical and bibliographical notes, end-of-chapter exercises, and glossaries, this book will serve as an ideal graduate-level textbook, as well as a good reference for researchers and practitioners who deal with the various problems involving semantics of natural language texts.

Features7 Substantially formal treatment of issues for designers of natural language processing systems 7 Presents an in-depth treatment of NL semantics and a mathematical model of a linguistics database 7 Extensive use of examples and illustrations to clarify complex material and demonstrate practical applications 7 End of chapter exercises, historical and bibliographical notes, and glossaries enrich the text

Fields of interestSystems Theory, Control; Language Translation and Linguistics; Algorithms

Target groupsGraduate students, researchers and practitioners

M. Giaquinta, Dipartimento di Matematica, Scuola Normale Superiore, Pisa, Italy; G. Modica, Diparti-mento di Matematica Applicata, Università di Firenze, Italy

Mathematical AnalysisAn Introduction to Functions of Several Variables

This self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables. The wide range of topics covered include: differ-ential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, differen-tial forms on curves, a general introduction to holomorphic functions, including singularities and residues, surfaces and level sets, and systems and stability of ordinary differential equations. An appendix highlights important mathemati-cians and other scientists whose contributions have made a great impact on the development of theories in analysis.

Features7 Introductory text for analysis of functions of several variables 7 Covers wide range of topics and applications 7 Motivates the topics with examples, observations, exercises, and illustrations 7 Exciting historical background motivates the subject

Fields of interestAnalysis; Measure and Integration; Calculus of Variations and Optimal Control; Optimization

Target groupsAdvanced undergraduates, graduate students, researchers in mathematics and physics, math-ematics instructors, and engineers

P. G. Goerss, Northwestern University, Evanston, IL, USA; J. F. Jardine, The University of Western Ontario, London, ON, Canada

Simplicial Homotopy Theory

Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computa-tion and basic theory. With the development of Quillen’s concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques. Discussed here are the homotopy theory of simpli-cial sets, and other basic topics such as simplicial groups, Postnikov towers, and bisimplicial sets. The more advanced material includes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence. Interspersed throughout are many results and ideas well-known to experts, but uncollected in the literature. Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed.

Features7 Introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed

Fields of interestMathematics, general

Target groupsIntended for second-year graduate students and beyond


Mathematics

Due December 2009

2010. XII, 348 p. 20 illus. (IFSR International Series on Systems Science and Engineering, Volume 27) Hardcover


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Mathematics

Due November 2009

2010. XI, 345 p. 105 illus. Softcover

7 € 64,90 | £58.997 * € (D) 69,44 | € (A) 71,39 | sFr 109,00ISBN 978-0-8176-4507-6

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Mathematics

Due October 2009

2010. XV, 510 p. (Modern Birkhäuser Classics) Softcover

7 € 39,95 | £35.997 * € (D) 42,75 | € (A) 43,95 | sFr 64,90ISBN 978-3-0346-0188-7

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S. Kantorovitz, Bar Ilan University, Ramat Gan, Israel

Topics in Operator Semigroups

This monograph is concerned with the interplay between the theory of operator semigroups and spectral theory. The basics on operator semigroups are concisely covered in this self-contained text. Part I deals with the Hille–Yosida and Lumer–Phil-lips characterizations of semigroup generators, the Trotter–Kato approximation theorem, Kato’s unified treatment of the exponential formula and the Trotter product formula, the Hille–Phillips perturbation theorem, and Stone’s representation of unitary semigroups. Part II explores generaliza-tions of spectral theory’s connection to operator semigroups. This monograph is suitable for graduate students and researchers interested in operator semigroups.

Features7 Concerned with the interplay between the theory of operator semigroups and spectral theory 7 The basics on operator semigroups are concisely covered in this self-contained text

ContentsIntroduction.- Part I. General Theory. Basic theory. The semi-simplicity space. Analyticity. The semigroup as a function of its generator. Large parameter. Boundary values.- Part II. Generaliza-tions. Pre-semigroups. The semi-simplicity space. Families of unbounded symmetric operators. Dependence on parameters.- Notes and Refer-ences. Bibliography.

