ABCD Yellow Sale 2011

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Yellow Sale 2011

March 01 - July 31 springer.com Abstract Harmonic Analysis 2

Abstract Harmonic Analysis

A. Deitmar S.G. Krantz A First Course in Harmonic Explorations in Harmonic Analysis C. Cabrelli, J.L. Torrea Analysis With Applications to Complex Function Theory From the reviews of the first edition: "This lovely book and the Heisenberg Group Recent Developments in Real and is intended as a primer in harmonic analysis at the This self-contained text provides an introduction to undergraduate level. All the central concepts of har- modern harmonic analysis in the context in which Harmonic Analysis monic analysis are introduced using Riemann integral In Honor of Carlos Segovia it is actually applied, in particular, through complex and metric spaces only. The exercises at the end of function theory and partial differential equations. It A collection of invited chapters dedicated to Carlos each chapter are interesting and challenging..." Sanjiv takes the novice mathematical reader from the rudi- Segovia, this unified and self-contained volume exam- Kumar Gupta for MathSciNet "... In this well-written ments of harmonic analysis (Fourier series) to the ines recent developments in real and harmonic analy- textbook the central concepts of Harmonic Analysis Fourier transform, pseudodifferential operators, and sis. The work begins with a chronological description are explained in an enjoyable way, while using very finally to Heisenberg analysis. Within the textbook, of Segovia’s mathematical life, his original ideas and little technical background. Quite surprisingly this the new ideas on the Heisenberg group are applied their evolution, which may be a source of inspira- approach works. It is not an exaggeration that each to the study of estimates for both the Szegö and Pois- tion for many mathematicians working in the fields undergraduate student interested in and each profes- son–Szegö integrals on the unit ball in complex space. of harmonic analysis, functional analysis, and par- sor teaching Harmonic Analysis will benefit from the Thus the main theme of the book is also tied into tial differential equations. Apart from this contribu- streamlined and direct approach of this book." Ferenc complex analysis of several variables. With a rigor- tion, two different types of chapters are featured in the Móricz for Acta Scientiarum Mathematicarum This ous but well-paced exposition, this text provides all work: surveys dealing with Carlos’ favorite topics, and book is a primer in harmonic analysis using an ele- the necessary background in singular and fractional PDE works written by students and colleagues close mentary approach. Its first aim is to provide an intro- integrals, as well as Hardy spaces and the function to Segovia whose careers were in some way influenced duction to Fourier analysis, leading up to the Poisson theory of several complex variables, needed to under- by him. Specific topics covered include: * Vector-val- Summation Formula. Secondly, it makes the reader stand Heisenberg analysis. Explorations in Harmonic ued singular integral equations * Harmonic analysis aware of the fact that both, the Fourier series and the Analysis is ideal for graduate students in mathemat- related to Hermite expansions * Gas flow in porous Fourier transform, are special cases of a more gen- ics, physics, and engineering. Prerequisites include a media * Global well-posedness of the KPI Equation eral theory arising in the context of locally compact fundamental background in real and complex analysis * Monge–Ampère type equations and applications * abelian groups. The third goal of this book is to intro- and some exposure to functional analysis. Spaces of homogeneous type * Hardy and Lipschitz duce the reader to the techniques used in harmonic More on www.springer.com/978-0-8176-4668-4 spaces * One-sided operators This book will be use- analysis of noncommutative groups. There are two ful to graduate students as well as pure and applied new chapters in this new edition. One on distribu- Available mathematicians interested in new mathematical tions will complete the set of real variable methods developments in areas related to real and harmonic introduced in the first part. The other on the Heisen- 2009. XIV, 360 p. 26 illus. (Applied and Numerical analysis. Contributors: H. Aimar, A. Bonami, O. berg Group provides an example of a group that is Harmonic Analysis, ) Blasco, L.A. Caffarelli, S. Chanillo, J. Feuto, L. Forzani, neither compact nor abelian, yet is simple enough to 978-0-8176-4668-4 C.E. Gutíerrez, E. Harboure, A.L. Karakhanyan, C.E. easily deduce the Plancherel Theorem. Professor Deit- Kenig, R.A. Macías, J.J. Manfredi, F.J. Martín-Reyes, mar is Professor of Mathematics at the University of P. Ortega, R. Scotto, A. de la Torre, J.L. Torrea T"ubingen, Germany. He is a former Heisenberg fellow and has taught in the U.K. for some years. In his More on www.springer.com/978-0-8176-4531-1 leisure time he enjoys hiking in the mountains and Available practicing Aikido. 2009. XXII, 196 p. 13 illus. (Applied and Numerical Harmonic More on www.springer.com/978-0-387-22837-2 Analysis, ) 978-0-8176-4531-1 Available

2005. XII, 204 p. (Universitext, ) 978-0-387-22837-2 springer.com Algebra 3

Algebra is Professor of Mathematics at Universität Osnabrück. Joseph Gubeladze is Professor of Mathematics at San Francisco State University. More on www.springer.com/978-0-387-76355-2 Available 2009. XIV, 461 p. 52 illus. (Springer Monographs in Mathematics, ) 978-0-387-76355-2

J. Elias, J.M. Giral, R.M. Miró-Roig, S. Zarzuela Six Lectures on Commutative M. Bronstein Algebra Symbolic Integration I Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent Transcendental Functions developments in this rapidly expanding field, the First edition received rave reviews The second edition Centre de Recerca Matematica in Bellaterra organized offers a new chapter on parallel integration Includes a ten-days Summer School on Commutative Algebra additional exercises in 1996. Lectures were presented by six high-level specialists, L. Avramov (Purdue), M.K. Green (UCLA), More on www.springer.com/978-3-540-21493-9 L.N. Childs C. Huneke (Purdue), P. Schenzel (Halle), G. Valla Available (Genova) and W.V. Vasconcelos (Rutgers), provid- 2005. XVI, 325 p. (Algorithms and Computation in A Concrete Introduction to Higher ing a fresh and extensive account of the results, tech- Mathematics, 1) Algebra niques and problems of some of the most active areas 978-3-540-21493-9 of research. The present volume is a synthesis of the This book is an informal and readable introduction lectures given by these authors. Research workers as to higher algebra at the post-calculus level. The con- well as graduate students in commutative algebra and cepts of ring and field are introduced through study nearby areas will find a useful overview of the field of the familiar examples of the integers and polyno- and recent developments in it. Reviews "All six articles mials. A strong emphasis on congruence classes leads are at a very high level; they provide a thorough sur- in a natural way to finite groups and finite fields. The vey of results and methods in their subject areas, illus- new examples and theory are built in a well-motivated trated with algebraic or geometric examples." - Acta fashion and made relevant by many applications - to Scientiarum Mathematicarum Avramov lecture: "... cryptography, error correction, integration, and espe- it contains all the major results [on infinite free res- cially to elementary and computational number the- olutions], it explains carefully all the different tech- ory. The later chapters include expositions of Rabin's niques that apply, it provides complete proofs (…). probabilistic primality test, quadratic reciprocity, the This will be extremely helpful for the novice as well classification of finite fields, and factoring polyno- as the experienced." - Mathematical reviews Huneke mials over the integers. Over 1000 exercises, ranging lecture: "The topic is tight closure, a theory developed from routine examples to extensions of theory, are by M. Hochster and the author which has in a short W. Bruns, J. Gubeladze found throughout the book; hints and answers for time proved to be a useful and powerful tool. (…) many of them are included in an appendix. The new The paper is extremely well organized, written, and Polytopes, Rings, and K-Theory edition includes topics such as Luhn's formula, Karat- motivated." - Zentralblatt MATH Schenzel lecture: suba multiplication, quotient groups and homomor- "… this paper is an excellent introduction to appli- This book treats the interaction between discrete con- phisms, Blum-Blum-Shub pseudorandom numbers, cations of local cohomology." - Zentralblatt MATH vex geometry, commutative ring theory, algebraic root bounds for polynomials, Montgomery multipli- Valla lecture: "… since he is an acknowledged expert K-theory, and algebraic geometry. The basic mathe- cation, and more. "At every stage, a wide variety of on Hilbert functions and since his interest has been so matical objects are lattice polytopes, rational cones, applications is presented...The user-friendly expo- broad, he has done a superb job in giving the readers affine monoids, the algebras derived from them, and sition is appropriate for the intended audience" - a lively picture of the theory." - Mathematical reviews toric varieties. The book discusses several proper- T.W. Hungerford, Mathematical Reviews "The style Vasconcelos lecture: "This is a very useful survey on ties and invariants of these objects, such as efficient is leisurely and informal, a guided tour through the invariants of modules over noetherian rings, relations generation, unimodular triangulations and covers, foothills, the guide unable to resist numerous side between them, and how to compute them." - Zentral- basic theory of monoid rings, isomorphism problems paths and return visits to favorite spots..." - Michael blatt MATH and automorphism groups, homological properties Rosen, American Mathematical Monthly and enumerative combinatorics. The last part is an More on www.springer.com/978-3-0346-0328-7 More on www.springer.com/978-0-387-74527-5 extensive treatment of the K-theory of monoid rings, Available Available with extensions to toric varieties and their intersec- 1998. 412 p. (Modern Birkhäuser Classics, ) tion theory. This monograph has been written with a 978-3-0346-0328-7 view towards graduate students and researchers who 2009. XIV, 603 p. (Undergraduate Texts in want to study the cross-connections of algebra and Mathematics, ) discrete convex geometry. While the text has been 978-0-387-74527-5 written from an algebraist's view point, also specialists in lattice polytopes and related objects will find an up-to-date discussion of affine monoids and their combinatorial structure. Though the authors do not explicitly formulate algorithms, the book takes a constructive approach wherever possible. Winfried Bruns 4 Algebra springer.com

also for self-study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition. More on www.springer.com/978-0-387-95183-6 Available

2001. XIX, 385 p. (Graduate Texts in Mathematics, 131) 978-0-387-95183-6

J.C. Jantzen, J. Schwermer S. Lang Algebra SL2 (R) Ausgehend von einer grundlegenden Einführung in SL2(R) gives the student an introduction to the infi- Begriffe und Methoden der Algebra werden im Buch nite dimensional representation theory of semisim- die wesentlichen Ergebnisse dargestellt und ein Ein- ple Lie groups by concentrating on one example - blick in viele Entwicklungen innerhalb der Algebra SL2(R). This field is of interest not only for its own gegeben, die mit anderen Gebieten der Mathematik sake, but for its connections with other areas such as stark verflochten sind. Beginnend mit Begriffsbildun- number theory, as brought out, for example, in the gen wie Gruppe und Ring führt das Buch hin zu den work of Langlands. The rapid development of repre- Körpererweiterungen und der Galoistheorie. Danach sentation theory over the past 40 years has made it werden zentrale Teile der Theorie der Moduln, Alge- increasingly difficult for a student to enter the field. bren und Ringe behandelt. Die Theorie der Divi- T. Lam This book makes the theory accessible to a wide audi- sionsalgebren und ihre Klassifikation mit Hilfe der ence, its only prerequisites being a knowledge of real Brauergruppe werden entwickelt. Es schließt sich eine A First Course in Noncommutative analysis, and some differential equations. Einführung in die zentralen Begriffe der algebraischen Zahlentheorie an. In zahlreichen Supplementen Rings More on www.springer.com/978-0-387-96198-9 Available findet man Ausblicke auf weiterführende Themen. This book, an outgrowth of the author¿s lectures at Betrachtet werden zum Beispiel allgemeine lineare the University of California at Berkeley, is intended 1985. 33 illus. (Graduate Texts in Mathematics, 105) Gruppen, Schiefpolynomringe, Erweiterungen von as a textbook for a one-semester course in basic ring 978-0-387-96198-9 Moduln, projektive Moduln und Frobenius-Algebren. theory. The material covered includes the Wedder- More on www.springer.com/978-3-540-21380-2 burn-Artin theory of semisimple rings, Jacobson¿s Available theory of the radical, representation theory of groups and algebras, prime and semiprime rings, local and 2006. IV, 396 S. (Springer-Lehrbuch, ) semilocal rings, perfect and semiperfect rings, etc. By 978-3-540-21380-2 aiming the level of writing at the novice rather than the connoisseur and by stressing the role of examples and motivation, the author has produced a text that is suitable not only for use in a graduate course, but also for self-study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition. More on www.springer.com/978-0-387-95325-0 Available S. Lang 2001. XIX, 385 p. (Graduate Texts in Mathematics, 131) Undergraduate Algebra 978-0-387-95325-0 Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on T. Lam the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite A First Course in Noncommutative fields, Galois Theory, and other topics. The author has also included a chapter on groups of matrices which Rings is unique in a book at this level. Throughout the book, This book, an outgrowth of the author¿s lectures at the author strikes a balance between abstraction and the University of California at Berkeley, is intended concrete results, which enhance each other. Illustra- as a textbook for a one-semester course in basic ring tive examples accompany the general theory. Numer- theory. The material covered includes the Wedder- ous exercises range from the computational to the burn-Artin theory of semisimple rings, Jacobson¿s theoretical, complementing results from the main theory of the radical, representation theory of groups text. For the third edition, the author has included and algebras, prime and semiprime rings, local and new material on product structure for matrices (e.g. semilocal rings, perfect and semiperfect rings, etc. By the Iwasawa and polar decompositions), as well as a aiming the level of writing at the novice rather than description of the conjugation representation of the the connoisseur and by stressing the role of examples diagonal group. He has also added material on poly- and motivation, the author has produced a text that nomials, culminating in Noah Snyder’s proof of the is suitable not only for use in a graduate course, but Mason-Stothers polynomial abc theorem. About the springer.com Algebra 5

First Edition: The exposition is down-to-earth and at ing topics are treated: ideal theory in rings of algebraic the same time very smooth. The book can be covered integers, p-adic fields and their finite extensions, ide- easily in a one-year course and can be also used in a les and adeles, zeta-functions, distribution of prime one-term course...the flavor of modern mathematics ideals, Abelian fields, the class-number of quadratic is sprinkled here and there. - Hideyuki Matsumura, fields, and factorization problems. Each chapter ends Zentralblatt with exercises and a short review of the relevant literature up to 2003. The bibliography has over 3400 More on www.springer.com/978-0-387-22025-3 items. Available More on www.springer.com/978-3-540-21902-6 2005. XI, 385 p. 1 illus. (Undergraduate Texts in Available Mathematics, ) 2004. XI, 708 p. (Springer Monographs in Mathematics, ) 978-0-387-22025-3 F. Lorenz 978-3-540-21902-6 Algebra Volume II: Fields with Structure, Algebras and Advanced Topics The present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The author leads the reader through interesting subject matter, while assuming only the background provided by a first course in linear algebra. The first volume focuses on field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions and algebraic J. Lepowsky, H. Li geometry. The main focus of the second volume is on V.V. Prasolov additional structure of fields and related topics. Much Introduction to Vertex material not usually covered in textbooks appears Polynomials Operator Algebras and Their here, including real fields and quadratic forms, the This comprehensive book covers both long-stand- Tsen rank of a field, the calculus of Witt vectors, the ing results in the theory of polynomials and recent Representations Schur group of a field, and local class field theory. developments which have until now only been avail- The deep and relatively new field of vertex operator Both volumes contain numerous exercises and can be able in the research literature. After initial chapters algebras is intimately related to a variety of areas in used as a textbook for advanced undergraduate stu- on the location and separation of roots and on irre- mathematics and physics: for example, the concepts dents. From Reviews of the German version: This is ducibility criteria, the book covers more specialized of "monstrous moonshine," infinite-dimensional Lie a charming textbook, introducing the reader to the polynomials, including those which are symmetric, theory, string theory, and conformal field theory. classical parts of algebra. The exposition is admirably integer-value or cyclotomic, and those of Chebyshev This book introduces the reader to the fundamen- clear and lucidly written with only minimal prereq- and Bernoulli. There follow chapters on Galois the- tal theory of vertex operator algebras and its basic uisites from linear algebra. The new concepts are, at ory and ideals in polynomial rings. Finally there is a techniques and examples. Beginning with a detailed least in the first part of the book, defined in the frame- detailed discussion of Hilbert’s 17th problem on the presentation of the theoretical foundations and pro- work of the development of carefully selected prob- representation of non-negative polynomials as sums ceeding to a range of applications, the text includes lems. - Stefan Porubsky, Mathematical Reviews of squares of rational functions and generalizations. a number of new, original results and also highlights More on www.springer.com/978-0-387-72487-4 From the reviews: "... Despite the appearance of this and brings fresh perspective to important works of Available book in a series titled Algorithms and Computation many researchers. After introducing the elementary of Mathematics, computation occupies only a small "formal calculus'' underlying the subject, the book 2008. X, 340 p. (Universitext, ) part of the monograph. It is best described as a use- provides an axiomatic development of vertex oper- 978-0-387-72487-4 ful reference for one's personal collection and a text ator algebras and their modules, expanding on the for a full-year course given to graduate or even senior early contributions of R. Borcherds, I. Frenkel, J. Lep- undergraduate students. [.....] the book under review owsky, A. Meurman, Y.-Z. Huang, C. Dong, Y. Zhu is worth purchasing for the library and possibly even and others. The concept of a "representation'' of a ver- for one's own collection. The author's interest in the tex (operator) algebra is treated in detail, following history and development of this area is evident, and and extending the work of H. Li; this approach is used we have pleasant glimpses of progress over the last to construct important families of vertex (operator) three centuries. He exercises nice judgment in selec- algebras and their modules. Requiring only a familiar- tion of arguments, with respect to both represen- ity with basic algebra, Introduction to Vertex Opera- tativeness of approaches and elegance, so that the tor Algebras and Their Representations will be useful reader gains a synopsis of and guide to the literature, for graduate students and researchers in mathemat- in which more detail can be found. ..." E. Barbeau, ics and physics. The book’s presentation of the core SIAM Review 47, No. 3, 2005 "... the volume is packed topics will equip readers to embark on many active with results and proofs that are well organised the- research directions related to vertex operator algebras, matically into chapters and sections. What is unusual group theory, representation theory, and string the- is to have a text that embraces and intermingles both ory. W. Narkiewicz analytic and algebraic aspects of the theory. Although the subject is about such basic objects, many tough More on www.springer.com/978-0-8176-3408-7 Elementary and Analytic Theory results of considerable generality are incorporated Available of Algebraic Numbers and it is striking that refinements, both in theorems and proofs continued throughout the latter part of 2004. XI, 318 p. (Progress in Mathematics, 227) This book gives an exposition of the classical part the Twentieth Century. [...] There is a plentiful of 978-0-8176-3408-7 of the theory of algebraic number theory, excluding problems, some of which might be challenging even class-field theory and its consequences. The follow- for polynomial people; solutions to selected prob- 6 Algebraic Geometry springer.com lems are also included." S.D.Cohen, MathSciNet, MR Algebraic Geometry 2082772, 2005 "Problems concerning polynomials have impulsed resp. accompanied the development of algebra from its very beginning until today and over the centuries a lot of mathematical gems have been brought to light. This book presents a few of them, some being classical, but partly probably unknown even to experts, some being quite recently discovered. […] Many historical comments and a clear style make the book very readable, so it can be recommended warmly to non-experts already at an undergraduate level and, because of its contents, to experts as well." G.Kowol, Monatshefte für Mathematik 146, Issue 4, J. Serre 2005 Galois Cohomology More on www.springer.com/978-3-642-03979-9 N. Baas, E. Friedlander, B. Jahren, P.A. Østvær Available This is an updated English translation of "Cohomolo- gie Galoisienne", published more than 30 years ago Algebraic Topology 2004. XIII, 301 p. 8 illus. (Algorithms and as one of the very first Lecture Notes in Mathematics The Abel Symposium 2007 Computation in Mathematics, 11) (LNM 5). It includes a reproduction of an influential 978-3-642-03979-9 paper of R. Steinberg, together with some new mate- The 2007 Abel Symposium took place at the Univer- rial and an expanded bibliography. sity of Oslo in August 2007. The goal of the symposium was to bring together mathematicians whose More on www.springer.com/978-3-540-42192-4 research efforts have led to recent advances in alge- Available braic geometry, algebraic K-theory, algebraic topol- 1997. X, 210 p. (Springer Monographs in Mathematics, ) ogy, and mathematical physics. A common theme 978-3-540-42192-4 of this symposium was the development of new perspectives and new constructions with a categorical flavor. As the lectures at the symposium and the papers of this volume demonstrate, these perspectives and constructions have enabled a broadening of vistas, a synergy between once-differentiated subjects, and solutions to mathematical problems both old and new. More on www.springer.com/978-3-642-01199-3 S. Roman Available 2009. XIV, 409 p. (Abel Symposia, 4) Field Theory 978-3-642-01199-3 Intended for graduate courses or for independent study, this book presents the basic theory of fields. H. Stichtenoth The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, Algebraic Function Fields and field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book Codes treats the theory of binomials. The book concludes The theory of algebraic function fields has its origins with a chapter on families of binomials – the Kummer in number theory, complex analysis (compact Rie- theory. This new edition has been completely rewrit- mann surfaces), and algebraic geometry. Since about ten in order to improve the pedagogy and to make the 1980, function fields have found surprising applica- text more accessible to graduate students. The exer- tions in other branches of mathematics such as cod- cises have also been improved and a new chapter on ing theory, cryptography, sphere packings and others. ordered fields has been included. About the first edi- The main objective of this book is to provide a purely tion: " ...the author has gotten across many impor- algebraic, self-contained and in-depth exposition of tant ideas and results. This book should not only work the theory of function fields. This new edition, pub- well as a textbook for a beginning graduate course C. Bartocci, U. Bruzzo, D. Hernández Ruipérez lished in the series Graduate Texts in Mathemat- in field theory, but also for a student who wishes to ics, has been considerably expanded. Moreover, the take a field theory course as independent study." -J.N. Fourier-Mukai and Nahm present edition contains numerous exercises. Some of Mordeson, Zentralblatt "The book is written in a clear them are fairly easy and help the reader to understand Transforms in Geometry and and explanatory style. It contains over 235 exercises the basic material. Other exercises are more advanced which provide a challenge to the reader. The book is Mathematical Physics and cover additional material which could not be recommended for a graduate course in field theory as included in the text. This volume is mainly addressed Integral transforms, such as the Laplace and Fourier well as for independent study." - T. Albu, MathSciNet to graduate students in mathematics and theoretical transforms, have been major tools in mathematics More on www.springer.com/978-0-387-27677-9 computer science, cryptography, coding theory and for at least two centuries. In the last three decades the Available electrical engineering. development of a number of novel ideas in algebraic geometry, category theory, gauge theory, and string More on www.springer.com/978-3-540-76877-7 2006. XII, 335 p. 18 illus. (Graduate Texts in theory has been closely related to generalizations of Available Mathematics, 158) integral transforms of a more geometric character. 978-0-387-27677-9 Fourier–Mukai and Nahm Transforms in Geometry 2008. XIII, 355 p. 14 illus. (Graduate Texts in and Mathematical Physics examines the algebro-geo- Mathematics, 254) metric approach (Fourier–Mukai functors) as well as 978-3-540-76877-7 the differential-geometric constructions (Nahm). Also springer.com Algebraic Geometry 7 included is a considerable amount of material from an ideal. There is a close relationship between ideals existing literature which has not been systematically and varieties which reveals the intimate link between organized into a monograph. Key features: * Basic algebra and geometry. Written at a level appropri- constructions and definitions are presented in prelim- ate to undergraduates, this book covers such topics inary background chapters * Presentation explores as the Hilbert Basis Theorem, the Nullstellensatz, applications and suggests several open questions invariant theory, projective geometry, and dimension * Extensive bibliography and index This self-con- theory. The algorithms to answer questions such as tained monograph provides an introduction to cur- those posed above are an important part of algebraic rent research in geometry and mathematical physics geometry. Although the algorithmic roots of alge- and is intended for graduate students and researchers braic geometry are old, it is only in the last forty years just entering this field. that computational methods have regained their earlier prominence. New algorithms, coupled with the More on www.springer.com/978-0-8176-3246-5 R. Bix power of fast computers, have led to both theoretical Available advances and interesting applications, for example in 2009. XVI, 418 p. 83 illus. (Progress in Mathematics, 276) Conics and Cubics robotics and in geometric theorem proving. In addi- 978-0-8176-3246-5 A Concrete Introduction to Algebraic Curves tion to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity Conics and Cubics is an accessible introduction to and correctness, this third edition of Ideals, Varieties algebraic curves. Its focus on curves of degree at most and Algorithms includes: A significantly updated sec- three keeps results tangible and proofs transparent. tion on Maple in Appendix C; Updated information Theorems follow naturally from high school algebra on AXIOM, CoCoA, Macaulay 2, Magma, Mathemat- and two key ideas, homogeneous coordinates and ica and SINGULAR; A shorter proof of the Extension intersection multiplicities. By classifying irreducible Theorem presented in Section 6 of Chapter 3.From cubics over the real numbers and proving that their the 2nd Edition: "I consider the book to be wonder- points form Abelian groups, the book gives readers ful. ... The exposition is very clear, there are many easy access to the study of elliptic curves. It includes helpful pictures, and there are a great many instruc- a simple proof of Bezout’s Theorem on the number tive exercises, some quite challenging ... offers the of intersections of two curves. The book is a text for heart and soul of modern commutative and algebraic a one-semester course. The course can serve either geometry." -The American Mathematical Monthly as the one undergraduate geometry course taken by More on www.springer.com/978-0-387-35650-1 S. Basu, R. Pollack, M. Coste-Roy mathematics majors in general or as a sequel to college geometry for prospective or current teachers of Available Algorithms in Real Algebraic secondary school mathematics. The only prerequisite is first-year calculus. The new edition additionally dis- 2007. XVI, 560 p. 93 illus. (Undergraduate Texts in Geometry cusses the use of power series to parametrize curves Mathematics, ) 978-0-387-35650-1 This is the first graduate textbook on the algorith- and analyze intersection multiplicities and envelopes. mic aspects of real algebraic geometry. The main More on www.springer.com/978-0-387-31802-8 ideas and techniques presented form a coherent and Available rich body of knowledge. Mathematicians will find relevant information about the algorithmic aspects. 2006. VIII, 352 p. 151 illus. (Undergraduate Texts in Researchers in computer science and engineering Mathematics, ) will find the required mathematical background. 978-0-387-31802-8 Being self-contained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. This second edition contains several recent results on discriminants of symmetric matrices and other relevant topics. More on www.springer.com/978-3-540-33098-1 Available O. Debarre 2006. X, 662 p. 40 illus. (Algorithms and Computation in Mathematics, 10) 978-3-540-33098-1 Higher-Dimensional Algebraic Geometry Higher-dimensional algebraic geometry studies the classification theory of algebraic varieties. This very D.A. Cox, J. Little, D. O'Shea active area of research is still developing, but an amazing quantity of knowledge has accumulated over the Ideals, Varieties, and Algorithms past twenty years. The author¿s goal is to provide An Introduction to Computational Algebraic an easily accessible introduction to the subject. The Geometry and Commutative Algebra book covers preparatory and standard definitions and Algebraic Geometry is the study of systems of poly- results, moves on to discuss various aspects of the nomial equations in one or more variables, asking geometry of smooth projective varieties with many such questions as: Does the system have finitely many rational curves, and finishes in taking the first steps solutions, and if so how can one find them? And if towards Mori¿s minimal model program of classifi- there are infinitely many solutions, how can they be cation of algebraic varieties by proving the cone and described and manipulated? The solutions of a sys- contraction theorems. The book is well organized tem of polynomial equations form a geometric object and the author has kept the number of concepts that called a variety; the corresponding algebraic object is are used but not proved to a minimum to provide a 8 Algebraic Geometry springer.com mostly self-contained introduction to graduate students and researchers. More on www.springer.com/978-0-387-95227-7 Available

2001. XIII, 233 p. 16 illus. (Universitext, ) 978-0-387-95227-7

J. Fresnel, M. van der Put D. Goldschmidt Rigid Analytic Geometry and Its Algebraic Functions and Applications Projective Curves The theory of rigid (analytic) spaces, originally This book provides a self-contained exposition of invented to describe degenerations, reductions, and the theory of algebraic curves without requiring any moduli of algebraic curves and abelian varieties, has of the prerequisites of modern algebraic geometry. undergone significant growth in the last two decades; The self-contained treatment makes this important today the theory has applications to arithmetic alge- and mathematically central subject accessible to non- A. Dimca braic geometry, number theory, the arithmetic of specialists. At the same time, specialists in the field function fields, and p-adic differential equations. This may be interested to discover several unusual top- Sheaves in Topology work, a revised and greatly expanded new English edi- ics. Among these are Tate's theory of residues, higher Constructible and perverse sheaves are the algebraic tion of the earlier French text by the same authors, derivatives and Weierstrass points in characteristic counterpart of the decomposition of a singular space is an accessible introduction to the theory of rigid p, the Stöhr--Voloch proof of the Riemann hypothe- into smooth manifolds, a great geometrical idea due spaces and now includes a large number of exercises. sis, and a treatment of inseparable residue field exten- to R. Thom and H. Whitney. These sheaves, general- Key topics: * Chapters on the applications of this the- sions. Although the exposition is based on the theory izing the local systems that are so ubiquitous in math- ory to curves and abelian varieties: the Tate curve, of function fields in one variable, the book is unusual ematics, have powerful applications to the topology stable reduction for curves, Mumford curves, Néron in that it also covers projective curves, including sin- of such singular spaces (mainly algebraic and analytic models, uniformization of abelian varieties * Uni- gularities and a section on plane curves. David Gold- complex varieties). This introduction to the subject fied treatment of the concepts: points of a rigid space, schmidt has served as the Director of the Center for can be regarded as a textbook on modern algebraic overconvergent sheaves, Monsky--Washnitzer coho- Communications Research since 1991. Prior to that topology, treating the cohomology of spaces with mology and rigid cohomology; detailed examination he was Professor of Mathematics at the University of sheaf (as opposed to constant)coefficients. The first of Kedlaya’s application of the Monsky--Washnitzer California, Berkeley. cohomology to counting points on a hyperelliptic 5 chapters introduce derived categories, direct and More on www.springer.com/978-0-387-95432-5 inverse images of sheaf complexes, Verdier duality, curve over a finite field * The work of Drinfeld on Available constructible and perverse sheaves, vanishing and "elliptic modules" and the Langlands conjectures for characteristic cycles. They also discuss relations to D- function fields use a background of rigid étale coho- 2003. XVI, 179 p. (Graduate Texts in Mathematics, modules and intersection cohomology. Later chapters mology; detailed treatment of this topic * Presenta- 215) apply this powerful tool to the study of the topology tion of the rigid analytic part of Raynaud’s proof of 978-0-387-95432-5 of singularities, polynomial functions and hyperplane the Abhyankar conjecture for the affine line, with only arrangements. Some fundamental results, for which the rudiments of that theory A basic knowledge of excellent sources exist, are not proved but just stated algebraic geometry is a sufficient prerequisite for this and illustrated by examples and corollaries. In this text. Advanced graduate students and researchers in way, the reader is guided rather quickly from the basic algebraic geometry, number theory, representation theory to current research questions, supported in this theory, and other areas of mathematics will benefit by examples and exercises. from the book’s breadth and clarity. More on www.springer.com/978-3-540-20665-1 More on www.springer.com/978-0-8176-4206-8 Available Available

2004. XVI, 236 p. (Universitext, ) 2003. XII, 300 p. 10 illus. (Progress in Mathematics, 978-3-540-20665-1 218) 978-0-8176-4206-8

M. Hindry, J.H. Silverman Diophantine Geometry An Introduction This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional springer.com Algebraic Geometry 9 mathematicians. In each part of the book, the reader product. Emphasis is given throughout the exposi- bert varieties in certain special flag varieties - the ordi- will find numerous exercises. tion to examples, heuristic discussions, and simple nary, orthogonal, and symplectic Grassmannians - on applications of the basic tools to best convey the intu- the other. Historically, this connection was the prime More on www.springer.com/978-0-387-98981-5 ition behind the subject. The book demystifies these motivation for the development of standard mono- Available new quantum techniques by showing how they fit into mial theory. Determinantal varieties and basic con- classical algebraic geometry. Some familiarity with cepts of geometric invariant theory arise naturally 2000. XIII, 558 p. 8 illus. (Graduate Texts in basic algebraic geometry and elementary intersection in establishing the connection. The book also treats, Mathematics, 201) theory is assumed. Each chapter concludes with some in the last chapter, some other applications of stan- 978-0-387-98981-5 historical comments and an outline of key topics and dard monomial theory, e.g., to the study of certain themes as a guide for further study, followed by a col- naturally occurring affine algebraic varieties that, like lection of exercises that complement the material cov- determinantal varieties, can be realized as open parts ered and reinforce computational skills. As such, the of Schubert varieties. book is ideal for self-study, as a text for a mini-course More on www.springer.com/978-3-540-76756-5 in quantum cohomology, or as a special topics text in a standard course in intersection theory. The book Available will prove equally useful to graduate students in the 2008. XIV, 266 p. (Encyclopaedia of Mathematical Sciences, classroom setting as to researchers in geometry and 137) physics who wish to learn about the subject. 978-3-540-76756-5 More on www.springer.com/978-0-8176-4456-7 Available

2007. XII, 159 p. (Progress in Mathematics, 249) D. Huybrechts 978-0-8176-4456-7 Complex Geometry An Introduction J. Kollar Easily accessible Includes recent developments Rational Curves on Algebraic Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on Varieties topics related to mirror symmetry (SUSY, Kaehler- The aim of this book is to provide an introduction to Einstein metrics, Tian-Todorov lemma) the structure theory of higher dimensional algebraic M. Levine, F. Morel More on www.springer.com/978-3-540-21290-4 varieties by studying the geometry of curves, espe- Available cially rational curves, on varieties. The main applica- Algebraic Cobordism tions are in the study of Fano varieties and of related Following Quillen's approach to complex cobordism, 2005. XII, 309 p. (Universitext, ) varieties with lots of rational curves on them. This 978-3-540-21290-4 Ergebnisse volume provides the first systematic intro- the authors introduce the notion of oriented coho- duction to this field of study. The book contains a mology theory on the category of smooth varieties large number of examples and exercises which serve over a fixed field. They prove the existence of a uni- to illustrate the range of the methods and also lead to versal such theory (in characteristic 0) called Alge- many open questions of current research. braic Cobordism. Surprisingly, this theory satisfies the analogues of Quillen's theorems: the cobordism of the More on www.springer.com/978-3-540-60168-5 base field is the Lazard ring and the cobordism of a Available smooth variety is generated over the Lazard ring by 1996. VIII, 321 p. (Ergebnisse der Mathematik und ihrer the elements of positive degrees. This implies in par- Grenzgebiete. 3. Folge A Series of Modern Surveys in ticular the generalized degree formula conjectured by Mathematics, 32) Rost. The book also contains some examples of com- 978-3-540-60168-5 putations and applications. More on www.springer.com/978-3-540-36822-9 Available V. Lakshmibai, K.N. Raghavan 2007. XII, 246 p. (Springer Monographs in Mathematics, ) J. Kock, I. Vainsencher Standard Monomial Theory 978-3-540-36822-9 An Invitation to Quantum Invariant Theoretic Approach Cohomology Schubert varieties lie at the cross roads of algebraic geometry, combinatorics, commutative algebra, and Kontsevich's Formula for Rational Plane Curves representation theory. They are an important class of This book is an elementary introduction to stable subvarieties of flag varieties, interesting in their own maps and quantum cohomology, starting with an right, and providing an inductive tool for studying introduction to stable pointed curves, and culminat- flag varieties. The literature on them is vast, for they ing with a proof of the associativity of the quantum are ubiquitous—they have been intensively studied product. The viewpoint is mostly that of enumera- over the last fifty years, from many different points tive geometry, and the red thread of the exposition of view and by many different authors. This book is is the problem of counting rational plane curves. mainly a detailed account of a particularly interest- Kontsevich's formula is initially established in the ing instance of their occurrence: namely, in relation to framework of classical enumerative geometry, then as classical invariant theory. More precisely, it is about a statement about reconstruction for Gromov–Wit- the connection between the first and second funda- ten invariants, and finally, using generating functions, mental theorems of classical invariant theory on the as a special case of the associativity of the quantum one hand and standard monomial theory for Schu- 10 Algebraic Geometry springer.com

understanding of the phenomena rather than a mas- for graduate students and researchers in constructive tery of the technique. A range of exercises is provided algebraic curve geometry. for each topic discussed, and a selection of problems More on www.springer.com/978-3-540-73724-7 and exam papers are collected in an appendix to provide material for further study. Available

More on www.springer.com/978-1-84800-055-1 2008. X, 270 p. 24 illus. (Algorithms and Computation Available in Mathematics, 22) 978-3-540-73724-7 2008. XII, 263 p. 8 illus. (Universitext, ) 978-1-84800-055-1

K. Matsuki C.A. Peters, J.H. Steenbrink Introduction to the Mori Program Mixed Hodge Structures This book gives a comprehensive account of Mori¿s Program, that is an approach to the following prob- This is comprehensive basic monograph on mixed lem: classify all the projective varieties X in P^n over Hodge structures. Building up from basic Hodge the- C up to isomorphism. Mori¿s Program is a fusion of ory the book explains Delingne's mixed Hodge the- the so-called Minimal Model Program and the Iitaka ory in a detailed and exhaustive fashion. Then both Program toward the biregular and/or birational clas- Hain's and Morgan's approaches to mixed Hodge the- sification of higher dimensional algebraic varieties. ory related to homotopy theory are sketched. Next The author presents this theory in an easy and under- comes the relative theory: variations of Hodge struc- E. Sernesi standable way with lots of background motivation. It tures, the limit mixed Hodge structure, and then, in is the first book in this extremely important and active the final chapter the all encompassing theory of mixed Deformations of Algebraic area of research and will become a key resource for Hodge modules. The book is interlaced with chapters graduate students. containing applications. Three large appendices com- Schemes plete the book. The book is intended for advanced More on www.springer.com/978-0-387-98465-0 The study of small and local deformations of algebraic graduate students, researchers in complex algebraic varieties originates in the classical work of Kodaira Available geometry as well as interested researchers in nearby and Spencer and its formalization by Grothendieck fields (algebraic geometry, mathematical physics). in the late 1950's. It has become increasingly impor- 2002. XXIII, 478 p. 61 illus. (Universitext, ) More on www.springer.com/978-3-540-77015-2 tant in algebraic geometry in every context where 978-0-387-98465-0 Available variational phenomena come into play, and in classification theory. Today deformation theory is highly 2008. XIV, 470 p. 6 illus. (Ergebnisse der Mathematik und formalized and has ramified widely. This self-con- ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics, 52) tained account of deformation theory in classical alge- 978-3-540-77015-2 braic geometry (over an algebraically closed field) brings together for the first time some results previously scattered in the literature, with relatively little known proofs, yet of everyday relevance to algebraic geometers. It also includes applications to the construction and properties of Severi varieties of families of plane nodal curves, space curves, deformations of quotient singularities, Hilbert schemes of points, local Picard functors, etc. The exposition, amenable at graduate student level, includes many examples.