Fields of interestOperator Theory; Group Theory and Generaliza-tions; Algebra

Target groupsGraduate and postdoc students in group theory as well as researchers and pure mathematicians

I. S. Kotsireas, E. V. Zima, Wilfried Laurier University, Waterloo, ON, Canada (Eds.)

Advances in Combinatorial MathematicsProceedings of the Waterloo Workshop in Computer Algebra 2008

The Second Waterloo Workshop on Computer Algebra (WWCA 2008) was held May 5-7, 2008 at Wilfrid Laurier University, Waterloo, Canada. This conference was dedicated to the 70th birthday of Georgy Egorychev (Krasnoyarsk, Russia), who is well known and highly regarded as the author of the influential, milestone book “Integral Repre-sentation and the Computation of Combinatorial Sums,” which described a regular approach to combinatorial summation, today also known as the method of coefficients. Another great success of this Russian mathematician came in 1980, when he solved the van der Waerden conjecture on the determination of the minimum of the permanent of a doubly stochastic matrix and was awarded the D. R. Fulkerson Prize. This book presents a collection of selected formally refereed papers submitted after the workshop. The topics discussed in this book are closely related to Georgy Egorychev’s influential works.

Features7 High-level conference dedicated to the combi-natorics pioneer Egorychev

From the contentsG.P.Egorychev : Method of Coefficients: an algebraic characterization and recent applica-tions.- G.E. Andrews: PartitionsWith Distinct Evens.- M.Ciucu, C.Krattenthaler: A Factorization Theorem for Classical Group Characters, with Applications to Plane Partitions and Rhombus Tilings.- L.Gurvits: On Multivariate Newton(like) Inequalities.

Fields of interestCombinatorics; Algebra; Symbolic and Algebraic Manipulation

Target groupsResearchers and graduate students in mathematics and computer science

A. Laptev, Imperial College London, UK (Ed.)

Around the Research of Vladimir Maz’ya IFunction spaces

The fundamental contributions of Professor Maz’ya to the theory of function spaces and especially Sobolev spaces are well known and often play a key role in the study of different aspects of the theory, which is demonstrated, in particular, by presented new results and reviews from world-recognized specialists. Sobolev type spaces, extensions, capacities, Sobolev inequalities, pseudo-Poincare inequalities, optimal Hardy-Sobolev-Maz’ya inequalities, Maz’ya’s isocapacitary inequalities in a measure-metric space setting and many other actual topics are discussed.

Features7 New results on actual topics of function spaces presented by leading world-recognized specialists and connected with earlier fundamental results of Prof. Maz’ya 7 Several collections of papers honored Prof. Maz’ya. Prof. Maz’ya published more than 20 monographs and more than 450 articles. The range of his interests is very wide and many of his results play a key role in many areas of analysis and PDEs

Fields of interestAnalysis; Partial Differential Equations; Functional Analysis

Target groupsMathematicians working in the fields of analysis, functional analysis, function theory, theory of partial differential equations, differential geometry, theory of stochastic equations, computational mathematics and related disciplines; can be useful also for postgraduates of the above mentioned disciplines


Mathematics

Due December 2009

2010. Approx. 305 p. (Progress in Mathematics, Volume 281) Hardcover


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Mathematics

Due November 2009


7 € 89,95 | £81.007 * € (D) 96,25 | € (A) 98,95 | sFr 140,00ISBN 978-3-642-03561-6

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Mathematics

Due November 2009

2010. Approx. 400 p. (International Mathematical Series, Volume 11) Hardcover

7 € 109,95 | £99.007 * € (D) 117,65 | € (A) 120,95 | sFr 171,00ISBN 978-1-4419-1340-1

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Around the Research of Vladimir Maz’ya IIPartial Differential Equations

Topics of this volume are close to scientific inter-ests of Professor Maz’ya and use, directly or indi-rectly, the fundamental influential Maz’ya’s works penetrating, in a sense, the theory of PDEs. In particular, recent advantages in the study of semilinear elliptic equations, stationary Navier-Stokes equations, the Stokes system in convex polyhedra, periodic scattering problems, problems with perturbed boundary at a conic point, singular perturbations arising in elliptic shells and other important problems in mathematical physics are presented.

Features7 Professor Maz’ya has received numerous awards for his outstanding contributions, in particular, the Humboldt Research Prize (1999), the Verdaguer Prize of the French Academy of Sciences (2003) 7 He was elected to the Royal Society of Edin-burgh (2001) and the Royal Swedish Academy of Sciences (2002) 7 Several international confer-ences were organised for the occasion of his 60th birthday

From the contentsLarge Solutions to Semilinear Elliptic Equations with Hardy Potential and Exponential Nonlin-earity.- Stability Estimates for Resolvents, Eigen-values, and Eigenfunctions of Elliptic Operators on Variable Domains.- Operator Pencil in a Domain with Concentrated Masses. A Scalar Analog of Linear Hydrodynamics.


Target groupsMathematicians working in the fields of analysis, functional analysis, theory of partial differential equations, theory of Sobolev spaces differential geometry, theory of stochastic equations and related disciplines; can be useful also for post-graduates of the above mentioned disciplines


Around the Research of Vladimir Maz’ya IIIAnalysis and Applications

This volume reflects the variety of areas where Maz’ya’s results are fundamental, influential and/or pioneering. New advantages in such areas are presented by world-recognized experts and include, in particularly, Beurling’s minimum principle, inverse hyperbolic problems, degenerate oblique derivative problems, the Lp-contractivity of the generated semigroups, some class of singular integral operators, general Cwikel-Lieb-Rozen-blum and Lieb-Thirring inequalities,domains with rough boundaries, integral and supremum opera-tors, finite rank Toeplitz operators, etc.

Features7 Focuses on the current state of research in anal-ysis, PDEs and function theory, detailing recent advances, selected in relation to Mazy’as results 7 All the results are new and never published earlier

From the contentsOptimal Control of a Biharmonic Obstacle Problem.- Minimal Thinness and Beurling’s Minimum Principle.- Progress in the Problem of Lp-Contractivity of Semigroups for Partial Differ-ential Operators.- Uniqueness and Nonuniqueness in Inverse Hyperbolic Problems and the Black Hole Phenomenon.- Global Green’s Function Esti-mates.- On Spectral Minimal Partitions: the Case of the Sphere.- Recurrence Relations for Orthog-onal Polynomials and Algebraicity of Solutions of the Dirichlet Problem.


Target groupsMathematicians working in the fields of analysis, functional analysis, theory of partial differential equations, theory of Sobolev spaces differential geometry, theory of stochastic equations and related disciplines; can be useful also for post-graduates of the above mentioned disciplines


Around the Research of Vladimir Maz’ya I - IIIFunciton Spaces, PDEs, Analysis, and Applications

Research articles and surveys from world-recognized mathematicians cover large areas in Analysis where the contributions of Prof. Maz’ya are fundamental, influential, and/or pioneering. Recent advantages in the study of Sobolev type spaces, PDEs and important boundary value prob-lems in mathematical physics, spectral problems, asymptotic expansions, various actual problems in Analysis and applications are presented. Archive photos and List of references to Maz’ya’s works companion the collection.

Features7 Professor Maz’ya has received numerous awards for his outstanding contributions, in particular, the Humboldt Research Prize (1999), the Verdaguer Prize of the French Academy of Sciences (2003) 7 He was elected to the Royal Society of Edin-burgh (2001) and the Royal Swedish Academy of Sciences (2002) 7 Several international confer-ences were organised for the occasion of his 60th birthday

Fields of interestAnalysis; Difference and Functional Equations; Functional Analysis

Target groupsMathematicians working in the fields of analysis, functional analysis, function theory, theory of partial differential equations, differential geometry, theory of stochastic equations, computational mathematics and related disciplines; can be useful also for postgraduates of the above mentioned disciplines


Mathematics

Due November 2009


7 € 109,95 | £99.007 * € (D) 117,65 | € (A) 120,95 | sFr 171,00ISBN 978-1-4419-1342-5

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Mathematics

Due November 2009


7 € 109,95 | £99.007 * € (D) 117,65 | € (A) 120,95 | sFr 171,00ISBN 978-1-4419-1344-9

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Mathematics

Due November 2009

2010. Approx. 1200 p. (International Mathematical Series, Volume 11-13) (3-volume-set)

7 € 279,00 | £251.007 * € (D) 298,53 | € (A) 306,90 | sFr 433,00ISBN 978-1-4419-1346-3

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L. Lerer, V. Olshevsky, University of Connecticut, Storrs, CT, USA; I. M. Spitkovsky, College of William and Mary, Williamsburg, VA, USA (Eds.)