D. Perrin More on www.springer.com/978-3-540-30608-5 Available Algebraic Geometry 2006. XI, 342 p. (Grundlehren der mathematischen An Introduction Wissenschaften, 334) 978-3-540-30608-5 Aimed primarily at graduate students and beginning researchers, this book provides an introduction to J.R. Sendra, F. Winkler, S. Pérez-Diaz algebraic geometry that is particularly suitable for those with no previous contact with the subject and Rational Algebraic Curves assumes only the standard background of undergrad- A Computer Algebra Approach uate algebra. It is developed from a masters course The central problem considered in this introduction given at the Université Paris-Sud, Orsay, and focusses for graduate students is the determination of ratio- on projective algebraic geometry over an algebraically nal parametrizability of an algebraic curve and, in closed base field. The book starts with easily-formu- the positive case, the computation of a good ratio- lated problems with non-trivial solutions – for exam- nal parametrization. This amounts to determining ple, Bézout’s theorem and the problem of rational the genus of a curve: its complete singularity struc- curves – and uses these problems to introduce the ture, computing regular points of the curve in small fundamental tools of modern algebraic geometry: coordinate fields, and constructing linear systems of dimension; singularities; sheaves; varieties; and coho- curves with prescribed intersection multiplicities. The mology. The treatment uses as little commutative book discusses various optimality criteria for ratio- algebra as possible by quoting without proof (or prov- nal parametrizations of algebraic curves. It is ideal ing only in special cases) theorems whose proof is not necessary in practice, the priority being to develop an springer.com Algebraic Topology 11

Algebraic Topology

J.H. Silverman J. Dieudonné The Arithmetic of Elliptic Curves A History of Algebraic and The theory of elliptic curves is distinguished by its M. Aguilar, S. Gitler, C. Prieto Differential Topology, 1900 - 1960 long history and by the diversity of the methods that Since the early part of the 20th century, topology has have been used in its study. This book treats the arith- Algebraic Topology from a gradually spread to many other branches of mathe- metic theory of elliptic curves in its modern formu- Homotopical Viewpoint matics, and this book demonstrates how the subject- lation, through the use of basic algebraic number continues to play a central role in the field. Written theory and algebraic geometry. The book begins with The purpose of this book is to introduce algebraic by a world-renowned mathematician, this classic a brief discussion of the necessary algebro-geometric topology using the novel approach of homotopy the- text traces the history of algebraic topology begin- results, and proceeds with an exposition of the geom- ory, an approach with clear applications in algebraic ning with its creation in the early 1900s and describes etry of elliptic curves, the formal group of an elliptic geometry as understood by Lawson and Voevodsky. in detail the important theories that were discov- curve, and elliptic curves over finite fields, the com- This method allows the authors to cover the mate- ered before 1960. Through the work of Poincaré, plex numbers, local fields, and global fields. Included rial more efficiently than the more common method de Rham, Cartan, Hureqicz, and many others, this are proofs of the Mordell–Weil theorem giving finite using homological algebra. The basic concepts of historical book also focuses on the emergence of generation of the group of rational points and Siegel's homotopy theory, such as fibrations and cofibrations, new ideas and methods that have led 21st-century- theorem on finiteness of integral points. For this sec- are used to construct singular homology and coho- mathematicians towards new research directions. ond edition of The Arithmetic of Elliptic Curves, mology, as well as K-theory. Throughout the text ***************************** This book is a well- there is a new chapter entitled Algorithmic Aspects many other fundamental concepts are introduced, informed and detailed analysis of the problems and of Elliptic Curves, with an emphasis on algorithms including the construction of the characteristic classes development of algebraic topology, from Poincaré over finite fields which have cryptographic applica- of vector bundles. Although functors appear con- and Brouwer to Serre, Adams, and Thom. The author tions. These include Lenstra's factorization algorithm, stantly throughout the text, no knowledge about cat- has examined each significant paper along this route Schoof's point counting algorithm, Miller's algorithm egory theory is expected from the reader. This book and describes the steps and strategy of its proofs and to compute the Tate and Weil pairings, and a descrip- is intended for advanced undergraduates and gradu- its relation to other work. Previously, the history tion of aspects of elliptic curve cryptography. There ate students with a basic knowledge of point set topol- of the many technical developments of 20th-cen- is also a new section on Szpiro's conjecture and ABC, ogy as well as group theory and can be used in a two tury mathematics had seemed to present insuperable as well as expanded and updated accounts of recent semester course. Marcelo Aguilar and Carlos Prieto obstacles to scholarship. This book demonstrates in developments and numerous new exercises. The book are Professors at the Instituto de Matemticas, Uni- the case of topology how these obstacles can be over- contains three appendices: Elliptic Curves in Char- versidad Nacional Autonoma de Mexico, and Samuel come, with enlightening results.... Within its chosen acteristics 2 and 3, Group Cohomology, and a third Gitler is a member of El Colegio Nacional and profes- boundaries the coverage of this book is superb. Read appendix giving an overview of more advanced topics. sor at the Centro de Investigacion y Estudios Avanza- it! —MathSciNet [The author] traces the develop- dos del IPN. More on www.springer.com/978-0-387-09493-9 ment of algebraic and differential topology from the innovative work by Poincaré at the turn of the century Available More on www.springer.com/978-0-387-95450-9 to the period around 1960. [He] has given a superb Available account of the growth of these fields.… The details are 2009. XX, 514 p. 14 illus. (Graduate Texts in interwoven with the narrative in a very pleasant fash- Mathematics, 106) 2002. XXIX, 478 p. 37 illus. (Universitext, ) 978-0-387-09493-9 978-0-387-95450-9 ion.… [The author] has previous written histories of functional analysis and of algebraic geometry, but neither book was on such a grand scale as this one. He has made it possible to trace the important steps in the growth of algebraic and differential topology, and to admire the hard work and major advances made by the founders. —Zentralblatt MATH More on www.springer.com/978-0-8176-4906-7 Available 2009. XXIV, 648 p. (Modern Birkhäuser Classics, ) 978-0-8176-4906-7 12 Algebraic Topology springer.com

are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms. The main benefit for the reader will be the prospect of fairly quickly getting to the forefront of modern research in this active field. More on www.springer.com/978-3-540-71961-8 Available

2008. XX, 390 p. 115 illus. (Algorithms and Computation in Mathematics, 21) 978-3-540-71961-8 M. Kreck, W. Lück B. Jahren, B.I. Dundas, M. Levine, P. Østvær, O. Röndigs, V. Voevodsky The Novikov Conjecture Motivic Homotopy Theory Geometry and Algebra Lectures at a Summer School in Nordfjordeid, These lecture notes contain a guided tour to the Norway, August 2002 Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They This book is based on lectures given at a summer begin with basics about higher signatures, White- school on motivic homotopy theory at the Sophus head torsion and the s-Cobordism Theorem. Then an Lie Centre in Nordfjordeid, Norway, in August 2002. introduction to surgery theory and a version of the Aimed at graduate students in algebraic topology and assembly map is presented. Using the solution of the algebraic geometry, it contains background material Novikov conjecture for special groups some applica- from both of these fields, as well as the foundations tions to the classification of low dimensional mani- of motivic homotopy theory. It will serve as a good folds are given. Finally, the most recent developments introduction as well as a convenient reference for a D. Kozlov concerning these conjectures are surveyed, including broad group of mathematicians to this important and a detailed status report. The prerequisites consist of a fascinating new subject. Vladimir Voevodsky is one Combinatorial Algebraic Topology solid knowledge of the basics about manifolds, vector of the founders of the theory and received the Fields bundles, (co-) homology and characteristic classes. medal for his work, and the other authors have all Combinatorial algebraic topology is a fascinating and done important work in the subject. dynamic field at the crossroads of algebraic topol- More on www.springer.com/978-3-7643-7141-8 ogy and discrete mathematics. This volume is the first Available More on www.springer.com/978-3-540-45895-1 comprehensive treatment of the subject in book form. Available The first part of the book constitutes a swift walk 2005. XV, 266 p. (Oberwolfach Seminars, 33) through the main tools of algebraic topology, includ- 978-3-7643-7141-8 2007. X, 226 p. (Universitext, ) ing Stiefel-Whitney characteristic classes, which are 978-3-540-45895-1 needed for the later parts. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Our presentation of standard topics is quite different from that of existing texts. In addition, several new themes, such as spectral sequences, are included. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms. The main benefit for the reader will be the prospect of fairly quickly getting to the forefront of modern research in this active field. J. Loday More on www.springer.com/978-3-540-73051-4 D. Kozlov Available Cyclic Homology Combinatorial Algebraic Topology From the reviews: "This is a very interesting book 2008. XX, 390 p. 115 illus. (Algorithms and Combinatorial algebraic topology is a fascinating and Computation in Mathematics, 21) containing material for a comprehensive study of the dynamic field at the crossroads of algebraic topol- 978-3-540-73051-4 cyclid homological theory of algebras, cyclic sets and ogy and discrete mathematics. This volume is the first S1-spaces. Lie algebras and algebraic K-theory and an comprehensive treatment of the subject in book form. introduction to Connes'work and recent results on The first part of the book constitutes a swift walk the Novikov conjecture. The book requires a knowl- through the main tools of algebraic topology, includ- edge of homological algebra and Lie algebra theory ing Stiefel-Whitney characteristic classes, which are as well as basic technics coming from algebraic topol- needed for the later parts. Readers - graduate students ogy. The bibliographic comments at the end of each and working mathematicians alike - will probably find chapter offer good suggestions for further reading and particularly useful the second part, which contains an research. The book can be strongly recommended to in-depth discussion of the major research techniques anybody interested in noncommutative geometry, of combinatorial algebraic topology. Our presenta- contemporary algebraic topology and related topics." tion of standard topics is quite different from that of European Mathematical Society Newsletter In this existing texts. In addition, several new themes, such as spectral sequences, are included. Although applications are sprinkled throughout the second part, they springer.com Algorithms 13 second edition the authors have added a chapter 13 ical content. Computational hardness of Julia sets is on MacLane (co)homology. the main subject of this book. By definition, a computable set in the plane can be visualized on a com- More on www.springer.com/978-3-540-63074-6 puter screen with an arbitrarily high magnification. Available There are countless programs to draw Julia sets. Yet, 1998. XIX, 513 p. 24 illus. (Grundlehren der mathematischen as the authors have discovered, it is possible to con- Wissenschaften, 301) structively produce examples of quadratic polynomi- 978-3-540-63074-6 als, whose Julia sets are not computable. This result is striking - it says that while a dynamical system can be described numerically with an arbitrary preci- sion, the picture of the dynamics cannot be visualized. The book summarizes the present knowledge W.S. Massey H. Zoladek about the computational properties of Julia sets in a The Monodromy Group self-contained way. It is accessible to experts and stu- Algebraic Topology: An dents with interest in theoretical computer science or Introduction In singularity theory and algebraic geometry the dynamical systems. monodromy group is embodied in the Picard-Lef- William S. Massey Professor Massey, born in Illinois schetz formula and the Picard-Fuchs equations. It More on www.springer.com/978-3-540-68546-3 in 1920, received his bachelor's degree from the Uni- has applications in the weakened 16th Hilbert prob- Available versity of Chicago and then served for four years in lem and in mixed Hodge structures. In the theory of 2009. XIV, 152 p. 31 illus. (Algorithms and Computation in the U.S. Navy during World War II. After the War systems of linear differential equations one has the Mathematics, 23) he received his Ph.D. from Princeton University and Riemann-Hilbert problem, the Stokes phenomena 978-3-540-68546-3 spent two additional years there as a post-doctoral and the hypergeometric functions with their multi- research assistant. He then taught for ten years on the dimensional generalizations. In the theory of homo- faculty of Brown University, and moved to his present morphic foliations there appear the Ecalle-Voronin- position at Yale in 1960. He is the author of numer- Martinet-Ramis moduli. On the other hand, there is ous research articles on algebraic topology and related a deep connection of monodromy theory with Galois Analysis topics. This book developed from lecture notes of theory of differential equations and algebraic func- courses taught to Yale undergraduate and graduate tions. All this is presented in this book, underlining students over a period of several years. the unifying role of the monodromy group. The mate- More on www.springer.com/978-0-387-90271-5 rial is addressed to a wide audience, ranging from specialists in the theory of ordinary differential equa- G. Allaire Available tions to algebraic geometers. The book contains a lot of results which are usually spread in many sources. Shape Optimization by the 1977. XXI, 292 p. (Graduate Texts in Mathematics, 56) Readers can quickly get introduced to modern and 978-0-387-90271-5 Homogenization Method vital mathematical theories, such as singularity theory, analytic theory of ordinary differential equations, "The book is very well structured, very clearly written, holomorphic foliations, Galois theory, and parts of very well motivated, and complete in its treatment of algebraic geometry, without searching in vast litera- modeling, analysis and simulation. It will be a basic J.J. Rotman ture. reference for whoever wants to deeply understand homogenization from the point of view of its appli- More on www.springer.com/978-3-7643-7535-5 An Introduction to Algebraic cation to optimal design. The treatment is right to Available the point, a quality that is very much appreciated by Topology 2006. XI, 580 p. (Monografie Matematyczne, 67) readers. In summary, I believe this text may become a main source for the subject of optimal design and A clear exposition, with exercises, of the basic ideas of 978-3-7643-7535-5 shape optimization." (Mathematical Reviews) algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowl- More on www.springer.com/978-0-387-95298-7 edge of point set topology and basic algebra. Although Available categories and functors are introduced early in the text, excessive generality is avoided, and the author Algorithms 2002. XV, 456 p. 54 illus. (Applied Mathematical explains the geometric or analytic origins of abstract Sciences, 146) concepts as they are introduced. 978-0-387-95298-7 More on www.springer.com/978-0-387-96678-6 Available

1988. XIII, 460 p. 95 illus. (Graduate Texts in Mathematics, 119) 978-0-387-96678-6

M. Braverman, M. Yampolsky Computability of Julia Sets Among all computer-generated mathematical images, Julia sets of rational maps occupy one of the most prominent positions. Their beauty and complexity can be fascinating. They also hold a deep mathemat- 14 Analysis springer.com

multivariable polynomial approximations. The presentation of each topic is meant to be an introduction with certain degree of depth. Comprehensive references on a particular topic are listed at the end V. Arnold, M. Levi of each chapter for further reading and study. In this third edition, a new chapter, Multivariable Polyno- Geometrical Methods in the mial Approximations, is included, numerous changes are made throughout the entire text, and new exer- Theory of Ordinary Differential cises are added. Review of earlier edition: "...the book Equations is clearly written, quite pleasant to read, and contains a lot of important material; and the authors have Since the first edition of this book, geometrical done an excellent job at balancing theoretical devel- S. Antman methods in the theory of ordinary differential equa- opments, interesting examples and exercises, numer- tions have become very popular and some progress ical experiments, and bibliographical references." R. Nonlinear Problems of Elasticity has been made partly with the help of computers. Glowinski, SIAM Review, 2003 Much of this progress is represented in this revised, This second edition is an enlarged, completely expanded edition, including such topics as the Feigen- More on www.springer.com/978-1-4419-0457-7 updated, and extensively revised version of the baum universality of period doubling, the Zoladec Available authoritative first edition. It is devoted to the detailed solution, the Iljashenko proof, the Ecalle and Voronin study of illuminating specific problems of nonlinear theory, the Varchenko and Hovanski theorems, and 2009. XVI, 625 p. (Texts in Applied Mathematics, 39) elasticity, directed toward the scientist, engineer, and the Neistadt theory. In the selection of material for 978-1-4419-0457-7 mathematician who wish to see careful treatments this book, the author explains basic ideas and meth- of precisely formulated problems. Special emphasis ods applicable to the study of differential equations. is placed on the role of nonlinear material response. Special efforts were made to keep the basic ideas free The mathematical tools from nonlinear analysis are from excessive technicalities. Thus the most funda- given self-contained presentations where they are mental questions are considered in great detail, while needed. This book begins with chapters on (geomet- of the more special and difficult parts of the theory rically exact theories of) strings, rods, and shells, and have the character of a survey. Consequently, the on the applications of bifurcation theory and the reader needs only a general mathematical knowledge calculus of variations to problems for these bodies. to easily follow this text. It is directed to mathemati- The book continues with chapters on tensors, three- cians, as well as all users of the theory of differential dimensional continuum mechanics, three-dimen- equations. sional elasticity, large-strain plasticity, general theories of rods and shells, and dynamical problems. Each More on www.springer.com/978-0-387-96649-6 chapter contains a wealth of interesting, challeng- Available ing, and tractable exercises. Reviews of the first edi- 1988. XIV, 372 p. (Grundlehren der mathematischen tion: ``A scholarly work, it is uncompromising in its Wissenschaften, 250) J. Aubin approach to model formulation, while achieving strik- 978-0-387-96649-6 ing generality in the analysis of particular problems. Optima and Equilibria It will undoubtedly become a standard research refer- An Introduction to Nonlinear Analysis ence in elasticity but will be appreciated also by teach- Progress in the theory of economic equilibria and in ers of both solid mechanics and applied analysis for game theory has proceeded hand in hand with that its clear derivation of equations and wealth of exam- of the mathematical tools used in the field, namely ples.'' --- J. M. Ball, (Bulletin of the American Math- nonlinear analysis and, in particular, convex analy- ematical Society), 1996. ``It is destined to become a sis. Jean-Pierre Aubin, one of the leading specialists in standard reference in the field which belongs on the nonlinear analysis and its application to economics, bookshelf of anyone working on the application of has written a rigorous and concise - yet still elemen- mathematics to continuum mechanics. For graduate tary and self-contained - textbook providing the students, it provides a fascinating introduction to an mathematical tools needed to study optima and equi- active field of mathematical research.'' --- M. Renardy, libria, as solutions to problems, arising in economics, (SIAM Review), 1995. ``The monograph is a master- management sciences, operations research, coopera- piece for writing a modern theoretical treatise on a tive and non-cooperative games, fuzzy games etc. It field of natural sciences. It is highly recommended to K.E. Atkinson, W. Han begins with the foundations of optimization theory, all scientists, engineers and mathematicians interested and mathematical programming, and in particular in a careful treatment of uncompromised nonlinear Theoretical Numerical Analysis convex and nonsmooth analysis. Nonlinear analysis problems of elasticity, and it is a `must' for applied A Functional Analysis Framework is then presented, first game-theoretically, then in the mathematicians working on such problems.'' --- L. v framework of set valued analysis. These results are Wolfersdorf, (Zeitschrift fur Angewandte Mathematik This textbook prepares graduate students for research then applied to the main classes of economic equilib- und Mechanik), 1995. in numerical analysis/computational mathematics ria. The book contains numerous exercises and prob- by giving to them a mathematical framework embed- More on www.springer.com/978-0-387-20880-0 lems: the latter allow the reader to venture into areas ded in functional analysis and focused on numerical of nonlinear analysis that lie beyond the scope of the Available analysis. This helps the student to move rapidly into book and of most graduate courses. 2005. XVIII, 838 p. 110 illus. (Applied Mathematical Sciences, a research program. The text covers basic results of 107) functional analysis, approximation theory, Fourier More on www.springer.com/978-3-540-64983-0 978-0-387-20880-0 analysis and wavelets, iteration methods for nonlinear Available equations, finite difference methods, Sobolev spaces and weak formulations of boundary value problems, 1998. XVII, 433 p. 28 illus. (Graduate Texts in finite element methods, elliptic variational inequal- Mathematics, 140) ities and their numerical solution, numerical meth- 978-3-540-64983-0 ods for solving integral equations of the second kind, boundary integral equations for planar regions, and springer.com Analysis 15

as well as complete proofs of state-of-the-art results;* suggests new aspects of that reality. The development Classical real variables and introduction to the role of of this process is discussed from the modern view- Cantor sets, later placed in the modern setting of self- point of differential forms. Using this concept, the similarity and fractals;* Evolution of the Riesz repre- student learns to compute orbits and rocket trajec- sentation theorem to Radon measures and distribu- tories, model flows and force fields, and derive the tion theory;* Deep results in modern differentiation laws of electricity and magnetism. These exercises and theory;* Systematic development of weak sequential observations of mathematical symmetry enable the convergence inspired by theorems of Vitali, Nikodym, student to better understand the interaction of physics and Hahn–Saks;* Thorough treatment of rearrange- and mathematics. ments and maximal functions;* The relation between More on www.springer.com/978-0-387-97606-8 surface measure and Hausforff measure;* Complete presentation of Besicovich coverings and differenti- Available E. Barbeau ation of measures.Integration and Modern Analysis will serve advanced undergraduates and graduate stu- 1991. 404 p. 98 illus. (Undergraduate Texts in Polynomials dents, as well as professional mathematicians. It may Mathematics, ) 978-0-387-97606-8 be used in the classroom or self-study. The book extends the high school curriculum and provides a backdrop for later study in calculus, mod- More on www.springer.com/978-0-8176-4306-5 ern algebra, numerical analysis, and complex variable Available theory. Exercises introduce many techniques and top- L. Carleson, T.W. Gamelin ics in the theory of equations, such as evolution and 2009. XIX, 575 p. 24 illus. (Birkhäuser Advanced Texts factorization of polynomials, solution of equations, Basler Lehrbücher, ) interpolation, approximation, and congruences. The 978-0-8176-4306-5 Complex Dynamics theory is not treated formally, but rather illustrated A discussion of the properties of conformal mappings through examples. Over 300 problems drawn from in the complex plane, closely related to the study of journals, contests, and examinations test understand- fractals and chaos. Indeed, the book ends in a detailed ing, ingenuity, and skill. Each chapter ends with a list study of the famous Mandelbrot set, which describes P. Borwein, T. Erdelyi of hints; there are answers to many of the exercises very general properties of such mappings. Focusing and solutions to all of the problems. In addition, 69 Polynomials and Polynomial on the analytic side of this contemporary subject, the "explorations" invite the reader to investigate research text was developed from a course taught over several problems and related topics. Inequalities semesters and aims to help students and instructors to More on www.springer.com/978-0-387-40627-5 familiarize themselves with complex dynamics. Top- After an introduction to the geometry of polynomials ics covered include: conformal and quasi-conformal Available and a discussion of refinements of the Fundamental mappings, fixed points and conjugations, basic ratio- 1989. XXII, 455 p. 36 illus. (Problem Books in Mathematics, ) Theorem of Algebra, the book turns to a considera- nal iteration, classification of periodic components, 978-0-387-40627-5 tion of various special polynomials. Chebyshev and critical points and expanding maps, some applications Descartes systems are then introduced, and Müntz of conformal mappings, the local geometry of the systems and rational systems are examined in detail. Fatou set, and quadratic polynomials and the Mandel- Subsequent chapters discuss denseness questions and brot set. the inequalities satisfied by polynomials and rational functions. Appendices on algorithms and computa- More on www.springer.com/978-0-387-97942-7 tional concerns, on the interpolation theorem, and on Available orthogonality and irrationality round off the text. The book is self-contained and assumes at most a senior- 1993. IX, 192 p. 28 illus. (Universitext, ) undergraduate familiarity with real and complex anal- 978-0-387-97942-7 ysis. More on www.springer.com/978-0-387-94509-5 Available R.F. Curtain, H. Zwart 1995. X, 496 p. (Graduate Texts in Mathematics, 161) J.J. Benedetto, W. Czaja 978-0-387-94509-5 An Introduction to Infinite- Integration and Modern Analysis Dimensional Linear Systems A paean to twentieth century analysis, this modern Theory text has several important themes and key features D.M. Bressoud which set it apart from others on the subject. A major Infinite dimensional systems is now an established thread throughout is the unifying influence of the area of research. Given the recent trend in systems concept of absolute continuity on differentiation and Second Year Calculus theory and in applications towards a synthesis of integration. This leads to fundamental results such From Celestial Mechanics to Special Relativity time- and frequency-domain methods, there is a need as the Dieudonné–Grothendieck theorem and other for an introductory text which treats both state-space Second Year Calculus: From Celestial Mechanics to and frequency-domain aspects in an integrated fash- intricate developments dealing with weak conver- Special Relativity covers multi-variable and vector cal- gence of measures.Key Features:* Fascinating histor- ion. The authors' primary aim is to write an introduc- culus, emphasizing the historical physical problems tory textbook for a course on infinite dimensional ical commentary interwoven into the exposition;* which gave rise to the concepts of calculus. The book Hundreds of problems from routine to challenging;* linear systems. An important consideration by the guides us from the birth of the mechanized view of authors is that their book should be accessible to grad- Broad mathematical perspectives and material, e.g., the world in Isaac Newton's Mathematical Principles in harmonic analysis and probability theory, for inde- uate engineers and mathematicians with a minimal of Natural Philosophy in which mathematics becomes background in functional analysis. Consequently, all pendent study projects;* Two significant appendices the ultimate tool for modelling physical reality, to on functional analysis and Fourier analysis.Key Top- the mathematical background is summarized in an the dawn of a radically new and often counter-intu- extensive appendix. For the majority of students, this ics:* In-depth development of measure theory and itive age in Albert Einstein's Special Theory of Rel- Lebesgue integration;* Comprehensive treatment of ativity in which it is the mathematical model which connection between differentiation and integration, 16 Analysis springer.com would be their only acquaintance with infinite dimen- strass Theorem More specialized chapters (8-10) major achievement and is sure to become a standard sional systems. cover topics often absent from classical introduc- reference on the topic. tiory texts in analysis: maximal functions and weak More on www.springer.com/978-0-387-94475-3 More on www.springer.com/978-0-387-87820-1 Lp spaces, the Calderón-Zygmund decomposition, Available functions of bounded mean oscillation, the Stein-Fef- Available ferman Theorem, the Marcinkiewicz Interpolation 1995. XVIII, 698 p. 29 illus. (Texts in Applied Theorem, potential theory, rearrangements, estima- 2009. XII, 376 p. 12 illus. (Springer Monographs in Mathematics, 21) tions of Riesz potentials including limiting cases Pro- Mathematics, ) 978-0-387-94475-3 978-0-387-87820-1 vides a self-sufficient introduction to Sobolev Spaces, Morrey Spaces and Poincaré inequalities as the backbone of PDEs and as an essential environment to develop modern and current analysis Comprehen- E. DiBenedetto sive index This clear, user-friendly exposition of real G. Evans, J. Blackledge, P. Yardley analysis covers a great deal of territory in a concise Degenerate Parabolic Equations fashion, with sufficient motivation and examples Analytic Methods for Partial throughout. A number of excellent problems, as well Mathematicians have only recently begun to under- as some remarkable features of the exercises, occur Differential Equations stand the local structure of solutions of degenerate at the end of every chapter, which point to additional The subject of partial differential equations holds an and singular parabolic partial differential equations. theorems and results. Stimulating open problems are exciting place in mathematics. At one extreme the The problem originated in the mid '60s with the work proposed to engage students in the classroom or in a interest lies in the existence and uniqueness of solu- of DeGiorgi, Moser, Ladyzenskajia and Uraltzeva. self-study setting. tions, and the functional analysis of the proofs of This book will be an account of the developments these properties. At the other extreme lies the applied in this field over the past five years. It evolved out More on www.springer.com/978-0-8176-4231-0 mathematical and engineering quest to find useful of the 1990-Lipschitz Lectures given by Professor Available solutions, either analytically or numerically, to these DiBenedetto at the Institut für angewandte Mathe- important equations which can be used in design matik of the University, Bonn. 2002. XXIV, 516 p. (Birkhäuser Advanced Texts Basler Lehrbücher, ) and construction. The objective of this book is to More on www.springer.com/978-0-387-94020-5 978-0-8176-4231-0 actually solve equations rather than discuss the the- Available oretical properties of their solutions. The topics are 1993. XV, 387 p. 12 illus. (Universitext, ) approached practically, without losing track of the 978-0-387-94020-5 underlying mathematical foundations of the subject. The topics covered include the separation of variables, the characteristic method, D'Alembert's method, integral transforms and Green's functions. Numerous exercises are provided as an integral part of the learning process, with solutions provided in a substantial appendix. More on www.springer.com/978-3-540-76124-2 Available

2000. XII, 316 p. 25 illus. (Springer Undergraduate A.L. Dontchev, R.T. Rockafellar Mathematics Series, ) 978-3-540-76124-2 Implicit Functions and Solution Mappings E. DiBenedetto A View from Variational Analysis Real Analysis The implicit function theorem is one of the most important theorems in analysis and its many variants The focus of this modern graduate text in real anal- are basic tools in partial differential equations and ysis is to prepare the potential researcher to a rigor- numerical analysis. This book treats the implicit func- ous "way of thinking" in applied mathematics and tion paradigm in the classical framework and beyond, partial differential equations. The book will provide focusing largely on properties of solution mappings excellent foundations and serve as a solid building of variational problems. The purpose of this self-con- block for research in analysis, PDEs, the calculus of tained work is to provide a reference on the topic and variations, probability, and approximation theory. to provide a unified collection of a number of results All the core topics of the subject are covered, from which are currently scattered throughout the litera- a basic introduction to functional analysis, to mea- ture. The first chapter of the book treats the classical sure theory, integration and weak differentiation of M. Fabian, P. Habala, P. Hajek, V. Montesinos Santalucia, J. implicit function theorem in a way that will be use- Pelant, V. Zizler functions, and in a presentation that is hands-on, ful for students and teachers of undergraduate cal- with little or no unnecessary abstractions. Additional culus. The remaining part becomes gradually more Functional Analysis and Infinite- features: Carefully chosen topics, some not touched advanced, and considers implicit mappings defined by upon elsewhere: fine properties of integrable func- relations other than equations, e.g., variational prob- Dimensional Geometry tions as they arise in applied mathematics and PDEs lems. Applications to numerical analysis and opti- This book introduces the reader to the basic principles – Radon measures, the Lebesgue Theorem for general mization are also provided. This valuable book is a Radon measures, the Besicovitch covering Theorem, of functional analysis theory that are close to nonlin- the Rademacher Theorem; topics in Marcinkiewicz ear analysis and topology. The presentation is self- integrals, functions of bounded variation, Legendre contained, including many folklore results, and the transform and the characterization of compact subset proofs are accessible to students with the usual back- of some metric function spaces and in particular of Lp ground in real analysis and topology. Several results spaces Constructive presentation of the Stone-Weier- are published here for the first time in a monograph. springer.com Analysis 17

The text can be used in graduate courses or for inde- nicht nur äußerst sorgfältig und umfassend in die in calculus, while parts of the book can be used for pendent study. It includes a large number of exer- Theorie ein, sondern vermittelt auch aufgrund der advanced undergraduate and graduate courses in real cises of different levels of difficulty, accompanied by zahlreichen vollständig durchgerechneten Beispiele analysis. Each chapter contains several examples and hints. The book is also directed to young researchers einen Einblick in deren Anwendungspraxis.Eine weit- a large selection of exercises, as well as "Notes and in functional analysis and can serve as a reference ere Besonderheit ist der Brückenschlag zur Comput- Comments" describing salient features of the exposi- book, to areas of Banach space. eranwendung. Mit ausgefeilten Maple-Arbeitsblättern tion, related developments and references to relevant wird gezeigt, wie man mit dem Computer gestal- literature. More on www.springer.com/978-0-387-95219-2 ten, Ideen vermitteln und eindrucksvoll visualisieren More on www.springer.com/978-0-387-30530-1 Available kann. So können auch rechnerisch anspruchsvollere Beispiele behandelt werden, als dies sonst üblich Available 2001. IX, 451 p. (CMS Books in Mathematics, ) ist.Mit seinem Reichtum an Material, dem klaren 978-0-387-95219-2 und präzisen Stil und der durchdachten didaktis- 2006. X, 432 p. 71 illus. (Undergraduate Texts in chen Konzeption ist das Buch bestens als Basis und Mathematics, ) 978-0-387-30530-1 Leitfaden für Studierende und Lehrende der Mathe- matik, Physik, Wirtschafts- wie auch Ingenieurwis- senschaften geeignet. More on www.springer.com/978-3-540-22226-2 Available F.J. Flanigan, J.L. Kazdan

2005. XV, 389 S. (Springer-Lehrbuch, ) Calculus Two 978-3-540-22226-2 Linear and Nonlinear Functions Calculus and linear algebra are two dominant themes in contemporary mathematics and its applications. The aim of this book is to introduce linear algebra in an intuitive geometric setting as the study of linear maps and to use these simpler linear functions to study more complicated nonlinear functions. In S. Hildebrandt this way, many of the ideas, techniques, and formulas in the calculus of several variables are clarified and Analysis 2 understood in a more conceptual way. After using this text a student should be well prepared for subsequent Der zweite Band dieses Lehrbuchs der Analysis advanced courses in both algebra and linear differen- umfaßt den Stoff des zweiten Semesters eines math- tial equations as well as the many applications where ematischen Grundstudiums für Studierende der linearity and its interplay with nonlinearity are signif- Mathematik, Physik und Informatik. Der klare und übersichtliche Aufbau berücksichtigt, daß schon icant. This second edition has been revised to clarify S.R. Ghorpade, B.V. Limaye the concepts. Many exercises and illustrations have frühzeitig die mathematischen Hilfsmittel erörtert been included to make the text more usable for stu- A Course in Calculus and Real werden, die zum Verständnis der physikalischen dents. Grundvorlesungen unerläßlich sind. In Verbindung Analysis mit Band 1 ist so ein Leitfaden für das Studium der More on www.springer.com/978-0-387-97388-3 Analysis entstanden, der das in den ersten beiden Available This book provides a self-contained and rigorous Studiensemestern zu erwerbende mathematische introduction to calculus of functions of one variable. Grundwissen umfaßt. Ausführliche Beweise und 1990. XVII, 644 p. 207 illus. (Undergraduate Texts in The presentation and sequencing of topics emphasizes Erläuterungen sowie zahlreiche Beispiele und interes- Mathematics, ) the structural development of calculus. At the same sante Übungsaufgaben eignen es sehr gut für das Selb- 978-0-387-97388-3 time, due importance is given to computational tech- ststudium. Ein klarer und übersichtlicher Aufbau und niques and applications. The authors have strived to eine geschickte Gliederung des Stoffes ermöglichen, make a distinction between the intrinsic definition of das erste Studium auf Kernbereiche zu beschränken. a geometric notion and its analytic characterization. Geometrische Intuition und historische Motivation in Throughout the book, the authors highlight the fact Verbindung mit einer maßvollen Abstraktion kennze- that calculus provides a firm foundation to several ichnen diese moderne Einführung in die Analysis. concepts and results that are generally encountered in high school and accepted on faith. For example, one More on www.springer.com/978-3-540-43970-7 can find here a proof of the classical result that the Available ratio of the circumference of a circle to its diameter is the same for all circles. Also, this book helps students 2003. X, 514 S. (Springer-Lehrbuch, ) get a clear understanding of the concept of an angle 978-3-540-43970-7 and the definitions of the logarithmic, exponential and trigonometric functions together with a proof of the fact that these are not algebraic functions. A num- W. Forst, D. Hoffmann ber of topics that may have been inadequately covered in calculus courses and glossed over in real analy- Gewöhnliche sis courses are treated here in considerable detail. As such, this book provides a unified exposition of calcu- Differentialgleichungen lus and real analysis. The only prerequisites for read- Theorie und Praxis - vertieft und visualisiert mit ing this book are topics that are normally covered in Maple® high school; however, the reader is expected to pos- sess some mathematical maturity and an ability to Die Theorie der Gewöhnlichen Differentialgleichun- understand and appreciate proofs. This book can be gen ist ein grundlegendes und unverändert aktuelles used as a textbook for a serious undergraduate course Gebiet der Mathematik.Das vorliegende Buch führt 18 Analysis springer.com

in recent years, relating it to broader themes in mathematical analysis. D. Kaplan, L. Glass More on www.springer.com/978-0-387-25364-0 Available Understanding Nonlinear 2006. XII, 262 p. (Applied Mathematical Sciences, 127) Dynamics 978-0-387-25364-0 This book presents the main concepts and applications of nonlinear dynamics at an elementary level. The book is based on a one-semester undergraduate course that has been given since 1975 at McGill University and has been constantly updated to keep up with current developments. Based on the authors' U. Hornung successful course for undergraduate students in the biological sciences, the primer presents the main con- Homogenization and Porous cepts of non-linear dynamics at a level requiring only Media one year of calculus. This text will appeal to courses being offered in both mathematics and biology. Top- This book discusses methods and results from the ics include finite difference equations, the concept theory of homogenization and their applications to of chaos, networks, cellular automata, on- and two- flow and transport in porous media. It offers a sys- dimensional differential equations, the dynamics of tematic and rigorous treatment of upscaling proce- non-linear equations, and linear stability analysis. dures related to physical modeling for porous media Examples are all from the biological sciences, exer- P.E. Jorgensen on micro-, meso- and macro-scales. The chapters are cises are included in each chapter, and basic mathe- devoted to percolation, Newtonian, non-Newtonian matical reviews are included in an appendix. phenomena, two phase flow, miscible displacement, Analysis and Probability More on www.springer.com/978-0-387-94440-1 thermal and elastic effects. Detailed studies of micro- Wavelets, Signals, Fractals Available structure systems and computational results for dual- This book, combining analysis and tools from mathe- porosity models are presented. This book will be of matical probability, focuses on a systematic and novel 1995. XIX, 425 p. 294 illus. (Textbooks in interest to readers who want to learn the main under- presentation of recent trends in pure and applied Mathematical Sciences, ) lying ideas and concepts of modern mathematical the- mathematics: the emergence of three fields, wavelets, 978-0-387-94440-1 ory, including the most recently obtained results and signals and fractals. The unity of basis constructions applications. Mathematicians, soil physicists, geo- and their expansions is emphasized as the starting hydrologists, chemical engineers, researchers working point for the development of bases that are computa- in an oil reservoir simulation and the environmental tionally efficient for use in several areas from wavelets sciences, will find this book of particular interest. to fractals. The book brings together tools from engi- More on www.springer.com/978-0-387-94786-0 neering and math, especially from signal- and image Available processing, and from harmonic analysis and operator theory. The presentation is aimed at graduate 1997. XVI, 279 p. 35 illus. (Interdisciplinary Applied students, as well as users from a diverse spectrum of Mathematics, 6) applications. Key features: • A hands-on approach 978-0-387-94786-0 for students, including tutorials and numerous exercises; • Excellent motivation throughout; • New pedagogical features: glossary of terms, their use in mathematics and in engineering, help for cross-audi- ences, image processing, visual presentation of key algorithms, structure and geometry of big matrix R. Kress computations, explanation of uses of the theory in applications outside of mathematics; • Includes more Linear Integral Equations than 50 figures with captions, illustrating the main ideas, plus engineering diagrams, graphic renditions The result of the author's fascination with the math- of algorithms, and separate illustrations; • Separate ematical beauty of integral equations, this book com- sections in the book explain engineering terms to bines theory, applications, and numerical methods, mathematicians, and operator theory to engineers; • and covers each of these fields with the same weight. Each chapter concludes with a helpful guide to the lit- In order to make the book accessible to mathemati- erature allowing students to follow up on the topics in cians, physicists, and engineers alike, the author has V. Isakov the book. Palle E.T. Jorgensen is a Professor of Math- made it as self-contained as possible, requiring only ematics at the University of Iowa. This book is based a solid foundation in differential and integral calcu- Inverse Problems for Partial in part on interdisciplinary courses that he has taught lus. The functional analysis which is necessary for an over the last several years, and on his work with his adequate treatment of the theory and the numerical Differential Equations current and former students. His most recent book solution of integral equations is developed within the book itself. Problems are included at the end of each A comprehensive description of the current theo- was written jointly with Ola Bratteli and is entitled- chapter. retical and numerical aspects of inverse problems in Wavelets through a Looking Glass, ©2002 Birkhäuser partial differential equations. Applications include Boston. More on www.springer.com/978-0-387-98700-2 recovery of inclusions from anomalies of their grav- More on www.springer.com/978-0-387-29519-0 Available ity fields, reconstruction of the interior of the human Available 1999. XIV, 388 p. 1 illus. (Applied Mathematical Sciences, 82) body from exterior electrical, ultrasonic, and magnetic 978-0-387-98700-2 measurement. By presenting the data in a readable 2006. XLVII, 276 p. 58 illus. (Graduate Texts in and informative manner, the book introduces both Mathematics, 234) scientific and engineering researchers as well as grad- 978-0-387-29519-0 uate students to the significant work done in this area springer.com Analysis 19

classical applications of the modulus techniques presented in many monographs. More on www.springer.com/978-0-387-85586-8 Available S. Lang 2009. XII, 367 p. 12 illus. (Springer Monographs in Undergraduate Analysis Mathematics, ) 978-0-387-85586-8 This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. Topics discussed include the classical S. Lang test for convergence of series, Fourier series, polynomial approximation, the Poisson kernel, the con- Complex Analysis struction of harmonic functions on the disc, ordinary Now in its fourth edition, the first part of this book differential equation, curve integrals, derivatives in is devoted to the basic material of complex analysis, vector spaces, multiple integrals, and others. One while the second covers many special topics, such as of the author's main concerns is to achieve a bal- the Riemann Mapping Theorem, the gamma function, ance between concrete examples and general theo- and analytic continuation. Power series methods are rems, augmented by a variety of interesting exercises. used more systematically than is found in other texts, Some new material has been added in this second edi- and the resulting proofs often shed more light on the tion, for example: a new chapter on the global ver- J. Nedelec results than the standard proofs. While the first part is sion of integration of locally integrable vector fields; suitable for an introductory course at undergraduate a brief discussion of L1-Cauchy sequences, introduc- Acoustic and Electromagnetic level, the additional topics covered in the second part ing students to the Lebesgue integral; more material give the instructor of a gradute course a great deal of Equations on Dirac sequences and families, including a section flexibility in structuring a more advanced course. Integral Representations for Harmonic Problems on the heat kernel; a more systematic discussion of orders of magnitude; and a number of new exercises. More on www.springer.com/978-0-387-98592-3 This self-contained book is devoted to the study of the acoustic wave equations and the Maxwell sys- More on www.springer.com/978-0-387-94841-6 Available tem, the two most common waves equations that are Available 1999. XIV, 485 p. 139 illus. (Graduate Texts in encountered in physics or in engineering. It presents Mathematics, 103) a detailed analysis of their mathematical and phys- 1997. XV, 668 p. 91 illus. (Undergraduate Texts in 978-0-387-98592-3 ical properties. In particular, the author focuses on Mathematics, ) the study of the harmonic exterior problems, building 978-0-387-94841-6 a mathematical framework which provides the existence and uniqueness of the solutions. This book will serve as a useful introduction to wave problems for graduate students in mathematics, physics, and engineering. More on www.springer.com/978-0-387-95155-3 Available S. Lang 2001. IX, 316 p. 2 illus. (Applied Mathematical Differential and Riemannian Sciences, 144) Manifolds 978-0-387-95155-3 This is the third version of a book on Differential Manifolds; in this latest expansion three chapters have been added on Riemannian and pseudo-Riemannian O. Martio, V. Ryazanov, U. Srebro, E. Yakubov geometry, and the section on sprays and Stokes' theorem have been rewritten.This text provides an intro- Moduli in Modern Mapping duction to basic concepts in differential topology, differential geometry and differential equations. In Theory differential topology one studies classes of maps and The purpose of this book is to present a modern the possibility of finding differentiable maps in them, account of mapping theory with emphasis on quasi- and one uses differentiable structures on manifolds to conformal mapping and its generalizations. The mod- determine their topological structure. In differential ulus method was initiated by Arne Beurling and Lars geometry one adds structures to the manifold (vector Ahlfors to study conformal mappings, and later this fields, sprays, a metric, and so forth) and studies their method was extended and enhanced by several others. properties. In differential equations one studies vector The techniques are geometric and they have turned N.S. Papageorgiou, S.T. Kyritsi-Yiallourou fields and their integral curves, singular points, stable out to be an indispensable tool in the study of quasi- and unstable manifolds, and the like. conformal and quasiregular mappings as well as their Handbook of Applied Analysis More on www.springer.com/978-0-387-94338-1 generalizations. The book is based on recent research Accurate models to describe real-world phenomena papers and extends the modulus method beyond the Available are indispensable for research in such scientific fields as physics, engineering, biology, chemistry, and eco- 1995. 384 p. 20 illus. (Graduate Texts in Mathematics, nomics. The tools and techniques of applied analy- 160) sis facilitate the development of mathematical models 978-0-387-94338-1 and can thereby serve as an excellent resource for 20 Analysis springer.com students and researchers in various scientific and mathematics. Readers will find this book to be a great mathematical disciplines. This self-contained, com- pleasure."--MATHEMATICAL REVIEWS R. Remmert prehensive handbook provides an in-depth examina- More on www.springer.com/978-3-540-85267-4 tion of important theoretical methods and procedures Classical Topics in Complex in applied analysis. Unique features of the Handbook Available of Applied Analysis: • Presents an accessible introduc- 1994. XVI, 544 p. 59 illus. (Springer Series in Computational Function Theory tion to modern analysis, while still serving as a useful Mathematics, 23) An ideal text for an advanced course in the theory of reference for researchers and practitioners; • Covers 978-3-540-85267-4 complex functions, this book leads readers to experi- a large number of diverse topics: smooth and non- ence function theory personally and to participate in smooth differential calculus, optimal control, fixed the work of the creative mathematician. The author point theory, critical point theory, linear and nonlin- includes numerous glimpses of the function theory ear eigenvalue problems, nonlinear boundary value B. Reddy of several complex variables, which illustrate how problems, set-valued analysis, game theory, stochas- autonomous this discipline has become. In addi- tic analysis, and evolutionary equations; • Serves as a tion to standard topics, readers will find Eisenstein's complete guide to the theory of nonlinear analysis; • Introductory Functional Analysis proof of Euler's product formula for the sine func- Includes numerous examples that demonstrate and With Applications to Boundary Value Problems tion; Wielandts uniqueness theorem for the gamma expand upon the topics presented; • Suggests many and Finite Elements function; Stirlings formula; Isssas theorem; Besses directions for further research and study. In this one Providing an introduction to functional analysis, this proof that all domains in C are domains of holomor- volume, the reader can find many of the most impor- text treats in detail its application to boundary-value phy; Wedderburns lemma and the ideal theory of tant theoretical trends in nonlinear analysis and appli- problems and finite elements, and is distinguished rings of holomorphic functions; Estermanns proofs cations to different fields. These features, together by the fact that abstract concepts are motivated and of the overconvergence theorem and Blochs theo- with an extensive bibliography, make the volume a illustrated wherever possible. It is intended for use by rem; a holomorphic imbedding of the unit disc in valuable tool for every researcher working with non- senior undergraduates and graduates in mathemat- C3; and Gausss expert opinion on Riemanns disser- linear analysis. ics, the physical sciences and engineering, who may tation. Remmert elegantly presents the material in More on www.springer.com/978-0-387-78906-4 not have been exposed to the conventional prerequi- short clear sections, with compact proofs and his- Available sites for a course in functional analysis, such as real torical comments interwoven throughout the text. analysis. Mature researchers wishing to learn the basic The abundance of examples, exercises, and historical 2009. XXIII, 793 p. (Advances in Mechanics and Mathematics, ideas of functional analysis will equally find this use- 19) remarks, as well as the extensive bibliography, com- ful. Offers a good grounding in those aspects of func- 978-0-387-78906-4 bine to make an invaluable source for students and tional analysis which are most relevant to a proper teachers alike understanding and appreciation of the mathematical More on www.springer.com/978-0-387-98221-2 aspects of boundary-value problems and the finite element method. Available

More on www.springer.com/978-0-387-98307-3 1997. 380 p. 16 illus. (Graduate Texts in Mathematics, Available 172) 978-0-387-98221-2 1998. XIV, 492 p. 145 illus. (Texts in Applied Mathematics, 27) 978-0-387-98307-3

A. Quarteroni, A. Valli R. Remmert Numerical Approximation of Theory of Complex Functions Partial Differential Equations A lively and vivid look at the material from function theory, including the residue calculus, supported by This book deals with the numerical approximation of examples and practice exercises throughout. There is partial differential equations. Its scope is to provide a also ample discussion of the historical evolution of the thorough illustration of numerical methods, carry out theory, biographical sketches of important contribu- R. Remmert, G. Schumacher their stability and convergence analysis, derive error tors, and citations - in the original language with their bounds, and discuss the algorithmic aspects relative English translation - from their classical works. Yet Funktionentheorie 2 to their implementation. A sound balancing of theo- the book is far from being a mere history of function retical analysis, description of algorithms and discus- theory, and even experts will find a few new or long Diese dritte Auflage wurde zusammen mit dem zweit- sion of applications is one of its main features. Many forgotten gems here. Destined to accompany students genannten Autor kritisch durchgesehen, ergänzt und kinds of problems are addressed. A comprehensive making their way into this classical area of mathemat- verbessert. Ein weiteres Kapitel über geometrische theory of Galerkin method and its variants, as well ics, the book offers quick access to the essential results Funktionentheorie und schlichte Funktionen enthält as that of collocation methods, are developed for the for exam preparation. Teachers and interested mathe- einen Beweis der Bieberbachschen Vermutung. spatial discretization. These theories are then specified maticians in finance, industry and science will profit "Der ... vorliegende zweite Band der Funktionen- to two numerical subspace realizations of remarkable from reading this again and again, and will refer back theorie erfüllt voll die Erwartungen, die der erste interest: the finite element method and the spectral to it with pleasure. Band geweckt hat. Wieder beeindrucken vor allem method. From the reviews:"...The book is excellent die hochinteressanten historischen Bemerkungen More on www.springer.com/978-0-387-97195-7 and is addressed to post-graduate students, research zu den einzelnen Themenkreisen, als besonderer workers in applied sciences as well as to specialists Available Leckerbissen wird das Gutachten von Gauß über Rie- in numerical mathematics solving PDE. Since it is manns Dissertation vorgestellt... Jedes einzelne Kapi- written very clearly, it would be acceptable for under- 1991. 484 p. 68 illus. (Graduate Texts in Mathematics, tel enthält ausführliche Literaturangaben. Ferner graduate students in advanced courses of numerical 122) werden oft sehr aufschlussreiche Hinweise auf die 978-0-387-97195-7 Funktionentheorie mehrerer Veränderlicher gegeben. Die vielen Beispiele und Übungsaufgaben bilden eine springer.com Analysis 21 wertvolle Ergänzung der brillant dargelegten Theorie. cal simulations of transition to turbulence and linear Der Rezensent bedauert, dass ihm nicht schon als Stu- analysis based on the initial-value problem. dent ein derartig umfassendes, qualitativ hochstehen- More on www.springer.com/978-0-387-98985-3 des Lehrbuch zur Verfügung stand."Monatshefte für Mathematik Available 2001. XIII, 556 p. 206 illus. (Applied Mathematical Sciences, More on www.springer.com/978-3-540-40432-3 142) Available 978-0-387-98985-3

2007. XVIII, 383 S. 19 Abb. (Springer-Lehrbuch, ) 978-3-540-40432-3

W. Schirotzek E. Zeidler Nonsmooth Analysis Applied Functional Analysis Applications to Mathematical Physics The book treats various concepts of generalized derivatives and subdifferentials in normed spaces, The first part of a self-contained, elementary text- their geometric counterparts (tangent and normal book, combining linear functional analysis, nonlin- cones) and their application to optimization prob- ear functional analysis, numerical functional analysis, lems. It starts with the subdifferential of convex anal- and their substantial applications with each other. ysis, passes to corresponding concepts for locally As such, the book addresses undergraduate students Lipschitz continuous functions and finally presents and beginning graduate students of mathematics, subdifferentials for general lower semicontinuous physics, and engineering who want to learn how func- functions. All basic tools are presented where they tional analysis elegantly solves mathematical prob- are needed; this concerns separation theorems, varia- lems which relate to our real world. Applications K. Saxe tional and extremal principles as well as relevant parts concern ordinary and partial differential equations, of multifunction theory. The presentation is rigorous, the method of finite elements, integral equations, Beginning Functional Analysis with detailed proofs. Each chapter ends with biblio- special functions, both the Schroedinger approach and the Feynman approach to quantum physics, and The unifying approach of functional analysis is to graphic notes and exercises. quantum statistics. As a prerequisite, readers should view functions as points in some abstract vector space More on www.springer.com/978-3-540-71332-6 be familiar with some basic facts of calculus. The sec- and the differential and integral operators relating Available ond part has been published under the title, Applied these points as linear transformations on these spaces. Functional Analysis: Main Principles and Their Appli- The author presents the basics of functional analy- 2007. XII, 378 p. 31 illus. (Universitext, ) cations. sis with attention paid to both expository style and 978-3-540-71332-6 technical detail, while getting to interesting results as More on www.springer.com/978-0-387-94442-5 quickly as possible. The book is accessible to students Available who have completed first courses in linear algebra and real analysis. Topics are developed in their historical 1995. XXIX, 516 p. 56 illus. (Applied Mathematical context, with accounts of the past ¿ including biogra- Sciences, 108) phies ¿ appearing throughout the text. The book offers 978-0-387-94442-5 suggestions and references for further study, and many exercises. Karen Saxe is Associate Professor of Mathematics at Macalester College in St. Paul, Min- nesota. She received her Ph.D. from the University of Oregon. Before joining the faculty at Macalester, she held a two-year FIPSE post-doctoral position at St. Olaf College in Northfield, Minnesota. She currently serves on the editorial board of the MAA's College Mathematics Journal. This is her first book. P.J. Schmid, D.S. Henningson More on www.springer.com/978-0-387-95224-6 Available Stability and Transition in Shear Flows 2002. XII, 197 p. 14 illus. (Undergraduate Texts in Mathematics, ) A detailed look at some of the more modern issues of V.A. Zorich 978-0-387-95224-6 hydrodynamic stability, including transient growth, eigenvalue spectra, secondary instability. It presents analytical results and numerical simulations, linear Mathematical Analysis II and selected nonlinear stability methods. By includ- This softcover edition of a very popular two-volume ing classical results as well as recent developments in work presents a thorough first course in analysis, the field of hydrodynamic stability and transition, the leading from real numbers to such advanced topics book can be used as a textbook for an introductory, as differential forms on manifolds, asymptotic meth- graduate-level course in stability theory or for a spe- ods, integral transforms, and distributions. Espe- cial-topics fluids course. It is equally of value as a ref- cially notable in this course is the clearly expressed erence for researchers in the field of hydrodynamic orientation toward the natural sciences and its infor- stability theory or with an interest in recent develop- mal exploration of the essence and the roots of the ments in fluid dynamics. Stability theory has seen a basic concepts and theorems of calculus. Clarity of rapid development over the past decade, this book exposition is matched by a wealth of instructive exer- includes such new developments as direct numeri- cises, problems and fresh applications to areas seldom touched on in real analysis books. The second volume 22 Applications of Mathematics springer.com expounds classical analysis as it is today, as a part of leading from real numbers to such advanced topics as Applications of Mathematics unified mathematics, and its interactions with mod- differential forms on manifolds, asymptotic methods, ern mathematical courses such as algebra, differential Fourier, Laplace, and Legendre transforms, elliptic geometry, differential equations, complex and func- functions and distributions. Especially notable in this tional analysis. The book provides a firm foundation course is the clearly expressed orientation toward the for advanced work in any of these directions. natural sciences and its informal exploration of the essence and the roots of the basic concepts and theo- More on www.springer.com/978-3-540-87453-9 rems of calculus. Clarity of exposition is matched by Available a wealth of instructive exercises, problems and fresh applications to areas seldom touched on in real anal- 2004. XV, 688 p. (Universitext, ) ysis books. The first volume constitutes a complete 978-3-540-87453-9 course on one-variable calculus along with the multivariable differential calculus elucidated in an up-today, clear manner, with a pleasant geometric flavor. More on www.springer.com/978-3-540-40386-9 Available J. Bergh, F. Ekstedt, M. Lindberg

2004. XVIII, 578 p. (Universitext, ) Wavelets mit Anwendungen in 978-3-540-40386-9 Signal- und Bildverarbeitung Dieses Buch ist eine „Interpolation“ zwischen einer Monographie und einem Handbuch. Angesprochen sind Leser, die sich mit den grundlegenden mathematischen Ideen und Techniken der Wavelets vertraut machen möchten, sich aber gleichzeitig auch einen V.A. Zorich Überblick darüber verschaffen wollen, wie die Theorie derzeit angewendet wird. Das Buch ist für Leser mit Mathematical Analysis I den Vorkenntnissen höherer Studienjahre gedacht: vorausgesetzt werden Kenntnisse über Anwendun- This softcover edition of a very popular two-volume gen der linearen Algebra, der Fourierreihen und der work presents a thorough first course in analysis, Fourierschen Integrale. Zum besseren Verständnis leading from real numbers to such advanced topics as der Theorie sind aber auch weitere Kenntnisse differential forms on manifolds, asymptotic methods, wünschenswert. Eine allzu übertriebene mathema- Fourier, Laplace, and Legendre transforms, elliptic tische Präzision stellt jedoch zu starke Anforderun- V.A. Zorich functions and distributions. Especially notable in this gen an die Leser, an die sich dieses Buch richtet. Die course is the clearly expressed orientation toward the Lösung dieses Dilemmas ist ein Kompromiss: Die natural sciences and its informal exploration of the Mathematical Analysis II Autoren verzichten auf einige mathematische Details essence and the roots of the basic concepts and theo- The second volume expounds classical analysis as it is und verweisen stattdessen auf weiterführende Darstel- rems of calculus. Clarity of exposition is matched by today, as a part of unified mathematics, and its inter- lungen. Ziel des Buches ist, die Schlüsselideen und a wealth of instructive exercises, problems and fresh actions with modern mathematical courses such as die grundlegenden Techniken in den Mittelpunkt zu applications to areas seldom touched on in real anal- algebra, differential geometry, differential equations, rücken. ysis books. The first volume constitutes a complete complex and functional analysis. The book provides More on www.springer.com/978-3-540-49011-1 course on one-variable calculus along with the multi- a firm foundation for advanced work in any of these variable differential calculus elucidated in an up-to- directions. Available day, clear manner, with a pleasant geometric flavor. More on www.springer.com/978-3-540-40633-4 2007. XII, 207 S. 85 Abb. (Springer-Lehrbuch More on www.springer.com/978-3-540-87451-5 Available Masterclass, ) Available 978-3-540-49011-1 2004. XV, 688 p. (Universitext, ) 2004. XVIII, 578 p. (Universitext, ) 978-3-540-40633-4 978-3-540-87451-5

G.S. Chirikjian Stochastic Models, Information V.A. Zorich Theory, and Lie Groups, Volume 1 Mathematical Analysis I Classical Results and Geometric Methods This softcover edition of a very popular two-volume The subjects of stochastic processes, information the- work presents a thorough first course in analysis, ory, and Lie groups are usually treated separately from springer.com Applications of Mathematics 23 each other. This unique two-volume set presents these bolic conservation laws from the basic theory up to cusses possible extensions of the theory. Exercises topics in a unified setting, thereby building bridges the research front. The approach is constructive, and are provided at the end of each chapter. Software for between fields that are rarely studied by the same the mathematical approach using front tracking can examples and algorithms are available on the author's individuals. Unlike the many excellent formal treat- be applied directly as a numerical method. After a website. ments available for each of these subjects individually, short introduction on the fundamental properties of More on www.springer.com/978-0-387-00893-6 the emphasis in both of these volumes is on the use of conservation laws, the theory of scalar conservation stochastic, geometric, and group-theoretic concepts laws in one dimension is treated in detail, showing Available in the modeling of physical phenomena. Volume 1 the stability of the Cauchy problem using front track- establishes the geometric and statistical foundations ing. The extension to multidimensional scalar conser- 2004. XX, 526 p. 170 illus. (Interdisciplinary Applied required to understand the fundamentals of contin- vation laws is obtained using dimensional splitting. Mathematics, 26) 978-0-387-00893-6 uous-time stochastic processes, differential geome- Inhomogeneous equations and equations with diffu- try, and the probabilistic foundations of information sive terms are included as well as a discussion of con- theory. Volume 2 delves deeper into relationships vergence rates. The classical theory of Kruzkov and between these topics, including stochastic geometry, Kuznetsov is covered. Systems of conservation laws geometric aspects of the theory of communications in one dimension are treated in detail, starting with and coding, multivariate statistical analysis, and error the solution of the Riemann problem. Solutions of the propagation on Lie groups. Key features and topics of Cauchy problem are proved to exist in a constructive Volume 1: * The author reviews stochastic processes manner using front tracking, amenable to numeri- and basic differential geometry in an accessible way cal computations. The book includes a detailed dis- for applied mathematicians, scientists, and engineers. cussion of the very recent proof of wellposedness of * Extensive exercises and motivating examples make the Cauchy problem for one-dimensional hyperbolic the work suitable as a textbook for use in courses that conservation laws. The book includes a chapter on emphasize applied stochastic processes or differen- traditional finite difference methods for hyperbolic tial geometry. * The concept of Lie groups as con- conservation laws with error estimates and a section tinuous sets of symmetry operations is introduced. * on measure valued solutions. Extensive examples are The Fokker–Planck Equation for diffusion processes given, and many exercises are included with hints and H. Ockendon, J.R. Ockendon in Euclidean space and on differentiable manifolds answers. Additional background material not easily is derived in a way that can be understood by non- available elsewhere is given in appendices. Waves and Compressible Flow specialists. * The concrete presentation style makes More on www.springer.com/978-3-540-43289-0 it easy for readers to obtain numerical solutions for This book covers compressible flow however the their own problems; the emphasis is on how to calcu- Available authors also show how wave phenomena in electro- late quantities rather than how to prove theorems. * magnetism and solid mechanics can be treated using A self-contained appendix provides a comprehensive 2002. XII, 364 p. 40 illus. (Applied Mathematical similar mathematical methods. It caters to the needs review of concepts from linear algebra, multivariate Sciences, 152) of the modern student by providing the tools nec- 978-3-540-43289-0 calculus, and systems of ordinary differential equa- essary for a mathematical analysis of most kinds of tions. Stochastic Models, Information Theory, and Lie waves liable to be encountered in modern science and Groups will be of interest to advanced undergraduate technology. At the same time emphasis is laid on the and graduate students, researchers, and practitioner- physical background and modeling that requires these s working in applied mathematics, the physical sci- tools. ences, and engineering. More on www.springer.com/978-0-387-40399-1 More on www.springer.com/978-0-8176-4802-2 Available Available 2004. IX, 188 p. 60 illus. (Texts in Applied 2009. XXII, 383 p. 13 illus. (Applied and Numerical Mathematics, 47) Harmonic Analysis, ) 978-0-387-40399-1 978-0-8176-4802-2