Convolution and Singular Integral Equations

Translated by: O. Karlovych

This volume contains English translations of 13 groundbreaking papers on Toeplitz matrices and Wiener-Hopf equations and other classes of discrete and continuous convolution operators and singular integral equations. The papers are both of theoretical and numerical interest. In particular, the papers examine fast algorithms for inversion of these operators, the theory of discrete and continuous resultants, inversion via factorization, and symbol construction. Origi-nally the papers were written in Russian more than thirty years ago; their English translation is published here for the first time. These papers solved difficult problems and opened new venues in the above-mentioned areas. They are still frequently quoted, and moreover, they exert a continuing influence on numerical analysis and other areas of Pure and Applied Mathematics and Engineering.

Features7 The papers selected for this volume have never been translated into English 7 Closes a gap in the English literature on the subject 7 The material can be used for advanced courses and seminars in mathematics and engineering

Fields of interestOperator Theory; Integral Equations

Target groupsResearchers in operator theory and integral equations

B. Luong, Department of Defense, Washington D.C., USA

Fourier Analysis on Finite Abelian Groups

Fourier analysis has been the inspiration for a technological wave of advances in fields such as imaging processing, financial modeling, algorithms and sequence design. This unified, self-contained book examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform to finite Abelian groups. With countless examples and unique exercise sets at the end of each section, Fourier Analysis on Finite Abelian Groups is a perfect companion to a first course in Fourier analysis. The first chapter provides the fundamental material that is a strong foundation for all subsequent chapters.

Features7 Examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform to finite Abelian groups 7 Provides countless examples and unique exercise sets at the end of each section 7 A perfect companion to a first course in Fourier analysis

Fields of interestFourier Analysis; Group Theory and Generaliza-tions

Target groupsAdvanced undergraduates, graduates, mathemati-cians and researchers, abstract algebra, complex analysis, and linear algebra being the prerequisites

V. Maz’ya, Linköping University, Sweden; A. Soloviev, Chelyabinsk State University, Russia

Boundary Integral Equations on Contours with Peaks

The purpose of this book is to give a comprehen-sive exposition of the theory of boundary integral equations for single and double layer potentials on curves with exterior and interior cusps. The theory was developed by the authors during the last twenty years and the present volume is based on their results. The first three chapters are devoted to harmonic potentials, and in the final chapter elastic poten-tials are treated. Theorems on solvability in various function spaces and asymptotic representations for solutions near the cusps are obtained. Kernels and cokernels of the integral operators are explicitly described. The method is based on a study of auxiliary boundary value problems which is of interest in itself.

Features7 The only book dedicated to boundary integral equations for non-Lipschitz domains 7 New method, different from the traditional approach based on the theories of Fredholm and singular integral operators 7 Detailed study of both functional analytic and asymptotic properties of solutions

Fields of interestIntegral Equations

Target groupsPostgraduates and researchers in integral equations, pde and operator theory

Type of publicationCollection of essays

Mathematics

Due March 2010


7 € 119,00 | £107.007 * € (D) 127,33 | € (A) 130,90 | sFr 189,00ISBN 978-3-7643-8955-0

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Mathematics

Due September 2009

2009. XVI, 160 p. 2 illus. (Applied and Numerical Harmonic Analysis) Hardcover

7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 77,50ISBN 978-0-8176-4915-9

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Mathematics

Due September 2009

2009. Approx. 360 p. (Operator Theory, Volume 195) Hardcover

7 € 149,00 | £134.007 * € (D) 159,43 | € (A) 163,90 | sFr 239,00ISBN 978-3-0346-0170-2

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A. Meucci, Bloomberg L.P., New York, NY, USA

Risk and Asset Allocation

This encyclopedic, detailed exposition spans all the steps of one-period allocation from the founda-tions to the most advanced developments. Multivariate estimation methods are analyzed in depth, including non-parametric, maximum-likeli-hood under non-normal hypotheses, shrinkage, robust, and very general Bayesian techniques. Evaluation methods such as stochastic domi-nance, expected utility, value at risk and coherent measures are thoroughly discussed in a unified setting and applied in a variety of contexts, including prospect theory, total return and bench-mark allocation. Portfolio optimization is presented with emphasis on estimation risk, which is tackled by means of Bayesian, resampling and robust optimization techniques. All the statistical and mathematical tools, such as copulas, location-dispersion ellipsoids, matrix-variate distributions, cone programming, are introduced from the basics.