Y. Ma, S. Soatto, J. Kosecká, S.S. Sastry An Invitation to 3-D Vision From Images to Geometric Models This book gives senior undergraduate and beginning graduate students and researchers in computer vision, applied mathematics, computer graphics, and robotics a self-contained introduction to the geometry of 3D vision; that is the reconstruction of 3D models of objects from a collection of 2D images. Follow- ing a brief introduction, Part I provides background G. Rempala, J. Wesolowski H. Holden, N.H. Risebro materials for the rest of the book. The two fundamental transformations, namely rigid body motion Symmetric Functionals on Front Tracking for Hyperbolic and perspective projection are introduced and image Conservation Laws formation and feature extraction discussed. Part II Random Matrices and Random covers the classic theory of two view geometry based Matchings Problems Hyperbolic conservation laws are central in the the- on the so-called epipolar constraint. Part III shows ory of nonlinear partial differential equations, and that a more proper tool for studying the geometry of This book is drawn from the recent literature on the in many applications in science and technology. In multiple views is the so- called rank considtion on asymptotic behavior of random permanents and ran- this book the reader is given a detailed, rigorous, and the multiple view matrix. Part IV develops practical dom matchings. In particular, the authors present an self-contained presentation of the theory of hyper- reconstruction algorithms step by step as well as dis- elegant connection between the problem of an asymp- 24 Approximations and Expansions springer.com totic behavior for a certain family of functionals on tages of SCEM are discussed in comparison with the random matrices and the asymptotic results in the standard method of matched asymptotic expansions. classical theory of the so-called U-statistics -- objects More on www.springer.com/978-3-540-31002-0 of fundamental importance in the non-parametric statistical inference. This book is self-contained and Available accessible to any mathematics, statistics or engineering graduate student who has taken basic introduc- 2006. XII, 396 p. 59 ill. (Mathématiques et tory courses in probability theory and mathematical Applications, 56) 978-3-540-31002-0 statistics. Dr.Grzegorz A. Rempala is a Professor of Statistics in the Department of Mathematics at the University of Louisville in Louisville, KY. Dr. Jacek Wesolowski is a Professor of Mathematics and Asso- U. Diwekar ciate Dean for Research at the Faculty of Mathematics and Information Science, Warsaw University of Tech- Calculus of Variations and Introduction to Applied nology in Warsaw, Poland. The volume is a result Optimal Control; Optimization of the authors’ collaborative effort initiated at the Optimization IMA during the Institute's 2003/04 annual program This text presents a multi-disciplined view of option "Probability and Statistics in Complex Systems: mization, providing students and researchers with a Genomics, Networks, and Finance Engineering". thorough examination of algorithms, methods, and More on www.springer.com/978-0-387-75145-0 tools from diverse areas of optimization without Available introducing excessive theoretical detail. This second edition includes additional topics, including global 2008. XIV, 184 p. (The IMA Volumes in Mathematics and its optimization and a real-world case study using im- Applications, 147) portant concepts from each chapter. Key Features: 978-0-387-75145-0 Provides well-written self-contained chapters, including problem sets and exercises, making it ideal for the classroom setting; Introduces applied optimization to the hazardous waste blending problem; Explores linear programming, nonlinear programming, discrete Approximations and optimization, global optimization, optimization under J. Bonnans, A. Shapiro Expansions uncertainty, multi-objective optimization, optimal control and stochastic optimal control; Includes an Perturbation Analysis of extensive bibliography at the end of each chapter and J. Cousteix, J. Mauss Optimization Problems an index; GAMS files of case studies for Chapters 2, 3, 4, 5, and 7 are linked to http://www.springer.com/ Analyse asymptotique et couche A presentation of general results for discussing local math/book/978-0-387-76634-8; Solutions manual optimality and computation of the expansion of value available upon adoptions. Introduction to Applied limite function and approximate solution of optimization Optimization is intended for advanced undergraduate problems, followed by their application to various Le but du livre est de donner aux enseignants et aux and graduate students and will benefit scientists from fields, from physics to economics. The book is thus diverse areas, including engineers. étudiants (à partir de Bac+4) en mathématiques an opportunity for popularizing these techniques appliquées et en mécanique des fluides un outil among researchers involved in other sciences, includ- More on www.springer.com/978-0-387-76634-8 d'enseignement et d'apprentissage illustré par cin- ing users of optimization in a wide sense, in mechan- Available quante problèmes accompagnés de leur correction ics, physics, statistics, finance and economics. Of use détaillée. Ce livre présente une nouvelle méthode to research professionals, including graduate students 2008. XXVI, 292 p. 100 illus. (Springer Optimization d'analyse asymptotique pour des problèmes de at an advanced level. and Its Applications, 22) "couche limite". Celle-ci est appelée MASC "Méthode 978-0-387-76634-8 des Approximations Successives Complémentaires". More on www.springer.com/978-0-387-98705-7 La première moitié du livre est consacrée, outre la Available présentation de la MASC, à ordonner les connais- 2000. XVIII, 601 p. (Springer Series in Operations Research sances nécessaires à l'analyse asymptotique et à don- and Financial Engineering, ) ner les clés permettant la compréhension de ce qu'est 978-0-387-98705-7 un problème dit de "couche limite" et des méthodes permettant de construire une approximation. La seconde partie est consacrée à l'application de la MASC en mécanique des fluides et à la comparaison avec les méthodes plus traditionnelles issues de la célèbre MDAR, "Méthode des Développements Asympto- tiques Raccordés". The book presents a new method of asymptotic analysis of boundary layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general presentation of the tools of asymptotic analysis. This G.E. Dullerud, F. Paganini part gives also the keys to understand a boundary layer problem and of the methods to construct an A Course in Robust Control Theory approximation.The second part is devoted to SCEM A Convex Approach and its applications in fluid mechanics. The advan- During the 90s robust control theory has seen major advances and achieved a new maturity, centered around the notion of convexity. The goal of this book is to give a graduate-level course on this theory that emphasizes these new developments, but at the same springer.com Calculus of Variations and Optimal Control; Optimization 25 time conveys the main principles and ubiquitous tools cialists, collecting results that so far have not appeared at the heart of the subject. Its pedagogical objectives in books. are to introduce a coherent and unified framework for More on www.springer.com/978-3-540-56850-6 studying the theory, to provide students with the control-theoretic background required to read and con- Available tribute to the research literature, and to present the 1993. XVII, 444 p. 113 illus. (Grundlehren der main ideas and demonstrations of the major results. mathematischen Wissenschaften, 305) The book will be of value to mathematical researchers 978-3-540-56850-6 and computer scientists, graduate students planning to do research in the area, and engineering practitioners requiring advanced control techniques. More on www.springer.com/978-0-387-98945-7 M. Hinze, R. Pinnau, M. Ulbrich, S. Ulbrich Available Optimization with PDE 2000. XX, 444 p. 36 illus. (Texts in Applied Constraints Mathematics, 36) 978-0-387-98945-7 This book presents a modern introduction of pde constrained optimization. It provides a precise functional analytic treatment via optimality conditions and a state-of-the-art, non-smooth algorithmical framework. Furthermore, new structure-exploiting discrete concepts and large scale, practically relevant applications are presented. The main focus is J. Hiriart-Urruty, C. Lemaréchal on the algorithmical and numerical treatment of pde constrained optimization problems on the infinite Fundamentals of Convex Analysis dimensional level. A particular emphasis is on sim- This book is an abridged version of the two volumes ple constraints, such as pointwise bounds on controls "Convex Analysis and Minimization Algorithms I and and states. For these practically important situations, II" (Grundlehren der mathematischen Wissenschaften tailored Newton- and SQP-type solution algorithms Vol. 305 and 306), which presented an introduction are proposed and a general convergence framework to the basic concepts in convex analysis and a study is developed. This is complemented with the numeri- of convex minimization problems. The "backbone" cal analysis of structure-preserving Galerkin schemes M. Giaquinta, S. Hildebrandt of both volumes was extracted, some material deleted for optimization problems with elliptic and parabolic that was deemed too advanced for an introduction, equations. Finally, along with the optimization of or too closely related to numerical algorithms. Some Calculus of Variations II semiconductor devices and the optimization of glass The Hamiltonian Formalism exercises were included and finally the index has been cooling processes, two challenging applications of pde considerably enriched. The main motivation of the This long-awaited book by two of the foremost constrained optimization are presented. They demon- authors was to "light the entrance" of the monument researchers and writers in the field is the first part of a strate the scope of this emerging research field for Convex Analysis. This book is not a reference book treatise that covers the subject in breadth and depth, future engineering applications. to be kept on the shelf by experts who already know paying special attention to the historical origins, More on www.springer.com/978-1-4020-8838-4 the building and can find their way through it; it is far partly in applications, e.g. from geometrical optics, of Available more a book for the purpose of learning and teaching. parts of the theory. A variety of aids to the reader is More on www.springer.com/978-3-540-42205-1 provided: besides the very detailed table of contents, 2009. XI, 270 p. 26 illus., 19 in color. (Mathematical an introduction to each chapter, section and subsec- Modelling: Theory and Applications, 23) Available tion, an overview of the relevant literature (in Vol. 2) 978-1-4020-8838-4 plus the references in the Scholia to each chapter, in 2001. X, 263 p. 66 illus. (Grundlehren Text Editions, ) the (historical) footnotes, and in the bibliography, and 978-3-540-42205-1 finally an index of the examples used throughout the book. Both individually and collectively these volumes J. Hiriart-Urruty, C. Lemarechal have already become standard references. More on www.springer.com/978-3-540-57961-8 Convex Analysis and Minimization Available Algorithms 1996. XXIX, 652 p. 82 illus. (Grundlehren der Part 1: Fundamentals mathematischen Wissenschaften, 311) 978-3-540-57961-8 Convex Analysis may be considered as a refinement of standard calculus, with equalities and approximations replaced by inequalities. As such, it can easily be integrated into a graduate study curriculum. Mini- mization algorithms, more specifically those adapted to non-differentiable functions, provide an immediate application of convex analysis to various fields related D. Jungnickel to optimization and operations research. These two topics making up the title of the book, reflect the two Optimierungsmethoden origins of the authors, who belong respectively to the academic world and to that of applications. Part I can Eine Einführung be used as an introductory textbook (as a basis for Das vorliegende Buch ist eine Einführung in die courses, or for self-study); Part II continues this at a Grundlagen der mathematischen Optimierung, die higher technical level and is addressed more to spe- sich dadurch auszeichnet, dass diskrete und kon- tinuierliche Methoden integriert behandelt werden. Es wendet sich an Studenten der Mathematik, der 26 Calculus of Variations and Optimal Control; Optimization springer.com

Wirtschaftswissenschaften und der Informatik, die used directly or as a building block in other solution convergence, set-valued mappings, epi-convergence, beginnen, etwas über Optimierung zu lernen. In der algorithms. duality, maximal monotone mappings, second-order Neuauflage sind ein ausführliches Kapitel über lin- More on www.springer.com/978-1-4020-7332-8 subderivatives, measurable selections and normal eare Programme sowie ein Kapitel über allgemeine integrands. The changes in this 3rd printing mainly Konvergenzsätze und ein Anhang zur affinen Geome- Available concern various typographical corrections, and ref- trie hinzugekommen. Im Übrigen wurde der bere- 2003. 352 p. (International Series in Operations Research & erence omissions that came to light in the previous its vorliegende Text gründlich überarbeitet: Neben Management Science, 61) printings. Many of these reached the authors' notice der Korrektur etlicher Druckfehler und kleinerer 978-1-4020-7332-8 through their own re-reading, that of their students Ungenauigkeiten wurden einige Beweise völlig and a number of colleagues mentioned in the Pref- umgeschrieben und mehr motivierende Bemerkun- ace. The authors also included a few telling examples gen sowie weitere Beispiele eingefügt. Insgesamt hat as well as improved a few statements, with slightly sich damit der Umfang des Buches etwa verdoppelt. weaker assumptions or have strengthened the conclusions in a couple of instances. More on www.springer.com/978-3-540-76789-3 Available More on www.springer.com/978-3-540-62772-2 Available 2008. XIV, 277 S. (Springer-Lehrbuch, ) 1998. XIII, 734 p. 151 illus. (Grundlehren der 978-3-540-76789-3 mathematischen Wissenschaften, 317) 978-3-540-62772-2

I. Maros B.S. Mordukhovich Computational Techniques of the Variational Analysis and Simplex Method Generalized Differentiation II Linear Programming (LP) is perhaps the most fre- Applications quently used optimization technique. One of the reasons for its wide use is that very powerful solution Comprehensive and state-of-the art study of the basic algorithms exist for linear optimization. Computer concepts and principles of variational analysis and programs based on either the simplex or interior generalized differentiation in both finite-dimensional point methods are capable of solving very large-scale and infinite-dimensional spaces Presents numerous problems with high reliability and within reasonable applications to problems in the optimization, equi- O. Scherzer, M. Grasmair, H. Grossauer, M. Haltmeier, F. time. Model builders are aware of this and often try libria, stability and sensitivity, control theory, eco- Lenzen to formulate real-life problems within this frame- nomics, mechanics, etc. work to ensure they can be solved efficiently. It is also More on www.springer.com/978-3-540-25438-6 Variational Methods in Imaging true that many real-life optimization problems can Available This book is devoted to the study of variational meth- be formulated as truly linear models and also many ods in imaging. The presentation is mathemati- others can well be approximated by linearization. 2006. XXII, 612 p. (Grundlehren der mathematischen cally rigorous and covers a detailed treatment of the The two main methods for solving LP problems are Wissenschaften, 331) approach from an inverse problems point of view. the variants of the simplex method and the interior 978-3-540-25438-6 Key Features: - Introduces variational methods with point methods (IPMs). It turns out that both vari- motivation from the deterministic, geometric, and ants have their role in solving different problems. It stochastic point of view - Bridges the gap between reg- has been recognized that, since the introduction of ularization theory in image analysis and in inverse the IPMs, the efficiency of simplex based solvers has problems - Presents case examples in imaging to illus- increased by two orders of magnitude. This increased trate the use of variational methods e.g. denoising, efficiency can be attributed to the following: (1) the- thermoacoustics, computerized tomography - Dis- oretical developments in the underlying algorithms, cusses link between non-convex calculus of variations, (2) inclusion of results of computer science, (3) using morphological analysis, and level set methods - Anal- the principles of software engineering, and (4) tak- yses variational methods containing classical analysis ing into account the state-of-the-art in computer of variational methods, modern analysis such as G- technology. Theoretically correct algorithms can be norm properties, and non-convex calculus of varia- implemented in many different ways, but the perfor- tions - Uses numerical examples to enhance the the- mance is dependent on how the implementation is ory This book is geared towards graduate students done. The success is based on the proper synthesis of and researchers in applied mathematics. It can serve the above mentioned (1-4) components. Computa- R.T. Rockafellar, R.J. Wets as a main text for graduate courses in image process- tional Techniques of the Simplex Method is a system- ing and inverse problems or as a supplemental text for atic treatment focused on the computational issues Variational Analysis courses on regularization. Researchers and computer of the simplex method. It provides a comprehensive From its origins in the minimization of integral func- scientists in the area of imaging science will also find coverage of the most important and successful algo- tionals, the notion of 'variations' has evolved greatly this book useful. rithmic and implementation techniques of the sim- in connection with applications in optimization, equi- plex method. It is a unique source of essential, never More on www.springer.com/978-0-387-30931-6 librium, and control. It refers not only to constrained discussed details of algorithmic elements and their movement away from a point, but also to modes of Available implementation. On the basis of the book the reader perturbation and approximation that are best describ- will be able to create a highly advanced implemen- able by 'set convergence', variational convergence 2009. XIV, 322 p. 72 illus. (Applied Mathematical tation of the simplex method which, in turn, can be Sciences, 167) of functions and the like. This book develops a uni- 978-0-387-30931-6 fied framework and, in finite dimension, provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set- springer.com Combinatorics 27

Combinatorics Mathematics, organized jointly with the University of Memphis. More on www.springer.com/978-3-540-69394-9 Available 2009. 600 p. (Bolyai Society Mathematical Studies, 18) 978-3-540-69394-9

M. Beck, S. Robins Computing the Continuous M.W. Baldoni, C. Ciliberto, G. Piacentini Cattaneo Discretely Elementary Number Theory, Integer-point Enumeration in Polyhedra This textbook illuminates the field of discrete math- Cryptography and Codes ematics with examples, theory, and applications of In this volume one finds basic techniques from alge- the discrete volume of a polytope. The authors have bra and number theory (e.g. congruences, unique fac- weaved a unifying thread through basic yet deep ideas C. Godsil, G.F. Royle torization domains, finite fields, quadratic residues, in discrete geometry, combinatorics, and number primality tests, continued fractions, etc.) which in theory. We encounter here a friendly invitation to Algebraic Graph Theory recent years have proven to be extremely useful for the field of "counting integer points in polytopes", applications to cryptography and coding theory. Both and its various connections to elementary finite Algebraic graph theory is a fascinating subject con- cryptography and codes have crucial applications in Fourier analysis, generating functions, the Frobenius cerned with the interplay between algebra and graph our daily lives, and they are described here, while the coin-exchange problem, solid angles, magic squares, theory. Algebraic tools can be used to give surpris- complexity problems that arise in implementing the Dedekind sums, computational geometry, and more. ing and elegant proofs of graph theoretic facts, and related numerical algorithms are also taken into due With 250 exercises and open problems, the reader there are many interesting algebraic objects associated account. Cryptography has been developed in great feels like an active participant. with graphs. The authors take an inclusive view of the subject, and present a wide range of topics. These detail, both in its classical and more recent aspects. More on www.springer.com/978-0-387-29139-0 In particular public key cryptography is extensively range from standard classics, such as the characteri- Available discussed, the use of algebraic geometry, specifically zation of line graphs by eigenvalues, to more unusual of elliptic curves over finite fields, is illustrated, and areas such as geometric embeddings of graphs and 2007. XVIII, 226 p. 33 illus. (Undergraduate Texts in a final chapter is devoted to quantum cryptography, the study of graph homomorphisms. The authors' Mathematics, ) goal has been to present each topic in a self-contained which is the new frontier of the field. Coding theory is 978-0-387-29139-0 not discussed in full; however a chapter, sufficient for fashion, presenting the main tools and ideas, with a good introduction to the subject, has been devoted an emphasis on their use in understanding concrete to linear codes. Each chapter ends with several com- examples. A substantial proportion of the book cov- plements and with an extensive list of exercises, the ers topics that have not appeared in book form before, solutions to most of which are included in the last and as such it provides an accessible introduction to chapter. Though the book contains advanced mate- the research literature and to important open ques- rial, such as cryptography on elliptic curves, Goppa tions in modern algebraic graph theory. This book is codes using algebraic curves over finite fields, and the primarily aimed at graduate students and researchers recent AKS polynomial primality test, the authors' in graph theory, combinatorics, or discrete mathemat- objective has been to keep the exposition as self-conics in general. However, all the necessary graph theory tained and elementary as possible. Therefore the book is developed from scratch, so the only pre-requisite will be useful to students and researchers, both in for reading it is a first course in linear algebra and a theoretical (e.g. mathematicians) and in applied sci- small amount of elementary group theory. It should ences (e.g. physicists, engineers, computer scientists, be accessible to motivated upper-level undergradu- etc.) seeking a friendly introduction to the important B. Bollobas, R. Kozma, D. Miklos ates. Chris Godsil is a full professor in the Department subjects treated here. The book will also be useful for of Combinatorics and Optimization at the Univer- teachers who intend to give courses on these topics. Handbook of Large-Scale Random sity of Waterloo. His main research interests lie in the interactions between algebra and combinatorics, in More on www.springer.com/978-3-540-69199-0 Networks particular the application of algebraic techniques to Available This handbook describes advances in large scale net- graphs, designs and codes. He has published more work studies that have taken place in the past 5 years than 70 papers in these areas, is a founding editor of 2009. XVI, 522 p. 10 illus. (Universitext, ) since the publication of the Handbook of Graphs and "The Journal of Algebraic Combinatorics" and is the 978-3-540-69199-0 Networks in 2003. It covers all aspects of large-scale author of the book "Algebraic Combinatorics". Gor- networks, including mathematical foundations and don Royle teaches in the Department of Computer rigorous results of random graph theory, modeling Science & Software Engineering at the University of and computational aspects of large-scale networks, Western Australia. His main research interests lie in as well as areas in physics, biology, neuroscience, the application of computers to combinatorial prob- sociology and technical areas. Applications range lems, in particular the cataloguing, enumeration and from microscopic to mesoscopic and macroscopic investigation of graphs, designs and finite geometries. models.The book is based on the material of the NSF workshop on Large-scale Random Graphs held in Budapest in 2006, at the Alfréd Rényi Institute of 28 Combinatorics springer.com

He has published more than 30 papers in graph the- pigeonhole principle. • Expanded coverage of Pólya the text). Moreover, recent developments have been ory, design theory and finite geometry. Theory to include de Bruijn’s method for counting discussed and referenced, in particular for the trav- arrangements when a second symmetry group acts on elling salesman problem. The presentation has been More on www.springer.com/978-0-387-95241-3 the set of allowed colors. • Topics in combinatorial improved in many places (for instance, in the chapters Available geometry, including Erdos and Szekeres’ development on shortest paths and on colorings), and a number of Ramsey Theory in a problem about convex poly- of proofs have been reorganized, making them more 2001. XIX, 439 p. 120 illus. (Graduate Texts in gons determined by sets of points. • Expanded cov- precise or more transparent. Mathematics, 207) erage of stable marriage problems, and new sections 978-0-387-95241-3 More on www.springer.com/978-3-540-72779-8 on marriage problems for infinite sets, both countable and uncountable. • Numerous new exercises through- Available out the book. About the First Edition: ". . . this is what a textbook should be! The book is comprehensive 2008. XX, 650 p. 209 illus. (Algorithms and without being overwhelming, the proofs are elegant, Computation in Mathematics, 5) 978-3-540-72779-8 clear and short, and the examples are well picked." — Ioana Mihaila, MAA Reviews More on www.springer.com/978-0-387-79710-6 Available

2008. XV, 381 p. 165 illus. (Undergraduate Texts in Mathematics, ) 978-0-387-79710-6 E. Gyori, G.O. Katona, L. Lovász Horizons of Combinatorics Hungarian mathematics has always been known for discrete mathematics, including combinatorial number theory, set theory and recently random structures, B. Korte, J. Vygen and combinatorial geometry as well. The recent volume contains high level surveys on these topics with Combinatorial Optimization authors mostly being invited speakers for the confer- Theory and Algorithms ence "Horizons of Combinatorics" held in Balatonal- madi, Hungary in 2006. The collection gives a very This comprehensive textbook on combinatorial opti- good overview of recent trends and results in a large mization places special emphasis on theoretical results part of combinatorics and related topics, and offers an and algorithms with provably good performance, in interesting reading for experienced specialists as well D. Jungnickel contrast to heuristics. It has arisen as the basis of sev- as to young researchers and students. eral courses on combinatorial optimization and more Graphs, Networks and Algorithms special topics at graduate level. It contains complete More on www.springer.com/978-3-540-77199-9 but concise proofs, also for many deep results, some Available From the reviews of the previous editions ".... The of which did not appear in a textbook before. Many 2008. 280 p. (Bolyai Society Mathematical Studies, 17) book is a first class textbook and seems to be indis- very recent topics are covered as well, and many ref- 978-3-540-77199-9 pensable for everybody who has to teach combina- erences are provided. Thus this book represents the torial optimization. It is very helpful for students, state of the art of combinatorial optimization. This teachers, and researchers in this area. The author fourth edition is again significantly extended, most finds a striking synthesis of nice and interesting math- notably with new material on linear programming, ematical results and practical applications. ... the the network simplex algorithm, and the max-cut author pays much attention to the inclusion of well- problem. Many further additions and updates are chosen exercises. The reader does not remain helpless; included as well. From the reviews of the previous solutions or at least hints are given in the appendix. editions: "This book on combinatorial optimization Except for some small basic mathematical and algo- is a beautiful example of the ideal textbook." Opera- rithmic knowledge the book is self-contained. ..." tions Research Letters 33 (2005), p.216-217 "The sec- K.Engel, Mathematical Reviews 2002 The substantial ond edition (with corrections and many updates) of development effort of this text, involving multiple edi- this very recommendable book documents the rele- tions and trailing in the context of various workshops, vant knowledge on combinatorial optimization and university courses and seminar series, clearly shows records those problems and algorithms that define through in this new edition with its clear writing, this discipline today. To read this is very stimulat- J. Harris, J.L. Hirst, M. Mossinghoff good organisation, comprehensive coverage of essen- ing for all the researchers, practitioners, and students tial theory, and well-chosen applications. The proofs interested in combinatorial optimization." OR News Combinatorics and Graph Theory of important results and the representation of key 19 (2003), p.42 "... has become a standard textbook in algorithms in a Pascal-like notation allow this book the field." Zentralblatt MATH 1099.90054 This book covers a wide variety of topics in combi- to be used in a high-level undergraduate or low-level More on www.springer.com/978-3-540-71843-7 natorics and graph theory. It includes results and graduate course on graph theory, combinatorial opti- problems that cross subdisciplines, emphasizing rela- mization or computer science algorithms. The well- Available tionships between different areas of mathematics. In worked solutions to exercises are a real bonus for self addition, recent results appear in the text, illustrat- study by students. The book is highly recommended. 2008. XVIII, 627 p. 77 illus. (Algorithms and ing the fact that mathematics is a living discipline. P .B. Gibbons, Zentralblatt für Mathematik 1061, 2005 Combinatorics, 21) The second edition includes many new topics and The third edition of this standard textbook contains 978-3-540-71843-7 features: • New sections in graph theory on distance, additional material: two new application sections (on Eulerian trails, and Hamiltonian paths. • New mate- graphical codes and their decoding) and about two rial on partitions, multinomial coefficients, and the dozen further exercises (with solutions, as throughout springer.com Combinatorics 29

maximum degree Delta has a Delta+C total colouring; Johansson's proof that a triangle free graph has a O(Delta over log Delta) colouring; algorithmic variants of the Local Lemma which permit the efficient construction of many optimal and near-optimal colourings.This begins with a gentle introduction to the probabilistic method and will be useful to researchers and graduate students in graph theory, discrete mathematics, theoretical computer science and probability. More on www.springer.com/978-3-540-42139-9 L. Lovász, J. Pelikan, K. Vesztergombi Available G.E. Martin 2002. XIV, 326 p. 19 illus. (Algorithms and Combinatorics, Diskrete Mathematik 23) Counting: The Art of Enumerative 978-3-540-42139-9 Die diskrete Mathematik ist im Begriff, zu einem der wichtigsten Gebiete der mathematischen Forschung Combinatorics zu werden mit Anwendungen in der Kryptographie, Counting: The Art of Enumerative Combinatorics der linearen Programmierung, der Kodierungsthe- provides an introduction to discrete mathematics that orie und Informatik. Dieses Buch richtet sich an addresses questions that begin, How many ways are P. Morris Studenten der Mathematik und Informatik, die ein there to...For example, ¿How many ways are there to Gefühl dafür entwickeln möchten, worum es in der- order a collection of 12 ice cream cones if 8 flavors are Introduction to Game Theory Mathematik geht, wobei Mathematik hilfreich sein available?¿ At the end of the book the reader should This is a textbook for a course in the theory of games. kann, und mit welcher Art Fragen sich Mathematiker be able to answer such nontrivial counting questions It is intended for advanced undergraduates and grad- auseinandersetzen. Die Autoren stellen eine Anzahl as, ¿How many ways are there to color the faces of a uate students in mathematics and other quantita- ausgewählter Ergebnisse und Methoden der diskreten cube if ¿k¿ colors are available with each face having tive disciplines, e.g., statistics, operations research, Mathematik vor, hauptsächlich aus den Bereichen exactly one color?¿ or ¿How many ways are there to etc. It treats the central topics in game theory and is Kombinatorik und Graphentheorie, teilweise aber stack ¿n¿ poker chips, each of which can be red, white, meant to give students a basis from which they can auch aus der Zahlentheorie, der Wahrscheinlichkeit- blue, or green, such that each red chip is adjacent to go on to more advanced topics. The subject matter is srechnung und der kombinatorischen Geometrie.Wo at least 1 green chip?¿ Since there are no prerequisites, approached in a mathematically rigorous way, but , immer es möglich war, haben die Autoren Beweise this book can be used for college courses in combina- within this constraint, an effort is made to keep it und Problemlösungen verwendet, um den Studenten torics at the sophomore level for either computer sci- interesting and lively. New definitions and topics are zu helfen, die Lösungen der Fragestellungen zu ver- ence or mathematics students. The first five chapters motivated as thoroughly as possible. The mathemati- stehen. Zusätzlich ist eine Vielzahl von Beispielen, have served as the basis for a graduate course for in- cal prerequisites for understanding the book are mod- Bildern und Übungsaufgaben über das Buch verteilt. service teachers. Chapter 8 introduces graph theory. László Lovász ist einer der Leiter der theoretischen est: basic probability together with a little calculus More on www.springer.com/978-0-387-95225-3 Forschungsabteilung der Microsoft Corporation. Er and linear algebra. Among others, two topics of great hat 1999 den Wolf-Preis sowie den Gödel-Preis für Available current interest are discussed in this book. The idea die beste wissenschaftliche Veröffentlichung in der of iterated Prisoner's Dilemma (super games) is con- Informatik erhalten. József Pelikán ist Professor am 2001. XI, 250 p. 56 illus. (Undergraduate Texts in sidered. It is specially of great interest to biologists, Institut für Algebra und Zahlentheorie der Eötvös Mathematics, ) sociologists and others who use it in studying the evo- Loránd Universität in Budapest. Katalin Veszter- 978-0-387-95225-3 lution of cooperative behavior both in nature and in gombi ist Senior Lecturer am Fachbereich Mathe- human society. Also covered are challenging game- matik der Universität von Washington in Seattle. playing computer programs. More on www.springer.com/978-3-540-20653-8 More on www.springer.com/978-0-387-94284-1 Available Available

2005. X, 362 S. (Springer-Lehrbuch, ) 1994. XXVI, 252 p. 44 illus. (Universitext, ) 978-3-540-20653-8 978-0-387-94284-1

M. Molloy, B. Reed Graph Colouring and the Probabilistic Method Over the past decade, many major advances have been made in the field of graph colouring via the probabilistic method. This monograph provides an acces- K. Murota sible and unified treatment of these results, using tools such as the Lovasz Local Lemma and Talagrand's Matrices and Matroids for concentration inequality.The topics covered include: Systems Analysis Kahn's proofs that the Goldberg-Seymour and List Colouring Conjectures hold asymptotically; a proof A matroid is an abstract mathematical structure that that for some absolute constant C, every graph of captures combinatorial properties of matrices. This 30 Commutative Rings and Algebras springer.com book offers a unique introduction to matroid the- Commutative Rings and a number of new proofs relating to Coxeter Trans- ory, emphasizing motivations from matrix theory and formations and the McKay Correspondence. They applications to systems analysis. This book serves also Algebras include ideas and formulae from a number of lumi- as a comprehensive presentation of the theory and naries including J. N. Bernstein, I. M. Gelfand and V. application of mixed matrices, developed primarily A. Ponomarev, as well as material from Coxeter and by the present author in the 1990's. A mixed matrix McKay themselves. Many other authors have mate- is a convenient mathematical tool for systems anal- rial published here too. One of the beautiful results ysis, compatible with the physical observation that in the representation theory of the finite groups is "fixed constants" and "system parameters" are to be McKay's theorem on a correspondence between rep- distinguished in the description of engineering sys- resentations of the binary polyhedral group of SU(2), tems. This book will be extremely useful to graduate and vertices of an extended simply-laced Dynkin dia- students and researchers in engineering, mathemat- gram. The Coxeter transformation is the main tool in ics and computer science. From the reviews: "…The the proof of the McKay correspondence, and is closely book has been prepared very carefully, contains a lot related to the Cartan matrix and Poincaré series. The of interesting results and is highly recommended for Coxeter functors constructed by Bernstein, Gelfand graduate and postgraduate students." András Recski, and Ponomarev play a distinguished role in the repre- Mathematical Reviews Clippings 2000m:93006 sentation theory of quivers. More on www.springer.com/978-3-642-03993-5 T. Lam More on www.springer.com/978-3-540-77398-6 Available Exercises in Classical Ring Theory Available 2000. XII, 483 p. 72 illus. (Algorithms and Combinatorics, 20) 2008. XX, 240 p. 28 illus. (Springer Monographs in 978-3-642-03993-5 This useful book, which grew out of the author's Mathematics, ) lectures at Berkeley, presents some 400 exercises of 978-3-540-77398-6 varying degrees of difficulty in classical ring theory, together with complete solutions, background information, historical commentary, bibliographic details, and indications of possible improvements or generalizations. The book should be especially helpful to Computational Mathematics graduate students as a model of the problem-solving process and an illustration of the applications of dif- and Numerical Analysis ferent theorems in ring theory. The author also discusses "the folklore of the subject: the `tricks of the trade' in ring theory, which are well known to the experts in the field but may not be familiar to others, and for which there is usually no good reference". The problems are from the following areas: the Wedder- burn-Artin theory of semisimple rings, the Jacobson P. Orlik, G. Floystad, V. Welker radical, representation theory of groups and algebras, Algebraic Combinatorics (semi)prime rings, (semi)primitive rings, division rings, ordered rings, (semi)local rings, the theory of Lectures at a Summer School in Nordfjordeid, idempotents, and (semi)perfect rings. Problems in the Norway, June 2003 areas of module theory, category theory, and rings of This book is based on two series of lectures given at quotients are not included, since they will appear in a a summer school on algebraic combinatorics at the later book. T. W. Hungerford, Mathematical Reviews Sophus Lie Centre in Nordfjordeid, Norway, in June More on www.springer.com/978-0-387-00500-3 P.B. Bochev, M.D. Gunzburger 2003, one by Peter Orlik on hyperplane arrangements, Available and the other one by Volkmar Welker on free res- olutions. Both topics are essential parts of current 2003. 328 p. (Problem Books in Mathematics, ) Least-Squares Finite Element research in a variety of mathematical fields, and the 978-0-387-00500-3 Methods present book makes these sophisticated tools available for graduate students. The book examines theoretical and computational aspects of least-squares finite element More on www.springer.com/978-3-540-68375-9 methods(LSFEMs) for partial differential equations Available (PDEs) arising in key science and engineering applications. It is intended for mathematicians, scientists, 2007. VIII, 182 p. 23 illus. (Universitext, ) and engineers interested in either or both the theory 978-3-540-68375-9 and practice associated with the numerical solution of PDEs.The first part looks at strengths and weak- nesses of classical variational principles, reviews alternative variational formulations, and offers a glimpse at the main concepts that enter into the formulation of LSFEMs. Subsequent parts introduce mathematical frameworks for LSFEMs and their analysis, apply the R. Stekolshchik frameworks to concrete PDEs, and discuss computational properties of resulting LSFEMs. Also included Notes on Coxeter Transformations are recent advances such as compatible LSFEMs, negative-norm LSFEMs, and LSFEMs for optimal control and the McKay Correspondence and design problems. Numerical examples illustrate Here is a key text on the subject of representation the- key aspects of the theory ranging from the importance ory in finite groups. The pages of this excellent lit- of norm-equivalence to connections between com- tle book, prepared by Rafael Stekolshchik, contain patible LSFEMs and classical-Galerkin and mixed- springer.com Computational Mathematics and Numerical Analysis 31

Galerkin methods.Pavel Bochev is a Distinguished Member of the Technical Staff at Sandia National Laboratories with research interests in compatible dis- cretizations for PDEs, multiphysics problems, and scientific computing.Max Gunzburger is Frances Eppes Professor of Scientific Computing and Mathematics at Florida State University and recipient of the W.T. and Idelia Reid Prize in Mathematics from the Society for Industrial and Applied Mathematics. More on www.springer.com/978-0-387-30888-3 Available 2009. XXII, 660 p. (Applied Mathematical Sciences, 166) P. Deuflhard 978-0-387-30888-3 S.C. Brenner, R. Scott The Mathematical Theory of Finite Newton Methods for Nonlinear Element Methods Problems Affine Invariance and Adaptive Algorithms This book develops the basic mathematical theory This book deals with the efficient numerical solu- of the finite element method, the most widely used tion of challenging nonlinear problems in science and technique for engineering design and analysis. The engineering, both in finite dimension (algebraic sys- third edition contains four new sections: the BDDC tems) and in infinite dimension (ordinary and partial domain decomposition preconditioner, convergence differential equations). Its focus is on local and global analysis of an adaptive algorithm, interior penalty Newton methods for direct problems or Gauss-New- methods and Poincara\'e-Friedrichs inequalities for ton methods for inverse problems. The term 'affine piecewise W^1_p functions. New exercises have also invariance' means that the presented algorithms and been added throughout. The initial chapter provides their convergence analysis are invariant under one an introducton to the entire subject, developed in out of four subclasses of affine transformations of the the one-dimensional case. Four subsequent chapters J. Boissonnat, M. Teillaud problem to be solved. Compared to traditional text- develop the basic theory in the multidimensional case, books, the distinguishing affine invariance approach and a fifth chapter presents basic applications of this Effective Computational leads to shorter theorems and proofs and permits theory. Subsequent chapters provide an introduction the construction of fully adaptive algorithms. Lots of Geometry for Curves and Surfaces to: - multigrid methods and domain decomposition numerical illustrations, comparison tables, and exer- methods - mixed methods with applications to elas- The intent of this book is to settle the foundations of cises make the text useful in computational mathe- ticity and fluid mechanics - iterated penalty and aug- non-linear computational geometry. It covers com- matics classes. At the same time, the book opens many mented Lagrangian methods - variational "crimes" binatorial data structures and algorithms, algebraic directions for possible future research. including nonconforming and isoparametric meth- issues in geometric computing, approximation of ods, numerical integration and interior penalty meth- More on www.springer.com/978-3-540-21099-3 curves and surfaces, and computational topology. ods - error estimates in the maximum norm with Each chapter provides a state of the art, as well as Available applications to nonlinear problems - error estimators, a tutorial introduction to important concepts and 2004. XII, 424 p. 48 illus. (Springer Series in Computational adaptive meshes and convergence analysis of an adap- results. The focus is on methods which are both well Mathematics, 35) tive algorithm - Banach-space operator-interpolation founded mathematically and efficient in practice. Ref- 978-3-540-21099-3 techniques The book has proved useful to mathemati- erences to open source software and discussion of cians as well as engineers and physical scientists. It potential applications of the presented techniques are can be used for a course that provides an introduc- also included. This book can serve as a textbook on tion to basic functional analysis, approximation the- non-linear computational geometry. It will also be ory and numerical analysis, while building upon and useful to engineers and researchers working in com- applying basic techniques of real variable theory. It putational geometry or other fields, like structural can also be used for courses that emphasize physi- biology, 3-dimensional medical imaging, CAD/CAM, cal applications or algorithmic efficiency. Reviews robotics, and graphics. of earlier editions: "This book represents an impor- More on www.springer.com/978-3-540-33258-9 tant contribution to the mathematical literature of Available finite elements. It is both a well-done text and a good reference." (Mathematical Reviews, 1995) "This is an 2006. XII, 344 p. 120 illus. (Mathematics and Visualization, ) 978-3-540-33258-9 excellent, though demanding, introduction to key mathematical topics in the finite element method, and at the same time a valuable reference and source for R. Farouki workers in the area." (Zentralblatt, 2002) Pythagorean-Hodograph More on www.springer.com/978-0-387-75933-3 Available Curves: Algebra and Geometry Inseparable 2008. XVIII, 402 p. 50 illus. (Texts in Applied Mathematics, 15) By virtue of their special algebraic structures, 978-0-387-75933-3 Pythagorean-hodograph (PH) curves offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. This book offers a comprehensive and self-contained treatment of the mathematical theory of PH curves, including algorithms for their construction and exam- 32 Computational Science and Engineering springer.com ples of their practical applications. Special features Partial Differential Equations - Data Approximation include an emphasis on the interplay of ideas from Techniques - Massive Data Applications This book algebra and geometry and their historical origins, presents a summary of the research ideas presented at detailed algorithm descriptions, and many figures and this workshop. worked examples. The book will appeal, in whole or More on www.springer.com/978-3-540-25076-0 in part, to mathematicians, computer scientists, and engineers. Available 2009. X, 350 p. 183 illus., 134 in color. (Mathematics and More on www.springer.com/978-3-540-73397-3 Visualization, ) Available 978-3-540-25076-0

2008. XVI, 728 p. 204 illus. (Geometry and Computing, 1) G. Karniadakis, A. Beskok, N. Aluru 978-3-540-73397-3 Microflows and Nanoflows Fundamentals and Simulation Subject area has witnessed explosive growth during the last decade and the technology is progressing at an astronomical rate. Previous edition was first to focus exclusively on flow physics within microdevices. It sold over 900 copies in North America since 11/01. New edition is 40 percent longer, with four new chapters on recent topics including Nanofluidics. More on www.springer.com/978-0-387-22197-7 M. Rappaz, M. Bellet, M. Deville Available 2005. XXII, 818 p. 395 illus. (Interdisciplinary Applied Numerical Modeling in Materials B. Gustafsson Mathematics, 29) Science and Engineering 978-0-387-22197-7 This book introduces the concepts and methodolo- High Order Difference Methods gies related to the modelling of the complex phenom- for Time Dependent PDE ena occurring in materials processing. After a short reminder of conservation laws and constitutive rela- This book covers high order finite difference meth- tionships, the authors introduce the main numerical ods for time dependent PDE. It gives an overview of methods: finite differences, finite volumes and finite the basic theory and construction principles by using elements. These techniques are developed in three model examples. The book also contains a general main chapters of the book that tackle more specific presentation of the techniques and results for well- problems: phase transformation, solid mechanics and posedness and stability, with inclusion of the three fluid flow. The two last chapters treat inverse meth- fundamental methods of analysis both for PDE in its ods to obtain the boundary conditions or the material original and discretized form: the Fourier transform, properties and stochastic methods for microstructural the eneregy method and the Laplace transform. In simulation. This book is intended for undergraduate addition, it treats various types of wave propagation and graduate students in materials science and engi- problems in specific detail, since high order methods T. Möller, B. Hamann, R.D. Russell neering, mechanical engineering and physics and for are particularly effective for these problems. engineering professionals or researchers who want to More on www.springer.com/978-3-540-74992-9 Mathematical Foundations of get acquainted with numerical simulation to model Available Scientific Visualization, Computer and compute materials processing. 2008. XVI, 334 p. (Springer Series in Computational Graphics, and Massive Data More on www.springer.com/978-3-540-42676-9 Mathematics, 38) Available 978-3-540-74992-9 Exploration 2003. XI, 540 p. 286 illus. (Springer Series in Computational Visualization is one of the most active and exciting Mathematics, 32) areas of Mathematics and Computing Science, and 978-3-540-42676-9 indeed one which is only beginning to mature. Cur- rent visualization algorithms break down for very large data sets. While present approaches use multi- resolution ideas, future data sizes will not be han- dled that way. New algorithms based on sophisticated Computational Science and mathematical modeling techniques must be devised which will permit the extraction of high-level topolog- Engineering ical structures that can be visualized. For these reasons a workshop was organized at the Banff International A. Ibrahimbegovic Research Station, focused specifically on mathematical issues. A primary objective of the workshop was to gather together a diverse set of researchers in the Nonlinear Solid Mechanics mathematical areas relevant to the recent advances Theoretical Formulations and Finite Element in order to discuss the research challenges facing this Solution Methods field in the next several years. The workshop was This volume provides insight into modelling and ulti- organized into five different thrusts: - Topology and mate limit computation of complex structures, with Discrete Methods - Signal and Geometry Processing - their components represented by solid deformable springer.com Convex and Discrete Geometry 33 bodies. The book examines practically all the impor- codes. The third edition is compatible with the new Convex and Discrete Geometry tant questions of current interests for nonlinear solid NumPy implementation and features updated infor- mechanics: plasticity, damage, large deformations, mation, correction of errors, and improved associated contact, dynamics, instability, localisation and failure, software tools. discrete models, multi-scale, multi-physics and par- More on www.springer.com/978-3-540-73915-9 allel computing, with special attention given to finite element solution methods. The presentation of top- Available ics is structured around different aspects of typical boundary value problems in nonlinear solid mechan- 2008. XXVI, 758 p. 62 illus. (Texts in Computational ics, which provides the best pedagogical approach Science and Engineering, 3) 978-3-540-73915-9 while keeping the book size reasonable despite its very broad contents. Other strong points are the exhaustive treatment of subjects, with each question studied from different angles of mechanics, mathematics and computation, as well as a successful merger of scientific cultures and heritage from Europe and the USA. G.M. Ziegler, B. Grünbaum The book content and style is also the product of rich international experience in teaching Master and Doc- Convex Polytopes toral level courses, as well as the courses organized for participants from industry (IPSI courses) in France, "The appearance of Grünbaum's book Convex Poly- and similar courses in Germany and Italy. Every effort topes in 1967 was a moment of grace to geometers was made to make the contents accessible to non-spe- and combinatorialists. The special spirit of the book cialists and users of computer programs. The orig- is very much alive even in those chapters where the inal French edition published by Hermes Science - book's immense influence made them quickly obso- Lavoisier Paris in 2006 was nominated for the Rober- lete. Some other chapters promise beautiful unex- val Award for University Textbooks in French. A. Quarteroni, F. Saleri plored land for future research. The appearance of the new edition is going to be another moment of More on www.springer.com/978-90-481-2330-8 Wissenschaftliches Rechnen mit grace. Kaibel, Klee and Ziegler were able to update Available the convex polytope saga in a clear, accurate, lively, MATLAB and inspired way." (Gil Kalai, The Hebrew University 2009. XX, 576 p. (Solid Mechanics and Its Aus den Rezensionen der englischen Auflage: of Jerusalem) "The original book of Grünbaum has Applications, 160) Dieses Lehrbuch ist eine Einführung in das Wis- provided the central reference for work in this active 978-90-481-2330-8 senschaftliche Rechnen und diskutiert Algorithmen area of mathematics for the past 35 years...I first con- und deren mathematischen Hintergrund. Ange- sulted this book as a graduate student in 1967; yet, sprochen werden im Detail nichtlineare Gleichungen, even today, I am surprised again and again by what I Approximationsverfahren, numerische Integration find there. It is an amazingly complete reference for und Differentiation, numerische Lineare Algebra, work on this subject up to that time and continues to gewöhnliche Differentialgleichungen und Randwert- be a major influence on research to this day." (Louis probleme. Zu den einzelnen Themen werden viele J. Billera, Cornell University) "The original edition Beispiele und Übungsaufgaben sowie deren Lösung of Convex Polytopes inspired a whole generation of präsentiert, die durchweg in MATLAB formuliert grateful workers in polytope theory. Without it, it is sind. Der Leser findet daher nicht nur die graue The- doubtful whether many of the subsequent advances in orie sondern auch deren Umsetzung in numerischen, the subject would have been made. The many seeds it in MATLAB formulierten Code. MATLAB select sowed have since grown into healthy trees, with vig- 2003, Issue 2, p. 50. [Die Autoren] haben ein aus- orous branches and luxuriant foliage. It is good to see gezeichnetes Werk vorgelegt, das MATLAB vorstellt it in print once again." (Peter McMullen, University und eine sehr nützliche Sammlung von MATLAB- College London) H.P. Langtangen Funktionen für die Lösung fortgeschrittener math- More on www.springer.com/978-0-387-40409-7 ematischer und naturwissenschaftlicher Probleme Python Scripting for bietet. [...] Die Präsentation des Stoffs ist durchgängig Available Computational Science gut und leicht verständlich und beinhaltet Lösungen für die Übungen am Ende jedes Kapitels. Als exzel- 2003. XVI, 466 p. 162 illus. (Graduate Texts in Mathematics, 221) The goal of this book is to teach computational sci- lenter Neuzugang für Universitätsbibliotheken- und 978-0-387-40409-7 entists how to develop tailored, flexible, and human- Buchhandlungen wird dieses Buch sowohl beim Selb- efficient working environments built from small ststudium als auch als Ergänzung zu anderen MAT- programs written in the easy-to-learn, high-level LAB-basierten Büchern von großem Nutzen sein. language Python. The focus is on examples and appli- Alles in allem: Sehr empfehlenswert. Für Studenten cations of relevance to computational scientists. These im Erstsemester wie für Experten gleichermassen. include binding together existing applications and S.T. Karris, University of California, Berkeley, Choice tools, e.g. for automating simulation, data analysis, 2003. and visualization. The book also covers steering sim- More on www.springer.com/978-3-540-25005-0 ulations and computational experiments; equipping old programs with graphical user interfaces; mak- Available ing computational Web applications; and creating interactive interfaces with a Maple/Matlab-like syn- 2006. X, 269 S. (Springer-Lehrbuch, ) tax to numerical applications in C/C++ or Fortran. 978-3-540-25005-0 The highly qualified author argues that scripting with Python makes you much more productive, increases the reliability of your scientific work and lets you have more fun - on Unix, Windows and Macintosh. All the tools and examples in this book are open source 34 Difference and Functional Equations springer.com

Difference and Functional Differential Geometry geometry, to which the author contributed essential results." - R. Sulanke, Zentralblatt Equations More on www.springer.com/978-0-387-74655-5 Available

2008. XII, 212 p. 26 illus. (Universitext, ) 978-0-387-74655-5

P. Halmos T. Cecil A Hilbert Space Problem Book P. Kannappan Lie Sphere Geometry From the Preface: "This book was written for the With Applications to Submanifolds active reader. The first part consists of problems, Functional Equations and This book provides a clear and comprehensive mod- frequently preceded by definitions and motivation, Inequalities with Applications ern treatment of Lie sphere geometry and its applica- and sometimes followed by corollaries and historical tions to the study of Euclidean submanifolds. It begins remarks... The second part, a very short one, consists Functional Equations and Inequalities with Applica- with the construction of the space of spheres, includ- of hints... The third part, the longest, consists of solutions presents a comprehensive, nearly encyclopedic, ing the fundamental notions of oriented contact, tions: proofs, answers, or contructions, depending on study of the classical topic of functional equations. parabolic pencils of spheres, and Lie sphere transfor- the nature of the problem.... This is not an introduc- Nowadays, the field of functional equations is an mations. The link with Euclidean submanifold theory tion to Hilbert space theory. Some knowledge of that ever-growing branch of mathematics with far-reach- is established via the Legendre map, which provides subject is a prerequisite: at the very least, a study of ing applications; it is increasingly used to investigate a powerful framework for the study of submanifolds, the elements of Hilbert space theory should proceed problems in mathematical analysis, combinatorics, especially those characterized by restrictions on their concurrently with the reading of this book." biology, information theory, statistics, physics, the curvature spheres. This new edition contains revised More on www.springer.com/978-0-387-90685-0 behavioral sciences, and engineering. This self-con- sections on taut submanifolds, compact proper Dupin Available tained monograph explores all aspects of functional submanifolds, reducible Dupin submanifolds, and equations and their applications to related topics, the cyclides of Dupin. Completely new material on 1982. 396 p. (Graduate Texts in Mathematics, 19) such as differential equations, integral equations, the isoparametric hypersurfaces in spheres and Dupin 978-0-387-90685-0 Laplace transformation, the calculus of finite differ- hypersurfaces with three and four principal curva- ences, and many other basic tools in analysis. Each tures is also included. The author surveys the known chapter examines a particular family of equations and results in these fields and indicates directions for fur- gives an in-depth study of its applications as well as ther research and wider application of the methods examples and exercises to support the material. The of Lie sphere geometry. Further key features of Lie book is intended as a reference tool for any student, Sphere Geometry 2/e: - Provides the reader with all professional (researcher), or mathematician studying the necessary background to reach the frontiers of in a field where functional equations can be applied. It research in this area - Fills a gap in the literature; no can also be used as a primary text in a classroom set- other thorough examination of Lie sphere geometry ting or for self-study. Finally, it could be an inspiring and its applications to submanifold theory - Complete entrée into an active area of mathematical exploration treatment of the cyclides of Dupin, including 11 com- for engineers and other scientists who would benefit puter-generated illustrations - Rigorous exposition from this careful, rigorous exposition. driven by motivation and ample examples. Reviews More on www.springer.com/978-0-387-89491-1 from the first edition: "The book under review sets out the basic material on Lie sphere geometry in mod- Available J. Jost ern notation, thus making it accessible to students 2009. XXIV, 816 p. 16 illus. (Springer Monographs in and researchers in differential geometry.....This is a Mathematics, ) carefully written, thorough, and very readable book. Riemannian Geometry and 978-0-387-89491-1 There is an excellent bibliography that not only pro- Geometric Analysis vides pointers to proofs that have been omitted, but gives appropriate references for the results presented. This established reference work continues to lead its It should be useful to all geometers working in the readers to some of the hottest topics of contemporary theory of submanifolds." - P.J. Ryan, MathSciNet "The mathematical research.This new edition introduces book under review is an excellent monograph about and explains the ideas of the parabolic methods that Lie sphere geometry and its recent applications to the have recently found such a spectacular success in the study of submanifolds of Euclidean space.....The book work of Perelman at the examples of closed geodesics is written in a very clear and precise style. It contains and harmonic forms. It also discusses further exam- about a hundred references, many comments of and ples of geometric variational problems from quan- hints to the topical literature, and can be considered tum field theory, another source of profound new as a milestone in the recent development of a classical ideas and methods in geometry. From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis. The author focuses on using analytic methods in the study of some fundamental theorems in Riemannian geometry, e.g., the Hodge theorem, the Rauch comparison theorem, the Lyusternik and Fet theorem and springer.com Dynamical Systems and Ergodic Theory 35 the existence of harmonic mappings. With the vast tems. The primary purpose of this book is to present a development of the mathematical subject of geomet- coherent framework for understanding the dynamics ric analysis, the present textbook is most welcome. [..] of piecewise-smooth and hybrid systems. An informal The book is made more interesting by the perspec- introduction asserts the ubiquity of such models with tives in various sections." Mathematical Reviews examples drawn from mechanics, electronics, control theory and physiology. The main thrust is to classify More on www.springer.com/978-3-540-77340-5 complex behavior via bifurcation theory in a system- Available atic yet applicable way. The key concept is that of a discontinuity-induced bifurcation, which generalizes 2008. XIV, 588 p. 14 illus., 4 in color. (Universitext, ) diverse phenomena such as grazing, border-collision, 978-3-540-77340-5 sliding, chattering and the period-adding route to chaos. The results are presented in an informal style and illustrated with copious examples, both theoret- M. Denker ical and experimental. Aimed at a wide audience of applied mathematicians, engineers and scientists at Einführung in die Analysis Dynamical Systems and Ergodic the early postgraduate level, the book assumes only dynamischer Systeme Theory the standard background of basic calculus and linear algebra for most of the presentation and will be an Dynamische Systeme stellen einen unverzichtbaren indispensable resource for students and researchers. Bestandteil mathematischer Modellbildung für 3rd Edition The inclusion of a comprehensive bibliography and Anwendungen aller Art dar, angefangen von Physik many open questions will also serve as a stimulus for über Biologie bis hin zur Informatik. Dieser Band V.I. Arnold, V. Kozlov, A.I. Neishtadt future research. führt in diese Theorie ein und beschreibt Methoden und Dynamiken, wie sie für eine systematische Mod- More on www.springer.com/978-1-84628-039-9 Mathematical Aspects of Classical ellbildung auch in den Anwendungen notwendig Available erscheinen. Wesentliche Grundzüge der Theorie and Celestial Mechanics 2008. XXII, 483 p. 234 illus. (Applied Mathematical Sciences, werden beispielhaft im ersten Kapitel erläutert. Es The main purpose of the book is to acquaint math- 163) schließt sich eine Einführung in niedrig-dimen- ematicians, physicists and engineers with classical 978-1-84628-039-9 sionale Dynamiken an (u.a. rationale Funktionen), mechanics as a whole, in both its traditional and its gefolgt von topologischer Dynamik (z.B. Attrak- contemporary aspects. As such, it describes the funda- toren, Entropie und chaotisches Verhalten), differen- mental principles, problems, and methods of classical J. Dedieu zierbarer Dynamik (z.B. Liapunoff-Exponenten, mechanics, with the emphasis firmly laid on the work- Strukturstabilität und Hyperbolizität), Ergodentheorie ing apparatus, rather than the physical foundations Points fixes, zéros et la méthode (z.B. Ergodensätze, invariante Maße, Konservativität) or applications. Chapters cover the n-body problem, und schließlich thermodynamischer Formalismus symmetry groups of mechanical systems and the cor- de Newton (z.B. Gibbs-Theorie, Zetafunktionen). responding conservation laws, the problem of the Cet ouvrage est consacré aux points fixes More on www.springer.com/978-3-540-20713-9 integrability of the equations of motion, the theory of d'applications différentiables, aux zéros de systèmes Available oscillations and perturbation theory. non-linéaires et à la méthode de Newton. Il s'adresse à des étudiants de mastère ou préparant l'agrégation More on www.springer.com/978-3-540-28246-4 2005. X, 285 S. 2 Abb. in Farbe. (Springer-Lehrbuch, ) de mathématique et à des chercheurs confirmés. Available 978-3-540-20713-9 La première partie est consacrée à la méthode des 2006. XIII, 518 p. 109 illus. (Encyclopaedia of Mathematical approximations successives et confronte un point Sciences, 3) de vue «systèmes dynamiques» (théorèmes de Grob- 978-3-540-28246-4 man-Hartman, de la variété stable) à des exem- ples issus de l'analyse numérique. La seconde partie de cet ouvrage expose la méthode de Newton et ses développements les plus récents (théorie alpha de Smale, systèmes sous ou sur-déterminés). Elle présente une nouvelle approche de ce sujet et un ensemble de résultats originaux publiés pour la première fois dans un ouvrage de langue française. This is an advanced text on fixed points, zeros of nonlinear systems and the Newton method. Its first part, devoted to fixed points, includes the Grobman-Hart- man and the stable manifold theorems. The second part describes the Newton method from a mod- J. Jost ern point of view: Smale's alpha theory, underdeter- mined and overdetermined systems of equations. Dynamical Systems These results are illustrated by various examples from Examples of Complex Behaviour M. Bernardo, C. Budd, A.R. Champneys, P. Kowalczyk numerical analysis. Breadth of scope is unique Author is a widely-known Piecewise-smooth Dynamical More on www.springer.com/978-3-540-30995-6 and successful textbook author Unlike many recent Available textbooks on chaotic systems that have superficial Systems treatment, this book provides explanations of the deep Theory and Applications 2006. XII, 198 p. 7 ill. (Mathématiques et underlying mathematical ideas No technical proofs, Traditional analysis of dynamical systems has Applications, 54) but an introduction to the whole field that is based restricted its attention to smooth problems, but it has 978-3-540-30995-6 become increasingly clear that there are distinctive phenomena unique to discontinuous systems that can be analyzed mathematically but which fall outside the usual methodology for smooth dynamical sys- 36 Field Theory and Polynomials springer.com on the specific analysis of carefully selected examples geophysical fluid dynamics that makes use of this new Includes a section on cellular automata approach. More on www.springer.com/978-3-540-22908-7 More on www.springer.com/978-0-387-33269-7 Available Available 2006. X, 150 p. 29 illus. (Interdisciplinary Applied 2005. VIII, 189 p. 65 illus., 15 in color. (Universitext, ) Mathematics, 31) 978-3-540-22908-7 978-0-387-33269-7

A.A. Pinto, D.A. Rand, F. Ferreira Field Theory and Polynomials Fine Structures of Hyperbolic Diffeomorphisms The study of hyperbolic systems is a core theme of modern dynamics. On surfaces the theory of the fine scale structure of hyperbolic invariant sets and their measures can be described in a very complete and ele- K. Meyer, G. Hall, D. Offin gant way, and is the subject of this book, largely self- contained, rigorously and clearly written. It covers the Introduction to Hamiltonian most important aspects of the subject and is based on several scientific works of the leading research work- Dynamical Systems and the N- ers in this field. This book fills a gap in the literature Body Problem of dynamics. We highly recommend it for any Ph.D student interested in this area. The authors are well- S.H. Weintraub This text grew out of graduate level courses in math- known experts in smooth dynamical systems and ematics, engineering and physics given at several uni- ergodic theory. Galois Theory versities. The courses took students who had some background in differential equations and lead them More on www.springer.com/978-3-540-87524-6 The book discusses classical Galois theory in con- through a systematic grounding in the theory of Available siderable generality, treating fields of characteristic zero and of positive characteristic with considera- Hamiltonian mechanics from a dynamical systems 2009. XVI, 354 p. 77 illus. (Springer Monographs in point of view. Topics covered include a detailed dis- Mathematics, ) tion of both separable and inseparable extensions, cussion of linear Hamiltonian systems, an introduc- 978-3-540-87524-6 but with a particular emphasis on algebraic exten- tion to variational calculus and the Maslov index, the sions of the field of rational numbers. While most of basics of the symplectic group, an introduction to the book is concerned with finite extensions, it dis- reduction, applications of Poincaré's continuation to cusses algebraic closure and infinite Galois extensions, periodic solutions, the use of normal forms, applica- and concludes with a new chapter on transcenden- tions of fixed point theorems and KAM theory. There tal extensions. Key topics and features of this second is a special chapter devoted to finding symmetric peri- edition: - Approaches Galois theory from the linear odic solutions by calculus of variations methods. The algebra point of view, following Artin; - Presents a main examples treated in this text are the N-body number of applications of Galois theory, including problem and various specialized problems like the symmetric functions, finite fields, cyclotomic fields, restricted three-body problem. The theory of the N- algebraic number fields, solvability of equations by body problem is used to illustrate the general theory. radicals, and the impossibility of solution of the three Some of the topics covered are the classical integrals geometric problems of Greek antiquity. Review from and reduction, central configurations, the existence the first edition: "The text offers the standard material of periodic solutions by continuation and variational of classical field theory and Galois theory, though in methods, stability and instability of the Lagrange tri- a remarkably original, unconventional and compre- angular point. Ken Meyer is an emeritus professor R.M. Samelson, S. Wiggins hensive manner … . the book under review must be at the University of Cincinnati, Glen Hall is an asso- seen as a highly welcome and valuable complement ciate professor at Boston University, and Dan Offin is Lagrangian Transport in to existing textbook literature … . It comes with its a professor at Queen's University. own features and advantages … it surely is a perfect Geophysical Jets and Waves introduction to this evergreen subject. The numerous More on www.springer.com/978-0-387-09723-7 The Dynamical Systems Approach explaining remarks, hints, examples and applications Available Written jointly by a specialist in geophysical fluid are particularly commendable … just as the out- 2009. XIII, 399 p. 67 illus. (Applied Mathematical Sciences, dynamics and an applied mathematician, this is the standing clarity and fullness of the text." (Zentralblatt 90) first accessible introduction to a new set of meth- MATH, Vol. 1089 (15), 2006) Steven H. Weintraub 978-0-387-09723-7 ods for analysing Lagrangian motion in geophysical is a Professor of Mathematics at Lehigh University flows. The book opens by establishing context and and the author of seven books. This book grew out of fundamental mathematical concepts and definitions, a graduate course he taught at Lehigh. He is also the exploring simple cases of steady flow, and touching on author of Algebra: An Approach via Module Theory important topics from the classical theory of Hamil- (with W. A. Adkins). tonian systems. Subsequent chapters examine the More on www.springer.com/978-0-387-87574-3 elements and methods of Lagrangian transport anal- Available ysis in time-dependent flows. The concluding chapter offers a brief survey of rapidly evolving research in 2009. XIV, 212 p. (Universitext, ) 978-0-387-87574-3 springer.com Fourier Analysis 37