Features7 The only book that truly discusses in a self-contained and general way all the practical and theoretical aspects of one-period asset alloca-tion, i.e. market Modeling, invariants estimation, portfolia evaluation, and portfolio optimization in the presence of estimation risk 7 The choice of the subjects is “bottom-up”, the approach is “top-down”

Fields of interestQuantitative Finance; Linear and Multilinear Algebras, Matrix Theory; Statistical Theory and Methods

Target groupsQuantitative portfolio managers, graduate and undergraduate students in finance, economics, physics, statistics and mathematics

P. M. Pardalos, T. M. Rassias, A. A. Khan (Eds.)

Nonlinear Analysis and Variational ProblemsIn Honor of George Isac

The chapters in this volume, written by interna-tional experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization. “Nonlinear Analysis and Variational Problems” is organized into two parts. Part I, Nonlinear Analysis, centers on stability issues for functional equations, fixed point theorems, critical point theorems, W*-algebras, the Brezis–Browder principle, and related topics. Part II, Varia-tional Problems, addresses several important aspects of optimization and variational methods. This includes equilibrium problems, projected dynamical system, set-valued and set-semidefinite optimization, variational inequalities, variational principles, complementarity problems, and prob-lems in optimal control.

Features7 Contains 25 research papers with a limited number of survey papers by leading math-ematicians in some important areas of nonlinear analysis and variational problems 7 Presents recent developments in complementarity theory, variational problems, stability theory of functional equations, and various other topics of nonlinear analysis and optimization 7 Includes properties of nuclear cones and variational principles

Fields of interestOperations Research, Mathematical Program-ming; Global Analysis and Analysis on Manifolds; Operator Theory

Target groupsGraduate students, researchers and practitioners in the field of pure and applied mathematics, social sciences, economics, operations research, engineering, and other related sciences

A. Pascucci, Bologna, Italy; W. Runggaldier, Università di Padova, Italy

Finanza matematicaTeoria e problemi per modelli multiperiodali

La finanza matematica ha visto un notevole sviluppo in tempi recenti, soprattutto per l’introduzione di strumenti finanziari atti a contenere il rischio nelle operazioni di mercato. Lo studio delle problematiche legate a tali strumenti richiede tecniche matematiche talvolta sofisticate e la maggior parte di queste tecniche sono legate alla teoria della Probabilità. Gli ambienti finanziari sono quindi divenuti uno sbocco professionale non solo per gli economisti, ma anche per i matematici ed in generale per i laureati delle discipline tecnico-scientifiche. Il presente libro è inteso come testo e nasce dall’esperienza d’insegnamento degli autori. Non esistono molti testi simili a livello internazionale ed il libro intende colmare tale lacuna. Benché concepito maggiormente per un corso di laurea triennale in matematica, esso dovrebbe adattarsi bene anche a corsi di tipo quantitativo per le facoltà di economia.

Fields of interestMatematica, generale; Scienze economiche, generale; Matematica finanziaria quantitativa

Target groupsStudenti dei corsi di Laurea in Matematica e Economia


Mathematics

Available

1st ed. 2005. Corr. 3rd printing 2009. XXVI, 532 p. (Springer Finance) Softcover

7 € 39,95 | £35.997 * € (D) 42,75 | € (A) 43,95 | sFr 66,50ISBN 978-3-642-00964-8

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Mathematics

Due December 2009

2010. Approx. 515 p. 13 illus. (Springer Optimization and Its Applications, Volume 35) Hardcover

7 € 129,95 | £117.007 * € (D) 139,05 | € (A) 142,95 | sFr 202,00ISBN 978-1-4419-0157-6

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Type of publicationLibro di testo introduttivo

Mathematics

Pubblicazione prevista per il mese di settembre 2009

2009. Ca. 270 pagg. (UNITEXT / La Matematica per il 3+2) Brossura


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A. Pressley, King’s College, London, UK

Elementary Differential Geometry

Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout.

Features7 This revised and expanded edition features a new chapter on non-Euclidean geometry plus coverage of topics such as parallel transport, map colouring, and holonomy and Gaussian curvature 7 Around 200 new exercises are available online to further assist lecturers and students 7 Solu-tions to all the exercises are available to lecturers via www.springer.com

ContentsCurves in the Plane and in Space.- How Much Does a Curve Curve?- Global Properties of Curves.- Surfaces in Three Dimensions.- Examples of Surfaces.- The First Fundamental Form.- Curva-ture of Surfaces.- Gaussian, Mean and Principal Curvatures.- Geodesics.- Gauss’s Theorema Egre-gium.- Hyperbolic Geometry.- Minimal Surfaces.- The Gauss-Bonnet Theorem.- Appendix 0, Inner Product Spaces and Self-Adjoint Linear Maps.- Appendix 1, Isometries of Euclidean Spaces.- Appendix 2, Möbius transformations.- Hints to Selected Exercises.- Solutions.