Fourier Analysis nections to harmonic analysis, complex analysis, integral geometry, and analysis on symmetric spaces. The main purpose of this book is the study of local aspects of spectral analysis and spectral synthesis on Euclidean spaces, Riemannian symmetric spaces of an arbitrary rank and Heisenberg groups. The subject can be viewed as arising from three classical topics: John's support theorem, Schwartz's fundamental principle, and Delsarte's two-radii theorem. Highly topical, the book contains most of the significant recent results in this area with complete and detailed proofs. In order to make this book accessible to a wide audience, the authors have included an introductory B. Luong section that develops analysis on symmetric spaces Fourier Analysis on Finite Abelian without the use of Lie theory. Challenging open problems are described and explained, and promising new L. Grafakos Groups research directions are indicated. Designed for both experts and beginners in the field, the book is rich in Fourier analysis has been the inspiration for a tech- Modern Fourier Analysis methods for a wide variety of problems in many areas nological wave of advances in fields such as imag- of mathematics. The primary goal of these two volumes is to present ing processing, financial modeling, cryptography, the theoretical foundation of the field of Euclidean algorithms, and sequence design. This self-contained More on www.springer.com/978-1-84882-532-1 Harmonic analysis. The original edition was pub- book provides a thorough look at the Fourier trans- Available lished as a single volume, but due to its size, scope, form, one of the most useful tools in applied mathe- 2009. XI, 671 p. (Springer Monographs in Mathematics, ) and the addition of new material, the second edition matics. With countless examples and unique exercise 978-1-84882-532-1 consists of two volumes. The present edition con- sets at the end of most sections, Fourier Analysis on tains a new chapter on time-frequency analysis and Finite Abelian Groups is a perfect companion for a the Carleson-Hunt theorem. The first volume con- first course in Fourier analysis. The first two chapters tains the classical topics such as Interpolation, Fourier provide fundamental material for a strong foundation Series, the Fourier Transform, Maximal Functions, to deal with subsequent chapters. Special topics cov- Functional Analysis Singular Integrals, and Littlewood-Paley Theory. The ered include: * Computing eigenvalues of the Fourier second volume contains more recent topics such as transform * Applications to Banach algebras * Tensor Function Spaces, Atomic Decompositions, Singu- decompositions of the Fourier transform * Quadratic lar Integrals of Nonconvolution Type, and Weighted Gaussian sums This book provides a useful introduc- Inequalities. These volumes are mainly addressed to tion for well-prepared undergraduate and graduate graduate students in mathematics and are designed students and powerful applications that may appeal to for a two-course sequence on the subject with addi- researchers and mathematicians. The only prerequi- tional material included for reference. The prerequisites are courses in group theory and linear algebra. sites for the first volume are satisfactory completion of courses in real and complex variables. The second More on www.springer.com/978-0-8176-4915-9 volume assumes material from the first. This book Available is intended to present the selected topics in depth and stimulate further study. Although the emphasis 2009. XVI, 159 p. (Applied and Numerical Harmonic falls on real variable methods in Euclidean spaces, a Analysis, ) chapter is devoted to the fundamentals of analysis on 978-0-8176-4915-9 the torus. This material is included for historical rea- R.P. Agarwal, D. O'Regan, D.R. Sahu sons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in Fixed Point Theory for several variables. About the first edition: "Grafakos's book is very user-friendly with numerous examples Lipschitzian-type Mappings with illustrating the definitions and ideas... The treatment Applications is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, In recent years, the fixed point theory of Lips- Grafakos has clearly spent a great deal of time prepar- chitzian-type mappings has rapidly grown into an ing the exercises." - Kenneth Ross, MAA Online important field of study in both pure and applied mathematics. It has become one of the most essential More on www.springer.com/978-0-387-09433-5 tools in nonlinear functional analysis. This self-con- Available tained book provides the first systematic presentation of Lipschitzian-type mappings in metric and Banach 2009. XV, 507 p. 27 illus. (Graduate Texts in spaces. The first chapter covers some basic properties Mathematics, 250) V.V. Volchkov, V.V. Volchkov of metric and Banach spaces. Geometric considera- 978-0-387-09433-5 tions of underlying spaces play a prominent role in Harmonic Analysis of Mean developing and understanding the theory. The next Periodic Functions on Symmetric two chapters provide background in terms of convexity, smoothness and geometric coefficients of Banach Spaces and the Heisenberg Group spaces including duality mappings and metric projection mappings. This is followed by results on exis- This book presents the first systematic and unified tence of fixed points, approximation of fixed points treatment of the theory of mean periodic functions by iterative methods and strong convergence theo- on homogeneous spaces. This area has its classical rems. The final chapter explores several applicable roots in the beginning of the twentieth century and problems arising in related fields. This book can be is now a very active research area, having close con- 38 Functional Analysis springer.com used as a textbook and as a reference for graduate stu- the aim is to show how the theory is combined with dents, researchers and applied mathematicians work- the study of operators in Hilbert space by methods ing in nonlinear functional analysis, operator theory, of functional analysis, with applications to partial approximations by iteration theory, convexity and and ordinary differential equations. Here, the author related geometric topics, and best approximation the- provides an introduction to unbounded operators in ory. Hilbert space, including a complete theory of extensions of operators, and applications using contrac- More on www.springer.com/978-0-387-75817-6 tion semigroups. In more advanced parts of the book, Available the author shows how distribution theory is used to 2009. X, 368 p. (Topological Fixed Point Theory and Its define pseudodifferential operators on manifolds, and Applications, 6) gives a detailed introduction to the pseudodifferen- 978-0-387-75817-6 tial boundary operator calculus initiated by Boutet de O. Christensen Monvel, which allows a modern treatment of elliptic boundary value problems. This book is aimed at An Introduction to Frames and graduate students, as well as researchers interested in its special topics, and as such, the author provides Riesz Bases careful explanations along with complete proofs, The theory for frames and bases has developed rapidly and a bibliography of relevant books and papers. in recent years because of its role as a mathematical Each chapter has been enhanced with many exercises tool in signal and image processing. In this self-con- and examples. Unique topics include: * the interplay tained work, frames and Riesz bases are presented between distribution theory and concrete operators; from a functional analytic point of view, emphasiz- * families of extensions of nonselfadjoint operators; * ing their mathematical properties. This is the first an illustration of the solution maps between distribu- comprehensive book to focus on the general prop- tion spaces by a fully worked out constant-coefficient erties and interplay of frames and Riesz bases, and case; * the pseudodifferential boundary operator cal- thus fills a gap in the literature. Key features: * Basic culus; * the Calderón projector and its applications. F. Albiac, N.J. Kalton results presented in an accessible way for both pure Gerd Grubb is Professor of Mathematics at University and applied mathematicians * Extensive exercises of Copenhagen. Topics in Banach Space Theory make the work suitable as a textbook for use in grad- More on www.springer.com/978-0-387-84894-5 uate courses * Full proofs included in introductory Available Assuming only a basic knowledge of functional chapters; only basic knowledge of functional analysis analysis, the book gives the reader a self-contained required * Explicit constructions of frames with appli- 2009. XII, 464 p. 8 illus. (Graduate Texts in overview of the ideas and techniques in the develop- cations and connections to time-frequency analysis, ment of modern Banach space theory. Special empha- Mathematics, 252) wavelets, and nonharmonic Fourier series * Selected 978-0-387-84894-5 sis is placed on the study of the classical Lebesgue research topics presented with recommendations for spaces Lp (and their sequence space analogues) and more advanced topics and further reading * Open spaces of continuous functions. The authors also problems to stimulate further research An Introduc- stress the use of bases and basic sequences techniques tion to Frames and Riesz Bases will be of interest to as a tool for understanding the isomorphic struc- graduate students and researchers working in pure ture of Banach spaces. The aim of this text is to pro- and applied mathematics, mathematical physics, and vide the reader with the necessary technical tools and engineering. Professionals working in digital signal background to reach the frontiers of research with- processing who wish to understand the theory behind out the introduction of too many extraneous con- many modern signal processing tools may also find cepts. Detailed and accessible proofs are included, this book a useful self-study reference. as are a variety of exercises and problems.Fernando Albiac received his PhD in 2000 from Universidad More on www.springer.com/978-0-8176-4295-2 Publica de Navarra, Spain. He is currently Visiting Available Assistant Professor of Mathematics at the University of Missouri,Columbia. Nigel Kalton is Professor of 2003. 464 p. 16 illus. (Applied and Numerical Mathematics at the University of Missouri, Columbia. Harmonic Analysis, ) E. Kaniuth He has written over 200 articles with more than 82 978-0-8176-4295-2 different co-authors, and most recently, was the recip- A Course in Commutative Banach ient of the 2004 Banach medal of the Polish Academy of Sciences. Algebras More on www.springer.com/978-0-387-28141-4 Requiring only a basic knowledge of functional analysis, topology, complex analysis, measure theory and Available group theory, this book provides a thorough and self- contained introduction to the theory of commutative 2006. XII, 376 p. (Graduate Texts in Mathematics, Banach algebras. The core are chapters on Gelfand's 233) 978-0-387-28141-4 theory, regularity and spectral synthesis. Special emphasis is placed on applications in abstract harmonic analysis and on treating many special classes of commutative Banach algebras, such as uniform algebras, group algebras and Beurling algebras, and tensor products. Detailed proofs and a variety of exercises are given. The book aims at graduate students and can G. Grubb be used as a text for courses on Banach algebras, with Distributions and Operators This book gives an introduction to distribution theory, in the spirit of Laurent Schwartz. Additionally, springer.com Functions of a Complex Variable 39 various possible specializations, or a Gelfand theory Functions of a Complex examples rather than definitions and theorems. This based course in harmonic analysis. self-contained monograph is an excellent resource Variable for a self-study guide and should appeal to a broad More on www.springer.com/978-0-387-72475-1 audience. The only prerequisite is a standard calcu- Available lus course. The first chapter deals with a beautiful presentation of special functions. . . . The third chap- 2009. XII, 353 p. (Graduate Texts in Mathematics, ter covers elliptic and modular functions. . . in much 246) more detail, and from a different point of view, than 978-0-387-72475-1 one can find in standard introductory books. . . . For [the] subjects that are omitted, the author has sug- gested 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. ---Mathematical Reviews Mainly original papers are cited to support the historical remarks. The book is well readable. --- E. Freitag, R. Busam Zentralblatt für Mathematik This is an unusual textbook, incorporating material showing how classical Complex Analysis function theory can be used. . . . The general scheme is to show the reader how things were developed with- The idea of this book is to give an extensive descrip- out following the traditional approach of most books tion of the classical complex analysis, here ''classical'' on functional theory. . . . This book can be recom- means roughly that sheaf theoretical and cohomologi- M. Ruzicka mended to those who like to see applications of the cal methods are omitted. The first four chapters cover theory taught in classical courses. ---EMS Nichtlineare Funktionalanalysis the essential core of complex analysis presenting their fundamental results. After this standard material, the More on www.springer.com/978-0-8176-4918-0 Eine Einführung authors step forward to elliptic functions and to ellip- Available Das vorliegende Lehrbuch enthält eine Einführung tic modular functions including a taste of all most in die nichtlineare Funktionalanalysis. Die Theme- beautiful results of this field. The book is rounded 1998. XIV, 228 p. 5 illus. (Modern Birkhäuser nauswahl beinhaltet Methoden und Techniken, die, by applications to analytic number theory including Classics, ) neben dem allgemeinen Interesse, bei der Unter- distinguished pearls of this fascinating subject as for 978-0-8176-4918-0 suchung von nichtlinearen elliptischen und parabolis- instance the Prime Number Theorem. Great impor- chen partiellen Differentialgleichungen benutzt tance is attached to completeness, all needed notions werden. Es wird insbesondere auf Fixpunktsätze, are developed, only minimal prerequisites (elemen- Differentiation und Integration in Banachräumen, tary facts of calculus and algebra) are required. More monotone Operatoren und den Abbildungsgrad than 400 exercises including hints for solutions and Game Theory, Economics, eingegangen. Der Darstellung des Stoffes liegt das many figures make this an attractive, indispensable Zusammenspiel und die gegenseitige Beeinflussung book for students who would like to have a sound Social and Behav. Sciences von Theorie und Anwendungen zugrunde. Kurze introduction to classical complex analysis. For the sec- Einführungen am Kapitelanfang, illustrative Beispiele ond edition the authors have revised the text carefully. sowie die detaillierte Herleitung von Ergebnissen More on www.springer.com/978-3-540-93982-5 erleichtern das Verständnis. Ein Appendix mit einer Kurzzusammenfassung von Ergebnissen aus der Available linearen Funktionalanalysis rundet die Darstellung ab. Das Buch richtet sich an Studierende ab dem 6. 2009. X, 532 p. 112 illus., 2 in color. (Universitext, ) 978-3-540-93982-5 Semester und umfasst den Lehrstoff für ein Semester. More on www.springer.com/978-3-540-20066-6 Available

2004. XII, 208 S. 10 Abb. (Springer-Lehrbuch Masterclass, ) 978-3-540-20066-6 Y. Narahari, D. Garg, R. Narayanam, H. Prakash Game Theoretic Problems in Network Economics and Mechanism Design Solutions With the advent of the Internet and other modern J. Stalker information and communication technologies, a mag- nificent opportunity has opened up for introducing Complex Analysis new, innovative models of commerce, markets, and Fundamentals of the Classical Theory of business. Creating these innovations calls for signifi- Functions cant interdisciplinary interaction among researchers in computer science, communication networks, oper- This clear, concise introduction to the classical theory ations research, economics, mathematics, sociology, of one complex variable is based on the premise that and management science. In the emerging era of new "anything worth doing is worth doing with interesting problems and challenges, one particular tool that has examples." The content is driven by techniques and found widespread applications is mechanism design. 40 Geometry springer.com

The focus of this book is to explore game theoretic tive geometry both synthetically and analytically, and modeling and mechanism design for problem solv- the new Chapter 5 uses a descriptive and exploratory ing in Internet and network economics. It provides a approach to introduce chaos theory and fractal sound foundation of relevant concepts and theory, to geometry, stressing the self-similarity of fractals and help apply mechanism design to problem solving in a their generation by transformations from Chapter rigorous way. 3. Throughout, each chapter includes a list of sug- gested resources for applications or related topics in More on www.springer.com/978-1-84800-937-0 areas such as art and history, plus this second edition Available points to Web locations of author-developed guides 2009. XXI, 274 p. 45 illus. (Advanced Information and for dynamic software explorations of the Poincaré Knowledge Processing, ) model, isometries, projectivities, conics and fractals. 978-1-84800-937-0 Parallel versions are available for "Cabri Geometry" D. Bao, S. Chern, Z. Shen and "Geometers Sketchpad". More on www.springer.com/978-0-387-98972-3 An Introduction to Riemann- Available Geometry Finsler Geometry 2001. 151 illus. (Undergraduate Texts in In Riemannian geometry, measurements are made Mathematics, ) with both yardsticks and protractors. These tools 978-0-387-98972-3 are represented by a family of inner-products. In Riemann-Finsler geometry (or Finsler geometry for short), one is in principle equipped with only a family of Minkowski norms. So ardsticks are assigned but protractors are not. With such a limited tool kit, it is R. Fenn natural to wonder just how much geometry one can uncover and describe?It now appears that there is a Geometry reasonable answer. Finsler geometry encompasses Geometry is probably the most accessible branch of a solid repertoire of rigidity and comparison theo- mathematics, and can provide an easy route to under- rems, most of them founded upon a fruitful analogue standing some of the more complex ideas that mathe- of the sectional curvature. There is also a bewilder- matics can present. This book is intended to introduce P. Anglès ing array of explicit examples, illustrating many phe- readers to the major geometrical topics taught at nomena which admit only Finslerian interpretations. undergraduate level, in a manner that is both accessi- Conformal Groups in Geometry This book focuses on the elementary but essential ble and rigorous. The author uses world measurement items among these results. Much thought has gone as a synonym for geometry - hence the importance and Spin Structures into making the account a teachable one. of numbers, coordinates and their manipulation - Conformal groups play a key role in geometry and More on www.springer.com/978-0-387-98948-8 and has included over 300 exercises, with answers to spin structures. This book provides a self-contained Available most of them. The text includes such topics as:- Coor- overview of this important area of mathematical dinates- Euclidean plane geometry- Complex num- physics, beginning with its origins in the works of 2000. XX, 431 p. 20 illus. (Graduate Texts in bers- Solid geometry- Conics and quadratic surfaces- Cartan and Chevalley and progressing to recent Mathematics, 200) Spherical geometry- QuaternionsIt is suitable for all research in spinors and conformal geometry. Key top- 978-0-387-98948-8 undergraduate geometry courses, but it is also a useful ics and features: * Focuses initially on the basics of resource for advanced sixth formers, research mathe- Clifford algebras * Studies the spaces of spinors for maticians, and those taking courses in physics, intro- some even Clifford algebras * Examines conformal ductory astronomy and other science subjects. spin geometry, beginning with an elementary study of More on www.springer.com/978-1-85233-058-3 the conformal group of the Euclidean plane * Treats Available covering groups of the conformal group of a regular pseudo-Euclidean space, including a section on the 2001. XII, 313 p. (Springer Undergraduate complex conformal group * Introduces conformal Mathematics Series, ) flat geometry and conformal spinoriality groups, fol- 978-1-85233-058-3 lowed by a systematic development of riemannian or pseudo-riemannian manifolds having a conformal spin structure * Discusses links between classical spin structures and conformal spin structures in the context of conformal connections * Examines pseudo- G.A. Jennings unitary spin structures and pseudo-unitary conformal spin structures using the Clifford algebra associ- J.N. Cederberg Modern Geometry with ated with the classical pseudo-unitary space * Ample exercises with many hints for solutions * Compre- A Course in Modern Geometries Applications hensive bibliography and index This text is suitable Designed for a junior-senior level course for math- This introduction to modern geometry differs from for a course in mathematical physics at the advanced ematics majors, including those who plan to teach other books in the field due to its emphasis on appli- undergraduate and graduate levels. It will also benefit in secondary school. The first chapter presents sev- cations and its discussion of special relativity as a researchers as a reference text. eral finite geometries in an axiomatic framework, major example of a non-Euclidean geometry. Addi- More on www.springer.com/978-0-8176-3512-1 while Chapter 2 continues the synthetic approach in tionally, it covers the two important areas of non- Euclidean geometry, spherical geometry and projec- Available introducing both Euclids and ideas of non-Euclidean geometry. There follows a new introduction to sym- tive geometry, as well as emphasising transformations, 2008. XXVIII, 284 p. 40 illus. (Progress in Mathematical metry and hands-on explorations of isometries that and conics and planetary orbits. Much emphasis is Physics, 50) precedes an extensive analytic treatment of similar- placed on applications throughout the book, which 978-0-8176-3512-1 ities and affinities. Chapter 4 presents plane projec- motivate the topics, and many additional applications springer.com Geometry 41 are given in the exercises. It makes an excellent intro- only the most elementary geometry and is appropriate ture, group actions and covering spaces. Second, the duction for those who need to know how geometry is for graduate courses for secondary teachers. prerequisites are modest and standard and include only a little linear algebra, calculus, basic group theory used in addition to its formal theory. More on www.springer.com/978-0-387-90636-2 and basic topology. Third and most important, the More on www.springer.com/978-0-387-94222-3 Available theory of surfaces of constant curvature has maximal Available connectivity with the rest of mathematics. They real- 1982. XII, 256 p. 222 illus. (Undergraduate Texts in ize all the topological types of compact two-dimen- 1994. VIII, 204 p. 150 illus. (Universitext, ) Mathematics, ) sional manifolds, and historically, they are the source 978-0-387-90636-2 978-0-387-94222-3 of the main concepts of complex analysis, differential geometry, topology, and combinatorial group theory, as well as such hot topics as fractal geometry and string theory. The formal coverage is extended by exercises and informal discussions throughout the text. More on www.springer.com/978-0-387-97743-0 Available

1992. XI, 236 p. 164 illus. (Universitext, ) 978-0-387-97743-0

D. Johnson G.E. Martin Symmetries The main object of study for this book is geometry, Geometric Constructions with group theory providing an appropriate language Geometric constructions have been a popular part in which to express geometrical ideas. Key features of mathematics throughout history. The first chap- include: An overview of the preliminaries from group ter here is informal and starts from scratch, introduc- theory and geometry Coverage of the discrete sub- ing all the geometric constructions from high school groups of the Euclidean group A clear and complete that have been forgotten or were never learned. The derivation and classification of the 17 plane crys- second chapter formalises Plato's game, and exam- tallographic groups Tessellations of various spaces ines problems from antiquity such as the impossibility (they are constructed, described and classified) A brief of trisecting an arbitrary angle. After that, variations introduction to hyperbolic geometry. Each chapter on Plato's theme are explored: using only a ruler, a contains a number of exercises, most with solutions, compass, toothpicks, a ruler and dividers, a marked Lectures on Discrete Geometry and suggestions for background, alternative and fur- rule, or a tomahawk, ending in a chapter on geomet- This book is primarily a textbook introduction to ther reading. The author's accessible and down-toric constructions by paperfolding. The author writes various areas of discrete geometry. In each area, it earth approach make this an ideal introduction for in a charming style and nicely intersperses history and explains several key results and methods, in an acces- readers in the second or third year of a mathematics philosophy within the mathematics, teaching a lit- sible and concrete manner. It also contains more undergraduate course. It is also recommended for tle geometry and a little algebra along the way. This advanced material in separate sections and thus it can mechanical engineers, architects, physicists and crys- is as much an algebra book as it is a geometry book, serve as a collection of surveys in several narrower tallographers needing an understanding of 3-dimen- yet since all the algebra and geometry needed is devel- subfields. The main topics include: basics on convex sional geometry, symmetry and trigonometry. oped within the text, very little mathematical back- sets, convex polytopes, and hyperplane arrangements; More on www.springer.com/978-1-85233-270-9 ground is required. This text has been class tested for combinatorial complexity of geometric configura- several semesters with a master's level class for sec- Available tions; intersection patterns and transversals of con- ondary teachers. vex sets; geometric Ramsey-type results; polyhedral 2001. XI, 216 p. 60 illus. (Springer Undergraduate More on www.springer.com/978-0-387-98276-2 combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed Mathematics Series, ) Available 978-1-85233-270-9 spaces. 1998. 224 p. 130 illus. (Undergraduate Texts in More on www.springer.com/978-0-387-95373-1 Mathematics, ) Available 978-0-387-98276-2 G.E. Martin 2002. XVI, 481 p. 206 illus. (Graduate Texts in Mathematics, 212) Transformation Geometry 978-0-387-95373-1 An Introduction to Symmetry J. Stillwell Transformation Geometry: An Introduction to Sym- metry is a modern approach to Euclidean Geometry. Geometry of Surfaces This study of the automorphism groups of the plane This text intends to provide the student with the and space gives the classical concrete examples that knowledge of a geometry of greater scope than the serve as a meaningful preparation for the standard classical geometry taught today, which is no longer undergraduate course in abstract algebra. The detailed an adequate basis for mathematics or physics, both development of the isometries of the plane is based on of which are becoming increasingly geometric. The geometry of surfaces is an ideal starting point for students learning geometry for the following reasons; first, the extensions offer the simplest possible introduction to fundamentals of modern geometry: curva- 42 Global Analysis and Analysis on Manifolds springer.com

Global Analysis and Analysis on Smale flows, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. Manifolds In addition, many examples, problems, and illustrations further enhance the value of this useful introduction to Morse Theory. More on www.springer.com/978-0-387-49509-5 Available

2007. XIV, 242 p. 32 illus. (Universitext, ) 978-0-387-49509-5

R. Goodman, N.R. Wallach Symmetry, Representations, and Group Theory and Invariants Symmetry is a key ingredient in many mathemati- A. Banyaga, D. Hurtubise Generalizations cal, physical, and biological theories. Using representation theory and invariant theory to analyze the Lectures on Morse Homology symmetries that arise from group actions, and with This book presents in great detail all the results one strong emphasis on the geometry and basic theory needs to prove the Morse Homology Theorem using of Lie groups and Lie algebras, Symmetry, Represen- classical techniques from algebraic topology and tations, and Invariants is a significant reworking of homotopy theory. Most of these results can be found an earlier highly-acclaimed work by the authors. The scattered throughout the literature dating from the result is a comprehensive introduction to Lie theory, mid to late 1900's in some form or other, but often representation theory, invariant theory, and algebraic the results are proved in different contexts with a groups, in a new presentation that is more accessible multitude of different notations and different goals. to students and includes a broader range of applica- This book collects all these results together into a sin- tions. The philosophy of the earlier book is retained, gle reference with complete and detailed proofs. The i.e., presenting the principal theorems of representa- core material in this book includes CW-complexes, tion theory for the classical matrix groups as motiva- Morse theory, hyperbolic dynamical systems (the tion for the general theory of reductive groups. The O. Ganyushkin, V. Mazorchuk Lamba-Lemma, the Stable/Unstable Manifold Theo- wealth of examples and discussion prepares the reader rem), transversality theory, the Morse-Smale-Witten for the complete arguments now given in the gen- boundary operator, and Conley index theory. More Classical Finite Transformation eral case. Key Features of Symmetry, Representations, advanced topics include Morse theory on Grassmann Semigroups and Invariants: • Early chapters suitable for honors manifolds and Lie groups, and an overview of Floer An Introduction undergraduate or beginning graduate courses, requir- homology theories. With the stress on completeness ing only linear algebra, basic abstract algebra, and and by its elementary approach to Morse homology, The aim of this monograph is to give a self-contained advanced calculus • Applications to geometry (cur- this book is suitable as a textbook for a graduate level introduction to the modern theory of finite transfor- vature tensors), topology (Jones polynomial via sym- course, or as a reference for working mathematicians mation semigroups with a strong emphasis on con- metry), and combinatorics (symmetric group and and physicists. crete examples and combinatorial applications. It Young tableaux) • Self-contained chapters, appen- covers the following topics on the examples of the dices, comprehensive bibliography • More than 350 More on www.springer.com/978-1-4020-2695-9 three classical finite transformation semigroups: exercises (most with detailed hints for solutions) fur- Available transformations and semigroups, ideals and Green's ther explore main concepts • Serves as an excellent relations, subsemigroups, congruences, endomor- main text for a one-year course in Lie group theory • 2004. IX, 326 p. (Texts in the Mathematical Sciences, phisms, nilpotent subsemigroups, presentations, Benefits physicists as well as mathematicians as a ref- 29) actions on sets, linear representations, cross-sections erence work 978-1-4020-2695-9 and variants. The book contains many exercises and More on www.springer.com/978-0-387-79851-6 historical comments and is directed, first of all, to both graduate and postgraduate students looking for Available an introduction to the theory of transformation semigroups, but should also prove useful to tutors and 2009. XX, 716 p. 10 illus. (Graduate Texts in researchers. Mathematics, 255) 978-0-387-79851-6 More on www.springer.com/978-1-84800-280-7 Available 2009. XII, 328 p. 4 illus. (Algebra and Applications, 9) 978-1-84800-280-7

L. Nicolaescu An Invitation to Morse Theory This book offers readers a taste of the "unreasonable effectiveness" of Morse theory. It covers many of the most important topics in Morse theory along with applications. The book details topics such as Morse- springer.com Group Theory and Generalizations 43

lutionary development of concepts that form a basis dental functions. This volume also treats these topics: for current investigations. This is accomplished by a proof of the main conjecture for rational characters, providing a thread that permits a natural flow from and Chinburg’s invariant; P. Delgne’s proof of a func- one concept to another rather than compartmental- tion field analogue; p-adic versions of the conjectures izing. Operators on sets and groups are introduced due to B. Gross and J.-P. Serre. This volume belongs early and used effectively throughout. The bibliogra- on the shelf of every mathematics library. phy provides excellent supplemental support...The More on www.springer.com/978-0-8176-3188-8 text is tight; there is no fluff. The format builds on concepts essential for later expansion and associ- Available ated reading. On occasion, results are stated with- 1984. 156 p. (Progress in Mathematics, 47) out proof; continuity is maintained. Several proofs 978-0-8176-3188-8 C. Kassel, V. Turaev are provided free of representation theory on which the originals were based. More generally the proofs Braid Groups are direct, perhaps at times brief. The focus is on the underlying structural components, with selected Braids and braid groups have been at the heart details left to the reader. As a result the reader devel- of mathematical development over the last two ops the maturity required for approaching the litera- decades. Braids play an important role in diverse areas ture with confidence. The first eight chapters have an of mathematics and theoretical physics. The special abundance of exercises, not prorated, and some of the beauty of the theory of braids stems from their attrac- more challenging are addressed later in the text. Due tive geometric nature and their close relations to other to the nature of the material, fewer exercises appear in fundamental geometric objects, such as knots, links, the remaining chapters." (H. Bechtell, Mathematical mapping class groups of surfaces, and configuration Reviews) spaces. In this presentation the authors thoroughly examine various aspects of the theory of braids, More on www.springer.com/978-0-387-40510-0 starting from basic definitions and then moving to Available B. Wehrfritz more recent results. The advanced topics cover the Burau and the Lawrence--Krammer--Bigelow repre- 2004. XII, 387 p. (Universitext, ) Group and Ring Theoretic sentations of the braid groups, the Alexander--Con- 978-0-387-40510-0 Properties of Polycyclic Groups way and Jones link polynomials, connections with the representation theory of the Iwahori--Hecke algebras, Polycyclic groups are built from cyclic groups in a and the Garside structure and orderability of the braid specific way. They arise in many contexts within groups. This book will serve graduate students, math- group theory itself but also more generally in alge- ematicians, and theoretical physicists interested in bra, for example in the theory of Noetherian rings. low-dimensional topology and its connections with They also touch on some aspects of topology, geom- representation theory. etry and number theory. The first half of this book develops the standard group theoretic techniques for More on www.springer.com/978-0-387-33841-5 studying polycyclic groups and the basic properties Available of these groups. The second half then focuses specifically on the ring theoretic properties of polycyclic 2008. XII, 340 p. 60 illus. (Graduate Texts in groups and their applications, often to purely group Mathematics, 247) theoretic situations. The book is not intended to be 978-0-387-33841-5 encyclopedic. Instead, it is a study manual for graduate students and researchers coming into contact with J. Serre polycyclic groups, where the main lines of the subject can be learned from scratch by any reader who has Algebraic Groups and Class Fields been exposed to some undergraduate algebra, especially groups, rings and vector spaces. Thus the book More on www.springer.com/978-0-387-96648-9 has been kept short and readable with a view that it Available can be read and worked through from cover to cover. 1988. IX, 224 p. 4 illus. (Graduate Texts in Mathematics, 117) At the end of each topic covered there is a description 978-0-387-96648-9 without proofs, but with full references, of further developments in the area. The book then concludes with an extensive bibliography of items relating to polycyclic groups.

J. Tate More on www.springer.com/978-1-84882-940-4 Available H. Kurzweil, B. Stellmacher Les Conjectures de Stark sur les 2009. VII, 128 p. (Algebra and Applications, 10) The Theory of Finite Groups Fonctions L d'Artin en s=0 978-1-84882-940-4 An Introduction Notes d'un cours a Orsay redigees par Dominique Bernardi From reviews of the German edition: "This is an exciting text and a refreshing contribution to an area in This book presents a self-contained introduction to which challenges continue to flourish and to captivate H.M. Stark’s remarkable conjectures about the lead- the viewer. Even though representation theory and ing term of the Taylor expansion of Artin’s L-func- constructions of simple groups have been omitted, the tions at s=0. These conjectures can be viewed as a vast text serves as a springboard for deeper study in many generalization of Dirichlet’s class number formula directions. One who completes this text not only gains and Kronecker’s limit formula. They provide an unex- an appreciation of both the depth and the breadth of pected contribution to Hilbert’s 12th problem on the the theory of finite groups, but also witnesses the evo- generalization of class fields by the values of transcen- 44 History of Mathematics springer.com

History of Mathematics

R. Wilson A. Hald The Finite Simple Groups A History of Parametric Statistical

The finite simple groups are the building blocks from R.E. Bradley, C.E. Sandifer Inference from Bernoulli to Fisher, which all the finite groups are made and as such they 1713-1935 are objects of fundamental importance throughout Cauchy’s Cours d’analyse This book offers a detailed history of parametric sta- mathematics. The classification of the finite simple An Annotated Translation groups was one of the great mathematical achieve- tistical inference. Covering the period between James ments of the twentieth century, yet these groups This is an annotated and indexed translation (from Bernoulli and R.A. Fisher, it examines: binomial remain difficult to study which hinders applications French into English) of Augustin Louis Cauchy's statistical inference; statistical inference by inverse of the classification. This textbook brings the finite 1821 classic textbook Cours d'analyse. This is the first probability; the central limit theorem and linear min- simple groups to life by giving concrete constructions English translation of a landmark work in mathemat- imum variance estimation by Laplace and Gauss; of most of them, sufficient to illuminate their struc- ics, one of the most influential texts in the history of error theory, skew distributions, correlation, sampling ture and permit real calculations both in the groups mathematics. It belongs in every mathematics library, distributions; and the Fisherian Revolution. Lively themselves and in the underlying geometrical or alge- along with Newton's Principia and Euclid's Elements. biographical sketches of many of the main characters braic structures. This is the first time that all the finite The authors' style mimics the look and feel of the are featured throughout, including Laplace, Gauss, simple groups have been treated together in this way second French edition. It is an essentially modern Edgeworth, Fisher, and Karl Pearson. Also examined and the book points out their connections, for exam- textbook style, about 75% narrative and 25% theo- are the roles played by DeMoivre, James Bernoulli, ple between exceptional behaviour of generic groups rems, proofs, corollaries. Despite the extensive nar- and Lagrange. rative, it has an essentially "Euclidean architecture" and the existence of sporadic groups, and discusses More on www.springer.com/978-0-387-46408-4 a number of new approaches to some of the groups. in its careful ordering of definitions and theorems. Available Many exercises of varying difficulty are provided. The It was the first book in analysis to do this. Cauchy's Finite Simple Groups is aimed at advanced under- book is essentially a precalculus book, with a rigorous 2007. XIV, 226 p. 11 illus. (Sources and Studies in the History graduate and graduate students in algebra as well as exposition of the topics necessary to learn calculus. of Mathematics and Physical Sciences, ) professional mathematicians and scientists who use Hence, any good quality calculus student can under- 978-0-387-46408-4 groups and want to apply the knowledge which the stand the content of the volume. The basic audience is classification has given us. The main prerequisite is an anyone interested in the history of mathematics, espe- undergraduate course in group theory up to the level cially 19th century analysis. In addition to being an of Sylow’s theorems. important book, the Cours d'analyse is well-written, packed with unexpected gems, and, in general, a thrill More on www.springer.com/978-1-84800-987-5 to read. Robert E. Bradley is Professor of Mathemat- Available ics at Adelphi University. C. Edward Sandifer is Pro- fessor of Mathematics at Western Connecticut State 2009. XV, 298 p. (Graduate Texts in Mathematics, University. 251) 978-1-84800-987-5 More on www.springer.com/978-1-4419-0548-2 Available 2009. XX, 412 p. 1 illus. in color. (Sources and Studies in the History of Mathematics and Physical Sciences, ) R. Krömer 978-1-4419-0548-2 Tool and Object A History and Philosophy of Category Theory Category theory is a general mathematical theory of structures and of structures of structures. It occupied a central position in contemporary mathematics as well as computer science. This book describes the history of category theory whereby illuminating its sym- biotic relationship to algebraic topology, homological algebra, algebraic geometry and mathematical logic and elaboratively develops the connections with the epistemological significance. More on www.springer.com/978-3-7643-7523-2 Available 2007. XXXVI, 367 p. (Science Networks. Historical Studies, 32) 978-3-7643-7523-2 springer.com K-Theory 45

L. Mazliak, R. Tazzioli Linear and Multilinear Mathematicians at war Algebras, Matrix Theory Volterra and his French colleagues in World War I J. Abdeljaoued, H. Lombardi Numerous scientists have taken part in the war effort during World War I, but few gave it the passion- Méthodes matricielles - ate energy of the prominent Italian mathematician Volterra. As a convinced supporter of the cause of Introduction à la complexité Britain and France, he struggled vigorously to carry algébrique Italy into the war in May 1915 and then developed a frenetic activity to support the war effort, going Ce livre est une introduction à la théorie de la himself to the front, even though he was 55. This M.S. Osborne complexité algébrique basée sur un panorama des activity found an adequate echo with his French col- méthodes algorithmiques en algèbre linéaire exacte. leagues Borel, Hadamard and Picard. The huge cor- Basic Homological Algebra Il donne en particulier les principaux algorithmes respondence they exchanged during the war, gives This book is intended for one-quarter or one pour le calcul du polynôme caractéristique. Il donne an extraordinary view of these activities, and raises semester-courses in homological algebra. The aim is aussi une discussion détaillée des méthodes de mul- numerous fundamental questions about the role of to cover Ext and Tor early and without distraction. tiplication rapide des polynômes et des matrices, a scientist, and particularly a mathematician during It includes several further topics, which can be pur- sans pour autant réclamer de prérequis théoriques de WW I. It also offers a vivid documentation about the sued independently of each other. Many of these, such haut niveau. Tout en étant centré sur les problèmes intellectual life of the time ; Volterra’s and Borel’s cir- as Lazard's theorem, long exact sequences in Abelian de complexité algébrique, il aborde aussi la com- cles in particular were extremely wide and the range categories with no cheating, or the relation between plexité binaire. Une place importante est accordée au of their interests was not limited to their field of spe- Krull dimension and global dimension, are hard to parallélisme. Le livre se termine par une introduction cialization. The book proposes the complete tran- find elsewhere. The intended audience is second or raisonnée à l'importante théorie de Valiant concer- scription of the aforementioned correspondence, third year graduate students in algebra, algebraic nant un analogue algébrique de la conjecture P = NP. annotated with numerous footnotes to give details topology, or any other field that uses homological Ce livre se remarque par l'étendue des sujets traités on the contents. It also offers a general historical algebra. tout en restant très lisible. introduction to the context of the letters and sev- More on www.springer.com/978-3-540-20247-9 eral complements on themes related to the academic More on www.springer.com/978-0-387-98934-1 Available exchanges between France and Italy during the war. Available More on www.springer.com/978-90-481-2739-9 2000. X, 395 p. (Graduate Texts in Mathematics, 196) 2004. XV, 376 p. (Mathématiques et Applications, 42) Available 978-0-387-98934-1 978-3-540-20247-9 2009. X, 187 p. 10 illus. (Archimedes, 22) 978-90-481-2739-9

J. Rosenberg

K-Theory Algebraic K-Theory and Its T. Banchoff, J. Wermer Applications Linear Algebra Through Geometry Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic Linear Algebra Through Geometry introduces the J.D. Dixon, B. Mortimer topology, number theory, and algebraic geometry, but concepts of linear algebra through the careful study of even including operator theory. The broad range of two and three-dimensional Euclidean geometry. This Permutation Groups these topics has tended to give the subject an aura of approach makes it possible to start with vectors, lin- inapproachability. This book, based on a course at the ear transformations, and matrices in the context of Following the basic ideas, standard constructions University of Maryland in the fall of 1990, is intended familiar plane geometry and to move directly to top- and important examples in the theory of permuta- to enable graduate students or mathematicians work- ics such as dot products, determinants, eigenvalues, tion groups, the book goes on to develop the combi- ing in other areas not only to learn the basics of alge- and quadratic forms. The later chapters deal with n- natorial and group theoretic structure of primitive braic K-Theory, but also to get a feel for its many dimensional Euclidean space and other finite-dimen- groups leading to the proof of the pivotal ONan-Scott applications. The required prerequisites are only the sional vector space. Topics include systems of linear Theorem which links finite primitive groups with standard one-year graduate algebra course and the equations in n variable, inner products, symmetric finite simple groups. Special topics covered include standard introductory graduate course on algebraic matrices, and quadratic forms. The final chapter treats the Mathieu groups, multiply transitive groups, and and geometric topology. Many topics from algebraic application of linear algebra to differential systems, recent work on the subgroups of the infinite symmet- topology, homological algebra, and algebraic num- least square approximations and curvature of surfaces ric groups. With its many exercises and detailed refer- ber theory are developed as needed. The final chapter in three spaces. The only prerequisite for reading this ences to the current literature, this text can serve as an gives a concise introduction to cyclic homology and book (with the exception of one section on systems of introduction to permutation groups in a course at the its interrelationship with K-Theory. differential equations) are high school geometry, alge- graduate or advanced undergraduate level, as well as bra, and introductory trigonometry. for self-study. More on www.springer.com/978-0-387-94248-3 More on www.springer.com/978-0-387-97586-3 More on www.springer.com/978-0-387-94599-6 Available Available Available 1994. X, 408 p. 2 illus. (Graduate Texts in Mathematics, 147) 1992. XII, 324 p. 92 illus. (Undergraduate Texts in 1996. 364 p. 10 illus. (Graduate Texts in Mathematics, 978-0-387-94248-3 Mathematics, ) 163) 978-0-387-97586-3 978-0-387-94599-6 46 Linear and Multilinear Algebras, Matrix Theory springer.com

treatment of linear spaces. The author maintains a good balance between modern algebraic interests and traditional linear algebra. Several chapters have been substantially rewritten for clarity of exposition, although their basic content is unchanged. A considerable number of exercises covering new material has also been added. More on www.springer.com/978-0-387-90110-7 Available

T. Blyth, E.F. Robertson 1975. XVII, 476 p. 5 illus. (Graduate Texts in Mathematics, 23) Further Linear Algebra 978-0-387-90110-7 S. Roman Further Linear Algebra is a natural sequel to the Advanced Linear Algebra authors' highly acclaimed SUMS volume "Basic Lin- ear Algebra". The more advanced topics covered here For the third edition, the author has added a new take the reader to the very heart of the subject, and chapter on associative algebras that includes the well include inner product spaces, direct sums of sub- known characterizations of the finite-dimensional spaces, the primary decomposition theorem and var- division algebras over the real field (a theorem of ious canonical forms for matrices. Furthermore, the Frobenius) and over a finite field (Wedderburn's the- authors provide a brief introduction to the use of orem); polished and refined some arguments (such MAPLE in linear algebra calculations, and biograph- as the discussion of reflexivity, the rational canonical ical profiles of eminent mathematicians associated form, best approximations and the definitions of ten- with the subject.An introductory chapter recaps the sor products); upgraded some proofs that were orig- prerequisites (for those readers unfamiliar with the inally done only for finite-dimensional/rank cases; first volume), and a wide range of worked examples added new theorems, including the spectral map- and exercises (with solutions) are strategically placed ping theorem; considerably expanded the reference M. Koecher throughout the text to consolidate understanding. section with over a hundred references to books on linear algebra. From the reviews of the second edi- More on www.springer.com/978-1-85233-425-3 Lineare Algebra und analytische tion: "In this 2nd edition, the author has rewritten the Available Geometrie entire book and has added more than 100 pages of new materials....As in the previous edition, the text is 2002. VII, 230 p. (Springer Undergraduate Der vorliegende Band wurde für die Neuauflage well written and gives a thorough discussion of many Mathematics Series, ) von Aloys Krieg, einem Schüler von Herrn Koecher, topics of linear algebra and related fields...the exer- 978-1-85233-425-3 ergänzt und aktualisiert. Wichtigste Ergänzungen cises are rewritten and expanded....Overall, I found sind der Spektralsatz für selbstadjungierte Endomor- the book a very useful one....It is a suitable choice as phismen in euklidischen und unitären Vektorräumen a graduate text or as a reference book." Ali-Akbar sowie die Anwendung der Jordanschen Normal- Jafarian, ZentralblattMATH "This is a formidable vol- form auf Differentialgleichungen. Auch sind neue ume, a compendium of linear algebra theory, clas- M.L. Curtis Übungsaufgaben hinzugekommen. Aus den Rezen- sical and modern... The development of the subject sionen: "... ein erfreulicher Lichtblick. Ohne die klare is elegant...The proofs are neat...The exercise sets Abstract Linear Algebra theoretische Linie zu verwirren, versteht der Autor are good, with occasional hints given for the solu- Beginning from scratch and developing the standard Querverbindungen zur Geometrie, Algebra, Zahlen- tion of trickier problems...It represents linear algebra topics of Linear Algebra, this book is intended as a theorie und (Funktional-) Analysis immer wieder and does so comprehensively." Henry Ricardo, MAA text for a first course on the subject. The goal to which aufzuhellen. Zwischenkommentare helfen dabei Online ebenso wie die eingehenden historischen Notizen und this work leads is the Theorem of Hurwitz - that the More on www.springer.com/978-0-387-72828-5 only normed algebras over the real numbers are the Einschübe, insbesondere über Graßmann, Hamilton Available real numbers, the complex numbers, the quaternions, und Cayley sowie die Geschichte der Determinanten. and the octonions. Unique in presenting this material Besondere Kapitel über die Elementargeometrie der 2008. XVIII, 526 p. 23 illus. (Graduate Texts in at an elementary level, the book stresses the complete Ebene des Raumes kommen endlich einmal auch auf Mathematics, 135) logical development of the subject and will provide a nichttriviale Sätze zu sprechen; Feuerbachkreis und 978-0-387-72828-5 bavuable reference for mathematicians in general. Euler-Gerade, Spiegelungspunkte und Sphärik. ... Stu- denten und Dozenten kann diese Buch wärmstens More on www.springer.com/978-0-387-97263-3 empfohlen werden." Zentralblatt für Mathematik Available More on www.springer.com/978-3-540-62903-0 1990. X, 184 p. (Universitext, ) Available 978-0-387-97263-3 1997. XIV, 292 S. 35 Abb. (Springer-Lehrbuch, ) 978-3-540-62903-0

W.H. Greub Linear Algebra This textbook gives a detailed and comprehensive presentation of the linear algebra based on axiomatic springer.com Manifolds and Cell Complexes (incl. Diff. Topology) 47

groups over arbitrary fields. Again, the author keeps Manifolds and Cell Complexes the treatment of prerequisites self-contained. The material of the first ten chapters covers the contents (incl. Diff. Topology) of the old book, but the arrangement is somewhat different and there are additions, such as the basic facts about algebraic varieties and algebraic groups over a ground field, as well as an elementary treatment of Tannaka's theorem. These chapters can serve as a text for an introductory course on linear algebraic groups. The last seven chapters are new. They deal with alge- R. Abraham, J.E. Marsden, T. Ratiu braic groups over arbitrary fields. Some of the mate- T.S. Shores rial has not been dealt with before in other texts, such Manifolds, Tensor Analysis, and as Rosenlicht's results about solvable groups in Chap- Applied Linear Algebra and ter 14, the theorem of Borel and Tits on the conjugacy Applications Matrix Analysis over the ground field of maximal split tori in an arbi- The purpose of this book is to provide core material trary linear algebraic group in Chapter 15, and the in nonlinear analysis for mathematicians, physicists, This new book offers a fresh approach to matrix and Tits classification of simple groups over a ground field engineers, and mathematical biologists. The main linear algebra by providing a balanced blend of appli- in Chapter 17. The book includes many exercises and goal is to provide a working knowledge of manifolds, cations, theory, and computation, while highlighting a subject index." –Zentralblatt Math (Review of the dynamical systems, tensors, and differential forms. their interdependence. Intended for a one-semester Second Edition) Some applications to Hamiltonian mechanics, fluid course, Applied Linear Algebra and Matrix Analysis mechanics, electromagnetism, plasma dynamics and places special emphasis on linear algebra as an exper- More on www.springer.com/978-0-8176-4839-8 control theory are given using both invariant and imental science, with numerous examples, computer Available index notation. The prerequisites required are solid exercises, and projects. While the flavor is heavily undergraduate courses in linear algebra and advanced computational and experimental, the text is inde- 1998. XII, 334 p. (Modern Birkhäuser Classics, ) calculus. pendent of specific hardware or software platforms. 978-0-8176-4839-8 Throughout the book, significant motivating exam- More on www.springer.com/978-0-387-96790-5 ples are woven into the text, and each section ends Available with a set of exercises. More on www.springer.com/978-0-387-33194-2 1988. XI, 672 p. 94 illus. (Applied Mathematical Sciences, 75) Available 978-0-387-96790-5

2007. XII, 388 p. 27 illus. (Undergraduate Texts in Mathematics, ) 978-0-387-33194-2

F. Zhang Matrix Theory Basic Results and Techniques The aim of this book is to concisely present fundamental ideas, results, and techniques in linear algebra M.R. Bridson, A. Häfliger and mainly matrix theory. The book contains eight chapters covering various topics ranging from simi- Metric Spaces of Non-Positive larity and special types of matrices to Schur comple- T. Springer ments and matrix normality. Each chapter focuses on Curvature the results, techniques, and methods that are beau- This book describes the global properties of sim- Linear Algebraic Groups tiful, interesting, and representative, followed by ply-connected spaces that are non-positively curved carefully selected problems. For many theorems sev- "[The first] ten chapters...are an efficient, accessible, in the sense of A. D. Alexandrov, and the structure eral different proofs are given. The book can be used and self-contained introduction to affine algebraic of groups which act on such spaces by isometries. as a text or a supplement for a linear algebra and groups over an algebraically closed field. The author The theory of these objects is developed in a man- matrix theory class or seminar for senior or gradu- includes exercises and the book is certainly usable ner accessible to anyone familiar with the rudiments ate students. The only prerequisites are a decent back- by graduate students as a text or for self-study...the of topology and group theory: non-trivial theorems ground in elementary linear algebra and calculus. The author [has a] student-friendly style… [The follow- are proved by concatenating elementary geometric book can also serve as a reference for instructors and ing] seven chapters... would also be a good intro- arguments, and many examples are given. Part I is an researchers in the fields of algebra, matrix analysis, duction to rationality issues for algebraic groups. A introduction to the geometry of geodesic spaces. In operator theory, statistics, computer science, engi- number of results from the literature…appear for Part II the basic theory of spaces with upper curvature neering, operations research, economics, and other the first time in a text." –Mathematical Reviews bounds is developed. More specialized topics, such as fields. (Review of the Second Edition) "This book is a com- complexes of groups, are covered in Part III. The book pletely new version of the first edition. The aim of the More on www.springer.com/978-0-387-98696-8 is divided into three parts, each part is divided into old book was to present the theory of linear algebraic Available chapters and the chapters have various subheadings. groups over an algebraically closed field. Reading that book, many people entered the research field of linear algebraic groups. The present book has a wider 1999. XIII, 277 p. (Universitext, ) 978-0-387-98696-8 scope. Its aim is to treat the theory of linear algebraic 48 Mathematical Biology in General springer.com

The chapters in Part III are longer and for ease of ref- Mathematical Biology in erence are divided into numbered sections. General More on www.springer.com/978-3-540-64324-1 Available 1999. XXI, 643 p. 84 illus. (Grundlehren der mathematischen Wissenschaften, 319) 978-3-540-64324-1

J. Nestruev Smooth Manifolds and Observables

Smooth Manifolds and Observables is about the dif- A. Deutsch, R. Bravo de la Parra, R.J. Boer, O. Diekmann, P. ferential calculus, smooth manifolds, and commuta- Jagers, E. Kisdi, M. Kretzschmar, P. Lansky, H. Metz tive algebra. While these theories arose at different times and under completely different circumstances, Mathematical Modeling of this book demonstrates how they constitute a unified C. Maclachlan, A.W. Reid whole. The motivation behind this synthesis is the Biological Systems, Volume II mathematical formalization of the process of obser- Epidemiology, Evolution and Ecology, The Arithmetic of Hyperbolic 3- vation in classical physics. The main objective of this Immunology, Neural Systems and the Brain, and book is to explain how differential calculus is a natu- Innovative Mathematical Methods Manifolds ral part of commutative algebra. This is achieved by This two-volume, interdisciplinary work is a unified For the past 25 years, the Geometrization Program of studying the corresponding algebras of smooth func- presentation of a broad range of state-of-the-art topics Thurston has been a driving force for research in 3- tions that result in a general construction of the differ- in the rapidly growing field of mathematical model- manifold topology. This has inspired a surge of activ- ential calculus on various categories of modules over ing in the biological sciences. Highlighted through- ity investigating hyperbolic 3-manifolds (and Kleinian the given commutative algebra. It is shown in detail out both works are mathematical and computational groups), as these manifolds form the largest and least that the ordinary differential calculus and differential approaches to examine central problems in the life well-understood class of compact 3-manifolds. Famil- geometry on smooth manifolds turns out to be pre- sciences, ranging from the organizational principles iar and new tools from diverse areas of mathematics cisely the particular case that corresponds to the cate- of individual cells to the dynamics of large popula- have been utilized in these investigations, from topol- gory of geometric modules over smooth algebras. This tions. Volume I covers a number of areas, including: ogy, geometry, analysis, group theory, and from the approach opens the way to numerous applications, * Cellular Biophysics * Regulatory Networks * Devel- point of view of this book, algebra and number the- ranging from delicate questions of algebraic geome- opmental Biology * Biomedical Applications * Data ory. This book is aimed at readers already familiar try to the theory of elementary particles. This unique Analysis and Model Validation Volume II examines with the basics of hyperbolic 3-manifolds or Kleinian textbook contains a large number of exercises and is a diverse range of subjects, including: * Epidemiology groups, and it is intended to introduce them to the intended for advanced undergraduates, graduate stu- * Evolution and Ecology * Immunology * Neural Sys- interesting connections with number theory and the dents, and research mathematicians and physicists. tems and the Brain * Innovative Mathematical Meth- tools that will be required to pursue them. While More on www.springer.com/978-0-387-95543-8 ods and Education Both volumes will be excellent there are a number of texts which cover the topologi- Available reference texts for a broad audience of researchers, cal, geometric and analytical aspects of hyperbolic 3- practitioners, and advanced students in this rapidly manifolds, this book is unique in that it deals exclu- 2003. XIV, 220 p. 30 illus. (Graduate Texts in growing field at the intersection of applied mathe- sively with the arithmetic aspects, which are not cov- Mathematics, 220) matics, experimental biology and medicine, computa- ered in other texts. Colin Maclachlan is a Reader in 978-0-387-95543-8 tional biology, biochemistry, computer science, and the Department of Mathematical Sciences at the Uni- physics. versity of Aberdeen in Scotland where he has served since 1968. He is a former President of the Edinburgh More on www.springer.com/978-0-8176-4555-7 Mathematical Society. Alan Reid is a Professor in Available the Department of Mathematics at The University 2008. XVIII, 390 p. 119 illus. (Modeling and Simulation in of Texas at Austin. He is a former Royal Society Uni- Science, Engineering and Technology, ) versity Research Fellow, Alfred P. Sloan Fellow and 978-0-8176-4555-7 winner of the Sir Edmund Whittaker Prize from The Edinburgh Mathematical Society. Both authors have published extensively in the general area of discrete groups, hyperbolic manifolds and low-dimensional topology. More on www.springer.com/978-0-387-98386-8 Available

2003. XIII, 463 p. 57 illus. (Graduate Texts in Mathematics, 219) 978-0-387-98386-8 springer.com Mathematical Biology in General 49

now being applied in every major discipline in the quickly find key words. ... I recommend the new and biomedical sciences. Though the field has become expanded third edition to any serious young student increasingly large and specialized, this book remains interested in mathematical biology who already has a important as a text that introduces some of the excit- solid basis in applied mathematics." ing problems that arise in biology and gives some More on www.springer.com/978-0-387-95223-9 indication of the wide spectrum of questions that modelling can address. Due to this tremendous devel- Available opment in recent years, for this new edition Murray is covering certain items in depth, giving new applica- 2002. XXIII, 551 p. 164 illus. (Interdisciplinary Applied tions such as modelling marital interaction, growth of Mathematics, 17) 978-0-387-95223-9 cancer tumours, temperature sex determination, wolf territoriality, wolf-deer survival etc. In other areas P. Macheras, A. Iliadis he discusses basic modelling concepts and provides further references as needed. He also provides even Modeling in Biopharmaceutics, closer links between models and experimental data throughout the text. The book continues to present a Pharmacokinetics and broad view of the field of theoretical and mathemati- Pharmacodynamics cal biology and gives us an excellent background from Homogeneous and Heterogeneous Approaches which to begin genuine interdisciplinary research in the biomedical sciences. The state of the art in Biopharmaceutics, Pharma- cokinetics, and Pharmacodynamics Modeling is pre- More on www.springer.com/978-0-387-95228-4 sented in this book. It shows how advanced physical Available and mathematical methods can expand classical models in order to cover heterogeneous drug-biological 2003. XXV, 811 p. 296 illus. (Interdisciplinary Applied B. Perthame processes and therapeutic effects in the body. The Mathematics, 18) book is divided into four parts; the first deals with 978-0-387-95228-4 Transport Equations in Biology the fundamental principles of fractals, diffusion and nonlinear dynamics; the second with drug dissolu- This book presents models written as partial differ- tion, release, and absorption; the third with empirical, ential equations and originating from various ques- compartmental, and stochastic pharmacokinetic mod- tions in population biology, such as physiologically els, and the fourth mainly with nonclassical aspects structured equations, adaptive dynamics, and bac- of pharmacodynamics. The classical models that have terial movement. Its purpose is to derive appropri- relevance and application to these sciences are also ate mathematical tools and qualitative properties of considered throughout. Many examples are used to the solutions (long time behavior, concentration phe- illustrate the intrinsic complexity of drug adminis- nomena, asymptotic behavior, regularizing effects, tration related phenomena in the human, justifying blow-up or dispersion). Original mathematical meth- the use of advanced modeling methods. This timely ods described are, among others, the generalized rela- and useful book will appeal to graduate students and tive entropy method - a unique method to tackle most researchers in pharmacology, pharmaceutical sci- of the problems in population biology, the descrip- ences, bioengineering, and physiology. tion of Dirac concentration effects using a new type of Hamilton-Jacobi equations, and a general point J.D. Murray More on www.springer.com/978-0-387-28178-0 of view on chemotaxis including various scales of Available Mathematical Biology description leading to kinetic, parabolic or hyperbolic 2006. XX, 442 p. 131 illus. (Interdisciplinary Applied equations. I. An Introduction Mathematics, 30) More on www.springer.com/978-3-7643-7841-7 978-0-387-28178-0 It has been over a decade since the release of the now Available classic original edition of Murray's Mathematical Biol- ogy. Since then mathematical biology has grown at 2007. VIII, 198 p. 28 illus. (Frontiers in Mathematics, ) an astonishing rate and is well established as a dis- 978-3-7643-7841-7 tinct discipline. Mathematical modeling is now being applied in every major discipline in the biomedical sciences. Though the field has become increasingly large and specialized, this book remains important as a text that introduces some of the exciting problems that arise in biology and gives some indication of the wide spectrum of questions that modeling can address. Due to the tremendous development in the field this book is being published in two volumes. This first volume is an introduction to the field, the mathematics mainly involves ordinary differential equations that are suitable for undergraduate and J. Murray graduate courses at different levels. For this new edition Murray is covering certain items in depth, giving Mathematical Biology II new applications such as modeling marital interac- Spatial Models and Biomedical Applications tions and temperature dependence sex determination. In the ten years since the first edition of this book SIAM, 2004: "Murray's Mathematical Biology is a clas- appeared the field of mathematical biology has grown sic that belongs on the shelf of any serious student or at an astonishing rate and has established itself as researcher in the field. Together the two volumes con- a distinct discipline. Mathematical modelling is tain well over 1000 references, a rich source of material, together with an excellent index to help readers 50 Mathematical Logic and Foundations springer.com

other areas that are discussed in this book are the Ishihara's tricks, Separation theorems, and Locally convex spaces. There are two appendices to the book. The first gathers together some basic notions about sets and orders, the second gives the axioms for intuitionistic logic. The intended readership of the book consists of postgraduate or senior undergraduate students, and professional research mathematicians. No background in intuitionistic logic or constructive analysis is needed in order to read the book, but some familiarity with the classical theories of metric, normed and Hilbert spaces is recommended. D. Wodarz R.W. Shonkwiler, J. Herod More on www.springer.com/978-0-387-33646-6 Available Mathematical Biology Killer Cell Dynamics Mathematical and Computational Approaches An Introduction with Maple and Matlab 2006. XVI, 216 p. 10 illus. (Universitext, ) to Immunology 978-0-387-33646-6 This text presents mathematical biology as a field with a unity of its own, rather than only the intrusion of This book reviews how mathematical and compu- one science into another. It updates an earlier suc- tational approaches can be useful to help us under- cessful edition and greatly expands the concept of the stand how killer T-cell responses work to fight viral "computer biology laboratory," giving students a gen- infections. It also demonstrates, in a writing style that eral perspective of the field before proceeding to more exemplifies the point, that such mathematical and specialized topics. The book focuses on problems of computational approaches are most valuable when contemporary interest, such as cancer, genetics, and coupled with experimental work through interdis- the rapidly growing field of genomics. It includes ciplinary collaborations. Designed to be useful to new chapters on parasites, cancer, and phylogenet- immunoligists and viroligists without extensive com- ics, along with an introduction to online resources for putational background, the book covers a broad vari- DNA, protein lookups, and popular pattern match- ety of topics, including both basic immunological ing tools such as BLAST. In addition, the emerging questions and the application of these insights to the field of algebraic statistics is introduced and its power understanding and treatment of pathogenic human illustrated in the context of phylogenetics. A unique diseases. feature of the book is the integration of a computer More on www.springer.com/978-0-387-30893-7 H. Ebbinghaus, J. Flum, W. Thomas algebra system into the flow of ideas in a supporting Available but unobtrusive role. Syntax for both the Maple and Mathematical Logic 2007. XIV, 226 p. 74 illus. (Interdisciplinary Applied Matlab systems is provided in a tandem format. The Mathematics, 32) This junior/senior level text is devoted to a study of use of a computer algebra system gives the students 978-0-387-30893-7 first-order logic and its role in the foundations of the opportunity to examine "what if" scenarios, allow- mathematics: What is a proof? How can a proof be ing them to investigate biological systems in a way justified? To what extent can a proof be made a purely never before possible. For students without access to mechanical procedure? How much faith can we have Maple or Matlab, each topic presented is complete. in a proof that is so complex that no one can follow Graphic visualizations are provided for all mathemat- Mathematical Logic and it through in a lifetime? The first substantial answers ical results. Mathematical Biology includes extensive to these questions have only been obtained in this exercises, problems and examples. A year of calcu- Foundations century. The most striking results are contained in lus with linear algebra is required to understand the Goedel's work: First, it is possible to give a simple material presented. The biology presented proceeds set of rules that suffice to carry out all mathemati- from the study of populations down to the molecu- cal proofs; but, second, these rules are necessarily lar level; no previous coursework in biology is neces- incomplete - it is impossible, for example, to prove all sary. The book is appropriate for undergraduate and true statements of arithmetic. The book begins with graduate students studying mathematics or biology an introduction to first-order logic, Goedel's theo- and for scientists and researchers who wish to study rem, and model theory. A second part covers exten- the applications of mathematics and computers in the sions of first-order logic and limitations of the formal natural sciences. methods. The book covers several advanced topics, More on www.springer.com/978-0-387-70983-3 not commonly treated in introductory texts, such as Available Trachtenbrot's undecidability theorem. Fraissé's elementary equivalence, and Lindstroem's theorem on 2009. XIV, 554 p. 156 illus. (Undergraduate Texts in the maximality of first-order logic. Mathematics, ) More on www.springer.com/978-0-387-94258-2 D.S. Bridges, L.S. Vita 978-0-387-70983-3 Available Techniques of Constructive 1994. X, 308 p. 13 illus. (Undergraduate Texts in Analysis Mathematics, ) This book is an introduction to constructive mathe- 978-0-387-94258-2 matics with an emphasis on techniques and results that have been obtained in the last twenty years. The text covers fundamental theory of the real line and metric spaces, focusing on locatedness in normed spaces and with associated results about operators and their adjoints on a Hilbert space. Some of the springer.com Mathematical Logic and Foundations 51

even more so if one knows a little French.)...I am con- algebraic-topological duality, including the dual- fident that a student who works through Gerstein's ity between ideals and open sets, homomorphisms book will really come away with (i) some mathemati- and continuous functions, subalgebras and quotient cal technique, and (ii) some mathematical knowledge. spaces, and direct products and Stone-Cech compact- - Steven Krantz, American Mathematical Monthly ifications. A special feature of the book is the large "This very elementary book is intended to be a text- number of exercises of varying levels of difficulty, book for a one-term course which introduces students from routine problems that help readers understand into the basic notions of any higher mathematics the basic definitions and theorems, to intermediate courses...The explanations of the basic notions are problems that extend or enrich material developed combined with some main theorems, illustrated by in the text, to harder problems that explore impor- examples (with solutions if necessary) and comple- tant ideas either not treated in the text, or that go sub- mented by exercises. The book is well written and stantially beyond its treatment. Hints for the solutions H. Ebbinghaus, J. Flum should be easily understandable to any beginning to the harder problems are given in an appendix. A student." - S. Gottwald, Zentralblatt This textbook is detailed solutions manual for all exercises is available Finite Model Theory intended for a one-term course whose goal is to ease for instructors who adopt the text for a course. The book presents the main results of descriptive the transition from lower-division calculus courses to More on www.springer.com/978-0-387-40293-2 upper-division courses in linear and abstract algebra, complexity theory, that is, the connections between Available axiomatizability of classes of finite structures and real and complex analysis, number theory, topology, combinatorics, etc. It contains a wide-ranging assort- their complexity with respect to time and space 2009. XIV, 574 p. 10 illus. (Undergraduate Texts in bounds. The logics that are important in this context ment of examples and imagery to motivate and to enhance the underlying intuitions, as well as numer- Mathematics, ) include fixed-point logics, transitive closure logics, 978-0-387-40293-2 and also certain infinitary languages; their model the- ous exercises and a solutions manual for professors. ory is studied in full detail. Other topics include DAT- More on www.springer.com/978-0-387-97997-7 ALOG languages, quantifiers and oracles, 0-1 laws, Available and optimization and approximation problems. The 1996. X, 350 p. 103 illus. (Textbooks in Mathematical book is written in such a way that the respective parts Sciences, ) on model theory and descriptive complexity theory 978-0-387-97997-7 may be read independently. This second edition is a thoroughly revised and enlarged version of the original text. More on www.springer.com/978-3-540-28787-2 Available 1999. XI, 360 p. (Springer Monographs in Mathematics, ) 978-3-540-28787-2 A. Kanamori The Higher Infinite Large Cardinals in Set Theory from Their Beginnings The theory of large cardinals is currently a broad S. Givant, P. Halmos mainstream of modern set theory, the main area of investigation for the analysis of the relative consis- Introduction to Boolean Algebras tency of mathematical propositions and possible new axioms for mathematics. The first of a projected In a bold and refreshingly informal style, this excit- multi-volume series, this book provides a compre- ing text steers a middle course between elementary hensive account of the theory of large cardinals from texts emphasizing connections with philosophy, logic, L.J. Gerstein its beginnings and some of the direct outgrowth- and electronic circuit design, and profound treatises s leading to the frontiers of contempory research. A Introduction to Mathematical aimed at advanced graduate students and profes- "genetic" approach is taken, presenting the subject in sional mathematicians. It is written for readers who the context of its historical development. With hind- Structures and Proofs have studied at least two years of college-level math- sight the consequential avenues are pursued and the ematics. With carefully crafted prose, lucid explana- "...Gerstein wants-very gently-to teach his students to most elegant or accessible expositions given. With tions, and illuminating insights, it guides students to think. He wants to show them how to wrestle with a open questions and speculations provided through- some of the deeper results of Boolean algebra --- and problem (one that is more sophisticated than "plug out the reader should not only come to appreciate the in particular to the important interconnections with and chug"), how to build a solution, and ultimately scope and coherence of the overall enterpreise but topology --- without assuming a background in alge- he wants to teach the students to take a statement also become prepared to pursue research in several bra, topology, and set theory. The parts of those sub- and develop a way to prove it...Gerstein writes with specific areas by studying the relevant sections. jects that are needed to understand the material are a certain flair that I think students will find appeal- developed within the text itself. Highlights of the More on www.springer.com/978-3-540-88866-6 ing. For instance, after his discussion of cardinals he book include the normal form theorem; the homo- Available has a section entitled Languages and Finite Automata. morphism extension theorem; the isomorphism the- This allows him to illustrate some of the ideas he has 2003. XXII, 536 p. (Springer Monographs in Mathematics, ) orem for countable atomless Boolean algebras; the been discussing with problems that almost anyone 978-3-540-88866-6 maximal ideal theorem; the celebrated Stone rep- can understand, but most importantly he shows how resentation theorem; the existence and uniqueness these rather transparent problems can be subjected theorems for canonical extensions and completions; to a mathematical analysis. His discussion of how a Tarski’s isomorphism of factors theorem for count- machine might determine whether the sequence of ably complete Boolean algebras, and Hanf’s related words "Celui fromage de la parce que maintenant" is counterexamples; and an extensive treatment of the a legitimate French sentence is just delightful (and 52 Mathematical Logic and Foundations springer.com

ematics students and at mathematically minded graduate students of computer science and philosophy. More on www.springer.com/978-0-387-28723-2 Available

2006. XII, 284 p. 48 illus. (Undergraduate Texts in Mathematics, ) 978-0-387-28723-2

P. Komjath, V. Totik S.M. Srivastava Problems and Theorems in A Course on Mathematical Logic Classical Set Theory This is a short, distinctive, modern, and motivated introduction to mathematical logic for senior under- This volume contains a variety of problems from clas- graduate and beginning graduate students in math- sical set theory and represents the first comprehensive ematics and computer science. Any mathematician collection of such problems. Many of these problems who is interested in knowing what logic is concerned are also related to other fields of mathematics, includ- with and who would like to learn Gödel’s incom- ing algebra, combinatorics, topology and real analysis. pleteness theorems should find this book particularly Rather than using drill exercises, most problems are W. Pohlers convenient. The treatment is thoroughly mathemat- challenging and require work, wit, and inspiration. ical, and the entire subject has been approached like They vary in difficulty, and are organized in such a a branch of mathematics. Serious efforts have been way that earlier problems help in the solution of later Proof Theory The First Step into Impredicativity made to make the book suitable for the classroom as ones. For many of the problems, the authors also trace well as for self-reading. The book does not strive to be the history of the problems and then provide proper This book verifies with compelling evidence the a comprehensive encyclopedia of logic. Still, it gives reference at the end of the solution. author’s intent to "write a book on proof theory that essentially all the basic concepts and results in math- More on www.springer.com/978-0-387-30293-5 needs no previous knowledge of proof theory". Avoid- ematical logic. The book prepares students to branch Available ing the cryptic terminology of proof theory as far as out in several areas of mathematics related to foun- possible, the book starts at an elementary level and dations and computability such as logic, axiomatic displays the connections between infinitary proof 2006. XII, 516 p. (Problem Books in Mathematics, ) set theory, model theory, recursion theory, and com- 978-0-387-30293-5 theory and generalized recursion theory, especially putability. The main prerequisite for this book is the the theory of inductive definitions. As a "warm up" willingness to work at a reasonable level of mathemat- Gentzen's classical analysis of pure number theory is ical rigor and generality. Shashi Mohan Srivastava is presented in a more modern terminology, followed a Professor at the Indian Statistical Institute, Kolkata, by an explanation and proof of the famous result of India. He is also the author of A Course on Borel Sets, Feferman and Schütte on the limits of predicativity. GTM 180. The author also provides an introduction to ordi- More on www.springer.com/978-0-387-76275-3 nal arithmetic, introduces the Veblen hierarchy and employs these functions to design an ordinal notation Available system for the ordinals below Epsilon 0 and Gamma 0, while emphasizing the first step into impredica- 2008. X, 150 p. (Universitext, ) tivity, that is, the first step beyond Gamma 0. This 978-0-387-76275-3 is first done by an analysis of the theory of non-iterated inductive definitions using Buchholz’s improve- ment of local predicativity, followed by Weiermann's observation that Buchholz’s method can also be used Y. Moschovakis for predicative theories to characterize their provably recursive functions. A second example presents an Notes on Set Theory ordinal analysis of the theory of $/Pi_2$ reflection, The axiomatic theory of sets is a vibrant part of pure a subsystem of set theory that is proof-theoretically mathematics, with its own basic notions, fundamental equivalent to Kripke-Platek set. The book is pitched at results, and deep open problems. At the same time, it undergraduate/graduate level, and thus addressed to is often viewed as a foundation of mathematics so that students of mathematical logic interested in the basics in the most prevalent, current mathematical practice of proof theory. It can be used for introductory as well "to make a notion precise" simply means "to define as more advanced courses in proof theory. An earlier it in set theory." This book tries to do justice to both version of this book was published in 1989 as volume aspects of the subject: it gives a solid introduction to 1407 of the "Lecture Notes in Mathematics" (ISBN "pure set theory" through transfinite recursion and 978-3-540-51842-6). Logic and Structure the construction of the cumulative hierarchy of sets More on www.springer.com/978-3-540-69318-5 New corrected printing of a well-established text on (including the basic results that have applications Available logic at the introductory level. to computer science), but it also attempts to explain precisely how mathematical objects can be faithfully More on www.springer.com/978-3-540-20879-2 2009. XIV, 374 p. 5 illus. (Universitext, ) modeled within the universe of sets. In this new edi- 978-3-540-69318-5 Available tion the author added solutions to the exercises, and 2004. X, 268 p. (Universitext, ) rearranged and reworked the text in several places 978-3-540-20879-2 to improve the presentation. The book is aimed at advanced undergraduate or beginning graduate math- springer.com Mathematical Modeling and Industrial Mathematics 53