Fields of interestDifferential Geometry

Target groupsUndergraduate students and lecturers

J. Rosales, P. García-Sánchez, University of Granada, Spain

Numerical Semigroups

This monograph is the first devoted exclusively to the development of the theory of numerical semigroups. In this concise, self-contained text, graduate students and researchers will benefit from this broad exposition of the topic.

Features7 First monograph devoted exclusively to the study of numerical semigroups 7 Presents various applications of numerical semigroups including number theory, coding theory, algebraic geometry, and others 7 Presents content ranging from the basics to open research problems 7 Accessible to any first year graduate student 7 Includes exercises that invite the reader to prove results published in recent mathematical journals

From the contents1. Notable Elements.- 2. Numerical Semigroups with Maximal Embedding Dimension.- 3. Irreduc-ible Numerical Semigropus.- 4. Proportionally Modular Numerical Semigroups.- 5. The Quotient of a Numerical Semigroup by a Positive Integer.- 6. Families of Numerical Semigroups Closed Under Finite Intersections and Adjoin of the Frobenius Number.- 7. Presentations of a Numer-ical Semigroup.- 8. The Gluing of Numerical Semigroups.- 9. Numerical Semigroups with Embedding Dimension Three.- 10. The Structure of a Numerical Semigroup.

Fields of interestGroup Theory and Generalizations; General Alge-braic Systems; Order, Lattices, Ordered Algebraic Structures

Target groupsFirst year graduate students, with only a basic knowledge of algebra required, giving the full background needed for readers not familiar with the topic; vesearchers will find the tools presented useful in producing examples and counterex-amples in other fields such as algebraic geometry, number theory, and linear programming

H. Rose, University of Bristol, UK

A Course on Finite Groups

Group Theory is a topic that has wide-ranging uses in the field of mathematics. Despite this, the only books still available on the market today are either too basic or too advanced for most European studying at the undergraduate level. This became apparent to Dr. Harvey Rose whilst he was lecturing at Bristol University, which led to the creation of this book, based upon Rose’s own lecture notes and years of expertise. Aimed primarily at being a textbook for universi-ties in the UK and mainland Europe, Rose’s book begins with the basic definitions and moves on to develop the theory, using examples to help students with their understanding. Dr. Rose offers a comprehensive account of the finite groups, this work being based upon his many years as a lecturer in the subject, although some of the early material within the book can be applied to both finite and infinite cases.

Features7 Combines physical book form with mate-rial on the internet so that students can use the physical book as a textbook and lecturers can use the website as a source of exercises, as well as providing more advanced students with a higher degree of material

ContentsThe Group Concept.- Elementary Group Proper-ties.- Group Construction and Representation.- Homomorphisms.- Action and the Orbit-Stabiliser Theorem.- p-Groups and Sylow Theory.- Products and Abelian Groups.- Groups of Order 24, Three Examples.- Series, Jordan Hölder Theorem and the Extension Problem.- Nilpotency.- Solubility.- Simple Groups of Order Less Than 10000.- Repre-sentation and Character Theory.- Character Tables and Theorems of Burnside and Frobenius.- Appen-dices.

Fields of interestGroup Theory and Generalizations

Target groups3rd/4th year undergraduate students


Mathematics

Available

2nd ed. 2010. Approx. 395 p. 179 illus. (Springer Undergraduate Mathematics Series) Softcover

7 € 39,95 | £29.997 * € (D) 42,75 | € (A) 43,95 | sFr 62,00ISBN 978-1-84882-890-2

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Mathematics

Due October 2009

2009. Approx. 190 p. 10 illus. (Developments in Mathematics, Volume 20) Hardcover

7 € 69,95 | £62.997 * € (D) 74,85 | € (A) 76,95 | sFr 109,00ISBN 978-1-4419-0159-0

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Mathematics

Due December 2009

2010. Approx. 290 p. 6 illus. (Universitext) Softcover

7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 77,50ISBN 978-1-84882-888-9

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V. Y. Rovenski, University of Haifa, Israel

Modeling of Curves and Surfaces Using Matlab

This concise text on geometry with applications in a variety of disciplines is devoted to three main geometrical topics: curves, surfaces, and polyhedra. It presents elementary methods for analytical modeling and their visualization, as well as demonstrating the potential of symbolic computational tools to support the development of analytical solutions. The author systematically examines powerful tools including 2D and 3D animation of geometric images, transformations, shadows and colors, and then further studies more complex geometrical modeling problems related to analysis and differ-ential equations. With over 150 stimulating exer-cises and problems, this text integrates traditional differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format. The book is also well-illus-trated, with over 300 figures reproducible using Matlab programs.

Features7 Covers basic Matlab as well as complex geometrical modeling problems related to analysis and differential equations 7 Integrates traditional differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format 7 Provides over 150 stimu-lating exercises and problems and over 300 figures reproducible using Matlab programs 7 System-atic and rigorous presentation

Fields of interestGeometry; Differential Geometry; Computer Graphics

Target groupsUndergraduates in a variety of disciplines, graduate students, engineers, computer scientists, and instructors of applied mathematics

P. Sachdev, Indian Institute of Science, India; C. S. Rao, Indian Institute of Science Madras, Indian

Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations

This book discusses nonlinear partial differential equations which, in exceptional circumstances, possess certain symmetries: they are invariant to a class of finite or infinitesimal transformations. The goals of this text are to prove the existence or otherwise solution of reduced nonlinear ODE’s by different analytic methods, and to show that these solutions form intermediate asymptotics of a class of initial/boundary conditions arising from physical considerations. The book covers both theory and computations. The asymptotic methods include self-similarity, balancing argument, and matched asymptotic expansions. The physical models discussed relate to porous media equation, heat equation with absorption, generalized Fisher’s equation, Burgers equation and its generalizations. A chapter is devoted to nonlinear diffusion and fluid mechanics. The book will be useful applied mathematicians, physicists, engineers and biologists, and would considerably help understand diverse natural phenomena.

ContentsIntroduction.- Large Time Asymptotics for Solu-tions of Nonlinear First-Order Partial Differential Equations.- Large Time Asymptotic Analysis of Some Nonlinear Parabolic Equations – Some Constructive Approaches.- Self-Similar Solutions as Large Time Asymptotics for Some Nonlinear Parabolic Equations.- Asymptotics in Fluid Mechanics.- Index.

Fields of interestPartial Differential Equations; Mathematical Methods in Physics; Mechanics, Fluids, Thermo-dynamics

Target groupsStudents at the postgraduate level, researchers, applied mathematicians, physicists, and engineers

O. Scherzer, University of Innsbruck, Austria (Ed.)

Handbook of Mathematical Methods in Imaging

The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions.

Features7 Comprehensive and rigorous treatment of mathematical methods in imaging 7 Entries in hyperlinked PDF and html format

Fields of interestApplications of Mathematics; Image Processing; Signal Processing

Target groupsStudents, scientists and researchers in academia and industry, commercial companies, institutes, libraries


Mathematics

Due December 2009

2010. Approx. 305 p. 300 illus. (Springer Undergraduate Texts in Mathematics and Technology ) Hardcover


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Mathematics

Due October 2009

2009. Approx. 250 p. (Springer Monographs in Mathematics) Hardcover

7 € 89,95 | £81.007 * € (D) 96,25 | € (A) 98,95 | sFr 140,00ISBN 978-0-387-87808-9

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Type of publicationHandbook

Mathematics

Due January 2011

2011. XX, 1100 p. 150 illus. (In 2 volumes, not available seperately) Hardcover

7 € 499,00 | £449.007 * € (D) 533,93 | € (A) 548,90 | sFr 774,50ISBN 978-0-387-92919-4

9<HTLDTH=jcjbje>2011. eReference.

7 € 499,00 | £449.007 ** € (D) 593,81 | € (A) 598,80 | sFr 814,00ISBN 978-0-387-92920-0

9<HTLDTH=jcjcaa>2011. XX, 1100 p. 150 illus. Print + eReference. (In 2 volumes, not available seperately)

7 € 624,00 | £561.507 * € (D) 667,68 | € (A) 686,40 | sFr 968,50ISBN 978-0-387-92921-7

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I. K. Shingareva, C. Lizárraga-Celaya, University of Sonora, Hermosillo, Mexico

Maple and MathematicaA Problem Solving Approach for Mathematics

This book compares the two computer algebra programs, Maple and Mathematica used by students, mathematicians, scientists, and engi-neers. Structured by presenting both systems in parallel, Mathematica’s users can learn Maple quickly by finding the Maple equivalent to Mathematica func-tions, and vice versa. This student reference handbook consists of core material for incorporating Maple and Mathematica as a working tool into different undergraduate mathematical courses (algebra, geometry, calculus, complex functions, special functions, integral transforms, mathematical equations). Part I describes the foundations of Maple and Mathematica (with equivalent problems and solu-tions). Part II describes Mathematics with Maple and Mathematica by using equivalent problems.

Features7 Side by side comparisons of practical solutions of the two computer algebra programs, Maple and Mathematica 7 First book to give a handy reference for these popular systems

ContentsFrom the contents Preface.- Foundations of Maple and Mathematica: Maple; Mathematica.- Mathematics: Maple and Mathematica: Graphics; Algebra; Geometry; Calculus; Complex Functions; Special Functions; Integral and Discrete Transforms; Mathematical Equations: References.- General Index.- Maple Index.- Mathematica Index.

Fields of interestMathematical Software; Math Applications in Computer Science; Numerical and Computational Methods in Engineering

Target groupsStudents, mathematicians, scientists, engineers

J. Stalker, School of Mathematics, Trinity College, Dublin, Ireland

Complex AnalysisFundamentals of the Classical Theory of Functions

This clear, concise introduction to the classical theory of one complex variable is based on the premise that “anything worth doing is worth doing with interesting examples.” The content is driven by techniques and examples rather than definitions and theorems. This self-contained monograph is an excellent resource for a self-study guide and should appeal to a broad audience. The only prerequisite is a standard calculus course.

From the reviews7 The first chapter deals with a beautiful presenta-tion of special functions. . . . The third chapter covers elliptic and modular functions. . . in much more detail, and from a different point of view, than one can find in standard introductory books. . . . For [the] subjects that are omitted, the author has suggested some excellent references for the reader who wants to go through these topics. The book is read easily and with great interest. It can be recommended to both students as a textbook and to mathematicians and physicists as a useful reference 7 Mathematical Reviews

Features7 An affordable softcover edition of a classic text 7 May be used as a textbook or as a self-study guide 7 Includes beautiful illustrations, a rich set of examples of key concepts, numerous exercises 7 Excellent bibliography and index

Fields of interestFunctions of a Complex Variable; Several Complex Variables and Analytic Spaces

Target groupsStudents: a textbook; and mathematicians and physicists: a reference

N. Woodhouse, University of Oxford, UK

Introduction to Analytical DynamicsRevised Edition

This is a revised edition of a text on classical mechanics which was originally published 20 years ago by Oxford University Press. The presentation has been simplified, while keeping to the original intention of confronting rather than evading the various notational and pedagogical difficulties that one encounters in the journey from Newton to Lagrange and Hamilton. Feedback has been incor-porated into this new and revised edition to make it a fresher, and more compelling read with greatly improved content and style. For example, the material and examples on systems have been gathered with one degree of freedom into a separate chapter. The intention of which is to give an initial introduction to the core ideas of the Lagrangian theory in a context in which they make strong contact with familiar elementary techniques from the treatment of ordinary differential equa-tions, without the distraction of indices and the summation convention. A chapter has also been added on differential geometric methods.

ContentsFrames of Reference.- One Degree of Freedom.- Lagrangian Mechanics.- Noether’s Theorem.- Rigid Bodies.- Oscillations.- Hamiltonian mechanics.- Geometry of Classical Mechanics.- Epilogue: Rela-tivity and Quantum Theory.- Notes on Exercises.

Fields of interestApplications of Mathematics; Mechanics; Theoretical and Applied Mechanics

Target groupsResearchers and professionals


Mathematics

Due August 2009

2nd ed. 2009. XVIII, 483 p. With CD-ROM. Softcover

7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 77,50ISBN 978-3-211-99431-3

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Mathematics

Due October 2009

Originally published as a monograph

1st ed. 1998. 2nd printing 2009. Approx. 245 p. 5 illus. (Modern Birkhäuser Classics) Softcover

7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 77,50ISBN 978-0-8176-4918-0

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Mathematics

Due November 2009

Originally published by Oxford University Press

2nd ed. 2010. Approx. 260 p. 42 illus. (Springer Undergraduate Mathematics Series) Softcover

7 € 39,95 | £29.997 * € (D) 42,75 | € (A) 43,95 | sFr 62,00ISBN 978-1-84882-815-5

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m. aigner m. e. alonso e. arrondo v. vinnikov g. m

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