Mathematical Modeling and MATICS IN OPERATIONS RESEARCH is a comprehensive survey of the mathematical concepts and Industrial Mathematics principles of industrial mathematics. Its purpose is to provide students and professionals with an understanding of the fundamental mathematical principles used in Industrial Mathematics/OR in modeling problems and application solutions. Over the past seven years, all the concepts presented in each chapter have undergone the learning scrutiny of the author and his students. The conceptual relationships within the chapter material have been developed in the class- M.H. Holmes room experience working with the students' level of understanding. The illustrative material throughout Introduction to the Foundations the book (i.e., worked-out problems and examples of the mathematical principles) was refined for stu- of Applied Mathematics dent comprehension as the manuscript developed The objective of this textbook is the construction, through its iterations. The chapter exercises were formulated each year and refined from the previous A. Deutsch, L. Brusch, H. Byrne, G.d. Vries, H. Herzel analysis, and interpretation of mathematical models to help us understand the world we live in. Rather year's exercises. The book uses a very broad spec- Mathematical Modeling of than follow a case study approach it develops the trum of industrial mathematical applications, which mathematical and physical ideas that are fundamental include applications from deterministic (continuous, Biological Systems, Volume I in understanding contemporary problems in science discrete, static, dynamic) modeling, combinatorics, Cellular Biophysics, Regulatory Networks, and engineering. Science evolves, and this means that regression, optimization, and graph theory. Also it's Development, Biomedicine, and Data Analysis the problems of current interest continually change. important to note that solutions of equation systems, What does not change as quickly is the approach used geometric and conceptual visualization of abstract This two-volume, interdisciplinary work is a unified to derive the relevant mathematical models, and the mathematical concepts have been included. In addi- presentation of a broad range of state-of-the-art topics methods used to analyze the models. Consequently, tion to the end-of-the-chapter exercises, active web in the rapidly growing field of mathematical model- this book is written in such a way as to establish the resources have been provided at the end of each chap- ing in the biological sciences. Highlighted through- mathematical ideas underlying model development ter as well. In sum, the author has carefully developed out both works are mathematical and computational independently of a specific application. This does not a pedagogically strong survey textbook of OR and approaches to examine central problems in the life mean applications are not considered, they are, and Industrial Mathematics. sciences, ranging from the organizational principles connections with experiment are a staple of this book. of individual cells to the dynamics of large popula- More on www.springer.com/978-0-387-37734-6 The book, as well as the individual chapters, is writ- tions. Volume I covers a number of areas, including: Available ten in such a way that the material becomes more * Cellular Biophysics * Regulatory Networks * Devel- sophisticated as you progress. This provides some opmental Biology * Biomedical Applications * Data 2007. XII, 300 p. 70 illus. (International Series in flexibility in how the book is used, allowing consider- Analysis and Model Validation Volume II examines Operations Research & Management Science, 97) ation for the breadth and depth of the material cov- a diverse range of subjects, including: * Epidemiology 978-0-387-37734-6 ered. Moreover, there are a wide spectrum of exercises * Evolution and Ecology * Immunology * Neural Sys- and detailed illustrations that significantly enrich the tems and the Brain * Innovative Mathematical Meth- material. Students and researchers interested in math- ods and Education Both volumes will be excellent ematical modelling in mathematics, physics, engineer- reference texts for a broad audience of researchers, ing and the applied sciences will find this text useful. practitioners, and advanced students in this rapidly growing field at the intersection of applied mathe- More on www.springer.com/978-0-387-87749-5 matics, experimental biology and medicine, computa- Available tional biology, biochemistry, computer science, and physics. 2009. XIV, 468 p. (Texts in Applied Mathematics, 56) More on www.springer.com/978-0-8176-4557-1 978-0-387-87749-5 Available 2007. XVIII, 382 p. 120 illus. (Modeling and Simulation in Science, Engineering and Technology, ) C. Rousseau, Y. Saint-Aubin 978-0-8176-4557-1 Mathematics and Technology Mathematics and Technology presents technologi- cal applications of mathematics making use of elegant mathematical concepts. The selected subjects consist of: public key cryptography, error correct- ing codes, the global positioning system (GPS) and cartography, image compression using fractals and the JPEG format, digital recording, robot movement, DNA computing, Google's PageRank algorithm, L. Kandiller savings and loans, gamma ray surgery and random number generators. The authors highlight how math- Principles of Mathematics in ematical modeling, together with the power of mathematical tools, have been crucial for innovation in Operations Research technology. The exposition is clear, straightforward, Operations Research is the application of scientific motivated by excellent examples, and user-friendly. models, mathematical and statistical ones, to decision Numerous exercises at the end of every chapter rein- making problems, and PRINCIPLES OF MATHE- force the material. An engaging quality is the vari- 54 Mathematical Software springer.com ous historical notes accompanying the mathematical Mathematics (general) wahrscheinlich keinen Bereich der akademischen development. This book is intended mainly for un- Kultur der Mathematik, in welchem jüdische Math- dergraduate students in pure and applied mathemat- ematiker nicht tätig waren. Von der Forschung und ics, physics and computer science, instructors, and Lehre über die Mitwirkung im Publikationswesen high school teachers. The main prerequisites are lin- und in Organisationen wie der Deutschen Math- ear algebra and Euclidean geometry. A few chapters ematiker-Vereinigung bis hin zum öffentlichen require multivariable calculus and elementary proba- Diskurs über die Mathematik wirkten sie in Kaiserre- bility theory. A clear indication of the more difficult ich und Weimarer Republik Seite an Seite mit ihren topics and relatively advanced references make it also nichtjüdischen Kollegen. Wie diese und gemeinsam suitable for an independent reader mastering the pre- mit ihnen prägten sie die deutschsprachige mathe- requisites. matische Kultur ihrer Zeit. Und zweitens war diese Aktivität so vielfältig und unterschiedlich, dass jedes More on www.springer.com/978-0-387-69215-9 damalige (oder auch heutige) Klischee, das jüdischen Available Mathematikern einen irgendwie gearteten besonderen Charakter in der Mathematik ihrer Zeit zuspricht, 2008. XVI, 582 p. 214 illus. (Springer Undergraduate rasch widerlegt wird. Texts in Mathematics and Technology, ) V.I. Arnold, B.A. Khesin 978-0-387-69215-9 More on www.springer.com/978-3-540-69250-8 Topological Methods in Available Hydrodynamics 2009. XI, 236 S. 978-3-540-69250-8 The first monograph to treat topological, group-the- Mathematical Software oretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry. More on www.springer.com/978-0-387-94947-5 Available 1998. XV, 376 p. 78 illus. (Applied Mathematical Sciences, 125) 978-0-387-94947-5 M. Grötschel, K. Lucas, V. Mehrmann

W. Bosma, J. Cannon Produktionsfaktor Mathematik Mathematik als Produktionsfaktor und Discovering Mathematics with Innovationsverstärker? Wer wissen und verste- Magma hen will, warum die Mathematik immer stärker zur Produktentwicklung und Produktionssicher- Reducing the Abstract to the Concrete heit, zur Wertschöpfung und Ressourcenschonung This volume celebrates the first decade of the Com- beiträgt, dem wird dieses Buch eine wahre Fund- puter Algebra system Magma. With a design based grube sein. Das Buch beschreibt das Verhältnis von on the ontology and semantics of algebra, Magma Mathematik und Technikwissenschaften, den Beitrag enables users to rapidly formulate and perform calder Mathematik zur industriellen Wertschöpfung culations in the more abstract parts of mathematics. und die Schlüsselstellung der Mathematik bei der This book introduces the reader to the role Magma Beherrschung komplexer Systeme. In 19 Beiträgen B. Bergmann, M. Epple plays in advanced mathematical research through zu unterschiedlichen ingenieurwissenschaftlichen 14 case studies which, in most cases, describe com- Themenfeldern werden die positiven Wechsel- putations underpinning new theoretical results. The Jüdische Mathematiker in der wirkungen zwischen den Gebieten deutlich. Einem authors of the chapters were chosen both for their deutschsprachigen akademischen breiten Leserkreis wird so ein tiefer Einblick in den expertise in the particular field and for their innova- gegenwärtigen Stand des Zusammenspiel von Mathe- tive use of Magma. Although by no means exhaustive, Kultur matik und Technik gegeben. Gleichzeitig werden auch the topics range over much of Magma's coverage of Der Band dokumentiert eine Wanderausstellung, Maßnahmen zur Verbesserung der Interaktion zwis- algorithmic algebra: from number theory and alge- die im Rahmen des Jahres der Mathematik 2008 in chen Mathematik und Technikwissenschaften, zwis- braic geometry, via representation theory and group sieben deutschen Städten gezeigt wurde. Die Ausstel- chen Forschung und Industrie vorgeschlagen. theory to some branches of discrete mathematics and lung führt die Tätigkeit jüdischer Mathematiker in More on www.springer.com/978-3-540-89434-6 graph theory. A basic introduction to the Magma lan- Deutschland von der rechtlichen und politischen Gle- Available guage is given in an appendix. The book is simulta- ichstellung jüdischer Bürger im 19. Jahrhundert bis neously an invitation to learn a new programming zur Verfolgung und Vertreibung im Nationalsozial- 2009. X, 480 S. (acatech DISKUTIERT, ) language in the context of contemporary research ismus vor Augen. Sie stellt dar, wie im deutschen 978-3-540-89434-6 problems, and an exposition of the types of problem Kaiserreich und in der Weimarer Republik jüdische that can be investigated using computational algebra. Mathematiker in allen Bereichen der mathematis- More on www.springer.com/978-3-540-37632-3 chen Kultur zunehmend eine tragende Rolle spielten, und sie erinnert an Emigration, Flucht und Ermor- Available dung nach 1933.Die Ausstellung, die auch auf bisher 2006. XXIV, 374 p. 9 illus. (Algorithms and Computation in unveröffentlichtem Material und neuer historischer Mathematics, 19) Forschung beruht, macht vor allem zwei Punkte deut- 978-3-540-37632-3 lich. Erstens gab es im hier behandelten Zeitraum springer.com Measure and Integration 55

recherche, propose divers modes glissants généralisés Measure and Integration P. Hilton, D. Holton, J. Pedersen et aspects théoriques, dans le cas des systèmes multi- entrée multi-sortie continus, discrets et hybrides. La Mathematical Reflections première partie constitue une formation (initiale et continue) à la pratique des algorithmes RG et un sup- In a Room with Many Mirrors port à l'enseignement de 3ème cycle (DEA) développé A relaxed and informal presentation conveying the dans la deuxième partie. joy of mathematical discovery and insight. Frequent More on www.springer.com/978-3-540-31003-7 questions lead readers to see mathematics as an accessible world of thought, where understanding can turn Available opaque formulae into beautiful and meaningful ideas. The text presents eight topics that illustrate the unity 2006. XVI, 338 p. 159 ill. (Mathématiques et Applications, 55) of mathematical thought as well as the diversity of 978-3-540-31003-7 mathematical ideas. Drawn from both "pure" and "applied" mathematics, they include: spirals in nature Z. Wang, G.J. Klir and in mathematics; the modern topic of fractals and the ancient topic of Fibonacci numbers; Pascals Tri- angle and paper folding; modular arithmetic and the Generalized Measure Theory arithmetic of the infinite. The final chapter presents This comprehensive text examines the relatively new some ideas about how mathematics should be done, mathematical area of generalized measure theory. and hence, how it should be taught. Presenting many This area expands classical measure theory by aban- recent discoveries that lead to interesting open ques- doning the requirement of additivity and replacing tions, the book can serve as the main text in courses it with various weaker requirements. Each of these dealing with contemporary mathematical topics or weaker requirements characterizes a class of non- as enrichment for other courses. It can also be read additive measures. This results in new concepts and with pleasure by anyone interested in the intellectu- methods that allow us to deal with many problems ally intriguing aspects of mathematics. in a more realistic way. For example, it allows us to More on www.springer.com/978-0-387-94770-9 work with imprecise probabilities. The exposition N. Sinclair, W. Higginson of generalized measure theory unfolds systemati- Available cally. It begins with preliminaries and new concepts, Mathematics and the Aesthetic followed by a detailed treatment of important new 1997. XVI, 351 p. 138 illus. (Undergraduate Texts in New Approaches to an Ancient Affinity results regarding various types of nonadditive mea- Mathematics, ) 978-0-387-94770-9 The essays in this book explore the ancient affinity sures and the associated integration theory. The latter between the mathematical and the aesthetic, focus- involves several types of integrals: Sugeno integrals, ing on the fundamental connections between these Choquet integrals, pan-integrals, and lower and upper integrals. All of the topics are motivated by numerous P. Lopez, A.S. Nouri two modes of reasoning and communicating. From historical, philosophical and psychological perspec- examples, culminating in a final chapter on applica- Théorie élémentaire et pratique tives, with particular attention to certain mathemat- tions of generalized measure theory. Some key fea- ical areas such as geometry and analysis, the authors tures of the book include: many exercises at the end de la commande par les régimes examine the ways in which the aesthetic is ever of each chapter along with relevant historical and bibliographical notes, an extensive bibliography, and glissants present in mathematical thinking and contributes to the growth and value of mathematical knowledge. name and subject indices. The work is suitable for a Cet ouvrage applique les algorithmes à Régimes Glis- classroom setting at the graduate level in courses or More on www.springer.com/978-0-387-30526-4 sants (RG) aux boucles industrielles de régulation et seminars in applied mathematics, computer science, d'asservissement pilotées jusqu'à ce jour par les tradi- Available engineering, and some areas of science. A sound back- tionnels PID et leurs variantes (RST, etc.). Le système 2007. XVI, 288 p. 78 illus., 13 in color. (CMS Books in ground in mathematical analysis is required. Since the réel à commander peut être de nature variée, avoir Mathematics, ) book contains many original results by the authors, it des parties mal ou non modélisées, être soumis à des 978-0-387-30526-4 will also appeal to researchers working in the emerg- perturbations. Les algorithmes numériques robustes ing area of generalized measure theory. About the RG calculent une commande ayant une composante Authors: Zhenyuan Wang is currently a Professor discontinue et donnent une évolution du point de in the Department of Mathematics of University of fonctionnement du système bouclé sur la surface Nebraska at Omaha. His research interests have been de glissement (l'équation de la surface définit la in the areas of nonadditive measures, nonlinear inte- dynamique du système bouclé). Pour les applications grals, probability and statistics, and data mining. He nous avons choisi le contexte de la formation ini- has published one book and many papers in these tiale et de la formation continue (théorie élémentaire, areas. George J. Klir is currently a Distinguished Pro- schéma-bloc, tableau de synthèse, diagrammes tem- fessor of Systems Science at Binghamton University porels, équations différentielles, formalisme de (SUNY at Binghamton). He has published 29 books Laplace, simulation numérique, commande par calcu- and well over 300 papers in a wide range of areas. His lateur). Le tableau de synthèse conduit à l'équation de current research interests are primarily in the areas of la commande et au calcul des paramètres de réglage. fuzzy systems, soft computing, and generalized infor- Des résultats de simulation et d'expérimentation sont mation theory. donnés pour différents actionneurs et plusieurs tech- More on www.springer.com/978-0-387-76851-9 nologies (électrique continue et alternative, pneuma- Available tique, hydraulique, muscles artificiels). Cette première édition comprend deux parties, des annexes et un 2009. XVI, 384 p. 25 illus. (IFSR International Series on index. La première partie est une initiation aux modes Systems Science and Engineering, 25) glissants complétée par divers aspects pratiques, dans 978-0-387-76851-9 le cas des systèmes continus mono-entrée mono-sortie. La deuxième partie, orientée troisième cycle et 56 Non-associative Rings and Algebras springer.com

Non-associative Rings and tation functions in additive number theory (M. B. Nathanson), and mock theta functions, ranks, and J. Brüdern Algebras Maass forms (K. Ono), and elliptic functions (M. Waldschmidt). All of the surveys were outgrowths of Einführung in die analytische featured talks given during the Special Year in Num- ber Theory and Combinatorics at the University of Zahlentheorie Florida, Gainesville, 2004-2005, and describe major Diese Einführung in die analytische Zahlentheo- progress on a broad range of topics. This volume is rie wendet sich an Studierende der Mathematik, intended for mathematicians and graduate students die bereits mit der Funktionentheorie und den ein- interested in number theory and related areas. fachsten Grundtatsachen der Zahlentheorie ver- More on www.springer.com/978-0-387-78509-7 traut sind und ihre Kenntnisse in Zahlentheorie Available vertiefen möchten. Die ausführliche, motivierende Darstellung der behandelten Themen soll den Ein- 2008. X, 188 p. (Developments in Mathematics, 17) 978-0-387-78509-7 stieg in die Ideen und technischen Details erleichtern. Geeignet als Begleitlektüre zu Vorlesungen und zum Selbststudium. Mit zahlreichen Aufgaben und Lösungshinweisen. P. Tauvel, R.W. Yu More on www.springer.com/978-3-540-58821-4 Lie Algebras and Algebraic Groups Available The theory of Lie algebras and algebraic groups has been an area of active research for the last 50 years. 1995. X, 238 S. (Springer-Lehrbuch, ) 978-3-540-58821-4 It intervenes in many different areas of mathematics: for example invariant theory, Poisson geometry, harmonic analysis, mathematical physics. The aim of this book is to assemble in a single volume the algebraic aspects of the theory, so as to present the foundations of the theory in characteristic zero. Detailed proofs are included and some recent results are discussed in the final chapters. All the prerequisites on commuta- P. Borwein, S. Choi, B. Rooney, A. Weirathmueller tive algebra and algebraic geometry are included. More on www.springer.com/978-3-540-24170-6 The Riemann Hypothesis Available A Resource for the Afficionado and Virtuoso 2005. XVI, 653 p. (Springer Monographs in Mathematics, ) Alike 978-3-540-24170-6 The Riemann Hypothesis has become the Holy Grail of mathematics in the century and a half since 1859 when Bernhard Riemann, one of the extraordinary C.J. Bushnell, G. Henniart mathematical talents of the 19th century, originally posed the problem. While the problem is notoriously The Local Langlands Conjecture Number Theory difficult, and complicated even to state carefully, it for GL(2) can be loosely formulated as "the number of integers with an even number of prime factors is the same as If F is a non-Archimedean local field, local class field the number of integers with an odd number of prime theory can be viewed as giving a canonical bijection factors." The Hypothesis makes a very precise con- between the characters of the multiplicative group nection between two seemingly unrelated mathemat- GL(1,F) of F and the characters of the Weil group of F. ical objects, namely prime numbers and the zeros If n is a positive integer, the n-dimensional analogue of analytic functions. If solved, it would give us proof a character of the multiplicative group of F is an found insight into number theory and, in particu- irreducible smooth representation of the general lin- lar, the nature of prime numbers. This book is an ear group GL(n,F). The local Langlands Conjecture introduction to the theory surrounding the Riemann for GL(n) postulates the existence of a canonical bijec- Hypothesis. Part I serves as a compendium of known tion between such objects and n-dimensional repre- results and as a primer for the material presented in sentations of the Weil group, generalizing class field the 20 original papers contained in Part II. The orig- theory. This conjecture has now been proved for all F K. Alladi inal papers place the material into historical context and n, but the arguments are long and rely on many and illustrate the motivations for research on and deep ideas and techniques. This book gives a complete Surveys in Number Theory around the Riemann Hypothesis. Several of these and self-contained proof of the Langlands conjecture papers focus on computation of the zeta function, in the case n=2. It is aimed at graduate students and at Number theory has a wealth of long-standing prob- while others give proofs of the Prime Number Theo- researchers in related fields. It presupposes no special lems, the study of which over the years has led to rem, since the Prime Number Theorem is so closely knowledge beyond the beginnings of the representa- major developments in many areas of mathemat- connected to the Riemann Hypothesis. The text is tion theory of finite groups and the structure theory of ics. This volume consists of seven significant chap- suitable for a graduate course or seminar or simply as local fields. It uses only local methods, with no appeal ters on number theory and related topics. Written a reference for anyone interested in this extraordinary to harmonic analysis on adele groups. by distinguished mathematicians, key topics focus conjecture. More on www.springer.com/978-3-540-31486-8 on multipartitions, congruences and identities (G. Andrews), the formulas of Koshliakov and Guinand More on www.springer.com/978-0-387-72125-5 Available in Ramanujan's Lost Notebook (B. C. Berndt, Y. Lee, Available 2006. XII, 354 p. (Grundlehren der mathematischen and J. Sohn), alternating sign matrices and the Weyl 2008. XIV, 538 p. 25 illus. (CMS Books in Mathematics, ) Wissenschaften, 335) character formulas (D. M. Bressoud), theta func- 978-0-387-72125-5 978-3-540-31486-8 tions in complex analysis (H. M. Farkas), represen- springer.com Number Theory 57

lier book will become the standard and indispensable reference on the subject. More on www.springer.com/978-0-387-98727-9 Available

2000. XV, 578 p. 7 illus. (Graduate Texts in Mathematics, 193) 978-0-387-98727-9

J. Coates, R. Sujatha G. Everest, T. Ward Cyclotomic Fields and Zeta Values An Introduction to Number Cyclotomic fields have always occupied a central place in number theory, and the so called "main con- Theory jecture" on cyclotomic fields is arguably the deepest An Introduction to Number Theory provides an and most beautiful theorem known about them. It introduction to the main streams of number theory. is also the simplest example of a vast array of subse- Starting with the unique factorization property of the quent, unproven "main conjectures'' in modern arith- integers, the theme of factorization is revisited sev- metic geometry involving the arithmetic behaviour of eral times throughout the book to illustrate how the motives over p-adic Lie extensions of number fields. W. Coppel ideas handed down from Euclid continue to rever- These main conjectures are concerned with what berate through the subject. In particular, the book one might loosely call the exact formulae of num- Number Theory shows how the Fundamental Theorem of Arithmetic, ber theory which conjecturally link the special values An Introduction to Mathematics handed down from antiquity, informs much of the of zeta and L-functions to purely arithmetic expres- teaching of modern number theory. The result is that sions. Written by two leading workers in the field, this "Number Theory" is more than a comprehensive number theory will be understood, not as a collec- short and elegant book presents in full detail the sim- treatment of the subject. It is an introduction to topics tion of tricks and isolated results, but as a coherent plest proof of the "main conjecture'' for cyclotomic in higher level mathematics, and unique in its scope; and interconnected theory. A number of different fields. Its motivation stems not only from the inherent topics from analysis, modern algebra, and discrete approaches to number theory are presented, and the beauty of the subject, but also from the wider arith- mathematics are all included. The book is divided different streams in the book are brought together in metic interest of these questions. The masterly expo- into two parts. Part A covers key concepts of number a chapter that describes the class number formula for sition is intended to be accessible to both graduate theory and could serve as a first course on the subject. quadratic fields and the famous conjectures of Birch students and non-experts in Iwasawa theory. Part B delves into more advanced topics and an explo- and Swinnerton-Dyer. The final chapter introduces More on www.springer.com/978-3-540-33068-4 ration of related mathematics. Part B contains, for some of the main ideas behind modern computational example, complete proofs of the Hasse–Minkowski number theory and its applications in cryptography. Available theorem and the prime number theorem, as well as Written for graduate and advanced undergraduate 2006. X, 116 p. (Springer Monographs in Mathematics, ) self-contained accounts of the character theory of students of mathematics, this text will also appeal to 978-3-540-33068-4 finite groups and the theory of elliptic functions. The students in cognate subjects who wish to learn some prerequisites for this self-contained text are elements of the big ideas in number theory. from linear algebra. Valuable references for the reader More on www.springer.com/978-1-85233-917-3 are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for Available H. Cohen undergraduates, or for self-study. From the reviews: "This is a book which many mathematicians could 2005. X, 302 p. 16 illus. (Graduate Texts in Advanced Topics in Computional enjoy browsing, and one which a good undergraduate Mathematics, 232) Number Theory could be encouraged to read to learn something of the 978-1-85233-917-3 interconnections, which exist between apparently dis- The present book addresses a number of specific top- parate parts of mathematics." —Canadian Mathemati- ics in computational number theory whereby the cal Society "As a source for information on the 'reach' author is not attempting to be exhaustive in the choice of number theory into other areas of mathematics, it C. Goldstein of subjects. The book is organized as follows. Chap- is an excellent work." —Mathematical Association of ters 1 and 2 contain the theory and algorithms con- America cerning Dedekind domains and relative extensions of Seminaire de Theorie des number fields, and in particular the generalization to More on www.springer.com/978-0-387-89485-0 Nombres, Paris 1985-86 the relative case of the round 2 and related algorithms. Available Chapters 3, 4, and 5 contain the theory and com- This is the sixth annual volume of papers based on plete algorithms concerning class field theory over 2009. XIII, 610 p. 17 illus. (Universitext, ) the outstanding lectures given at the Séminaire de number fields. The highlights are the algorithms for 978-0-387-89485-0 Théorie des Nombres de Paris. The results presented computing the structure of (Z_K/m)^*, of ray class in 1985-86 by an international group of mathemati- groups, and relative equations for Abelian extensions cians reflect the most recent work in many areas of of number fields using Kummer theory. Chapters 1 to number theory. 5 form a homogeneous subject matter which can be More on www.springer.com/978-0-8176-3369-1 used for a 6 months to 1 year graduate course in com- Available putational number theory. The subsequent chapters deal with more miscellaneous subjects. Written by an 1987. 228 p. (Progress in Mathematics, 71) authority with great practical and teaching experience 978-0-8176-3369-1 in the field, this book together with the author's ear- 58 Number Theory springer.com

G. Greaves in such a way that interest seldom flags." — Mathe- matical Reviews (Review of First Edition) Sieves in Number Theory More on www.springer.com/978-0-8176-4837-4 This book surveys the current state of the "small" sieve Available methods developed by Brun, Selberg and later workers.. A self-contained treatment is given to topics that 1984. XVIII, 333 p. 8 illus. (Modern Birkhäuser are of central importance in the subject. These include Classics, ) the upper bound method of Selberg, Brun's method, 978-0-8176-4837-4 Rosser's sieve as developed by Iwaniec, with a bilinear form of the remainder term, the sieve with weights, and the use of Selberg's ideas in deriving lower-bound sieves. Further developments are introduced with the support of references t. The book is suitable for M. Jacobson, H. Williams university graduates making their first acquaintance with the subject, leading them towards the frontiers of Solving the Pell Equation modern research and unsolved problems in the sub- Pell's equation is a very simple, yet fundamental ject area. Diophantine equation which is believed to have More on www.springer.com/978-3-540-41647-0 been known to mathematicians for over 2000 years. Available Because of its popularity, the Pell equation is often 2001. XII, 304 p. (Ergebnisse der Mathematik und ihrer discussed in textbooks and recreational books con- Grenzgebiete. 3. Folge A Series of Modern Surveys in cerning elementary number theory, but usually not Mathematics, 43) J. Hoffstein, J. Pipher, J. Silverman in much depth. This book provides a modern and 978-3-540-41647-0 deeper approach to the problem of solving the Pell An Introduction to Mathematical equation. The main component of this will be computational techniques, but in the process of deriving Cryptography these it will be necessary to develop the correspond- This self-contained introduction to modern cryp- ing theory. One objective of this book is to provide a tography emphasizes the mathematics behind the less intimidating introduction for senior undergradu- theory of public key cryptosystems and digital sig- ates and others with the same level of preparedness to nature schemes. The book focuses on these key top- the delights of algebraic number theory through the ics while developing the mathematical tools needed medium of a mathematical object that has fascinated for the construction and security analysis of diverse people since the time of Archimedes. To achieve this, cryptosystems. Only basic linear algebra is required this work is made accessible to anyone with some of the reader; techniques from algebra, number the- knowledge of elementary number theory and abstract ory, and probability are introduced and developed algebra. Many references and notes are provided for as required. The book covers a variety of topics that those who wish to follow up on various topics, and the are considered central to mathematical cryptography. authors also describe some rather surprising appli- E. Grosswald Key topics include: * classical cryptographic construc- cations to cryptography. The intended audience is tions, such as Diffie-Hellmann key exchange, discrete number theorists, both professional and amateur, and Topics from the Theory of logarithm-based cryptosystems, the RSA cryptosys- students, but we wish to emphasize that this is not tem, and digital signatures; * fundamental mathe- intended to be a textbook; its focus is much too nar- Numbers matical tools for cryptography, including primality row for that. It could, however be used as supplemen- testing, factorization algorithms, probability theory, tary reading for students enrolled in a second course Many of the important and creative developments in information theory, and collision algorithms; * an in- in number theory. modern mathematics resulted from attempts to solve depth treatment of important recent cryptographic questions that originate in number theory. The pub- More on www.springer.com/978-0-387-84922-5 innovations, such as elliptic curves, elliptic curve and lication of Emil Grosswald’s classic text presents an Available pairing-based cryptography, lattices, lattice-based illuminating introduction to number theory. Com- cryptography, and the NTRU cryptosystem. This bining the historical developments with the analytical book is an ideal introduction for mathematics and 2009. XX, 500 p. 20 illus. (CMS Books in approach, Topics from the Theory of Numbers offers Mathematics, ) computer science students to the mathematical foun- the reader a diverse range of subjects to investigate, 978-0-387-84922-5 dations of modern cryptography. The book includes including: * divisibility * congruences * the Riemann an extensive bibliography and index; supplementary zeta function * Diophantine equations and Fermat’s materials are available online. conjecture * the theory of partitions Comprehen- sive in nature, Topics from the Theory of Numbers is More on www.springer.com/978-0-387-77993-5 an ideal text for advanced undergraduates and grad- Available uate students alike. "In my opinion it is excellent. It is carefully written and represents clearly a work 2008. XVI, 524 p. 29 illus. (Undergraduate Texts in of a scholar who loves and understands his subject. Mathematics, ) One can only wish more authors would take such 978-0-387-77993-5 pains and would be as good and honest expositors as Grosswald." — Marc Kac "This book is designed for use in a first course in number theory at the junior or senior level...The author has certainly planned his book well, chosen material that will be stimulating to its intended audience, and carried the project through springer.com Number Theory 59

zur Sprache kommen, die so weder im Unterricht noch im Studium behandelt werden, ergänzt die Einführung ideal den Vorlesungsstoff für Lehramt- skandidaten und Diplomstudenten. More on www.springer.com/978-3-540-20391-9 Available

2004. X, 406 S. (Springer-Lehrbuch, ) 978-3-540-20391-9

A. Klein N. Koblitz Visuelle Kryptographie Algebraic Aspects of Seit der Erfindung der Schrift hat es auch immer das Cryptography Bedürfnis gegeben, Geschriebenes vor unbefugten S. Lang This is a textbook for a course (or self-instruction) in Lesern zu verbergen. Die Lehre von den Geheim- cryptography with emphasis on algebraic methods. schriften ist daher fast ebenso alt wie die Schrift Cyclotomic Fields I-II The first half of the book is a self-contained informal selbst. Als Wissenschaft im modernen Sinn ist die introduction to areas of algebra, number theory, and This book is a combined edition of the books previ- Kryptographie jedoch noch sehr jung. Bei dem 1994 computer science that are used in cryptography. Most ously published as Cyclotomic Fields, Vol. I and II. It von Naor und Shamir erfundenen Verfahren der of the material in the second half - "hidden mono- continues to provide a basic introduction to the the- visuellen Kryptographie wird ein Bild so auf zwei mial" systems, combinatorial-algebraic systems, and ory of these number fields, which are of great interest Folien verteilt, dass auf jeder einzelnen Folie nur hyperelliptic systems - has not previously appeared in in classical number theory, as well as in other areas, ein zufälliges Punktmuster zu sehen ist, aber beide monograph form. The appendix by Menezes, Wu, and such as K-theory. Cyclotomic Fields begins with basic Folien übereinandergelegt das geheime Bild ergeben. Zuccherato gives an elementary treatment of hyper- material on character sums, and proceeds to treat Das Buch gibt einen Einblick in dieses aktuelle elliptic curves. This book is intended for graduate class number formulas, p-adic L-functions, Iwasawa Forschungsgebiet, wobei bewußt auf die sogenan- students, advanced undergraduates, and scientists theory, Lubin-Tate theory, and explicit reciprocity nte höhere Mathematik verzichtet wurde. Es eignet working in various fields of data security. laws, and the Ferrero-Washington theorems, which sich daher ideal als Grundlage für Proseminare und prove Iwasawa's conjecture on the growth of the p- Mathematik-AGs der Sekundarstufe. Aufgaben mit More on www.springer.com/978-3-540-63446-1 primary part of the ideal class group. Musterlösungen helfen, das Gelesene zu vertiefen. Available More on www.springer.com/978-0-387-96671-7 More on www.springer.com/978-3-540-72361-5 1998. IX, 206 p. 7 illus. (Algorithms and Computation in Available Available Mathematics, 3) 978-3-540-63446-1 1990. XVII, 460 p. 28 illus. (Graduate Texts in 2007. X, 167 S. 21 Abb. (Springer-Lehrbuch, ) Mathematics, 121) 978-3-540-72361-5 978-0-387-96671-7

A. Leutbecher Zahlentheorie N. Koblitz Eine Einführung in die Algebra P-adic Numbers, p-adic Analysis, Auf der Grundlage der Mathematikkenntnisse des ersten Studienjahres bietet der Autor eine Einführung and Zeta-Functions in die Zahlentheorie mit Schwerpunkt auf der ele- The first edition of this work has become the standard mentaren und algebraischen Zahlentheorie. Da er die H. Koch introduction to the theory of p-adic numbers at both benötigten algebraischen Hilfsmittel nicht voraus- the advanced undergraduate and beginning graduate setzt, sondern permanent mitentwickelt, wendet level. This second edition includes a deeper treatment Einführung in die Mathematik sich das Buch auch an Nichtspezialisten, denen es of p-adic functions in Ch. 4 to include the Iwasawa Hintergründe der Schulmathematik über die Zahlen frühzeitig den Weg in die Algebra logarithm and the p-adic gamma-function, the rear- Diese Einführung besticht durch zwei ungewöhnliche öffnet. Angestrebte Ziele sind: Der Satz von Kro- rangement and addition of some exercises, the inclu- Aspekte: Sie gibt einen Einblick in die Mathematik necker-Weber zur Krönung der Galois-Theorie, der sion of an extensive appendix of answers and hints to als Bestandteil unserer Kultur, und sie vermittelt die Minkowskische Gitterpunktsatz, der Dirichletsche the exercises, as well as numerous clarifications. Hintergründe der Mathematik vom Schulstoff ausge- Primzahlsatz und die Bewertungstheorie der Körper. Ein umfangreicher Aufgabenteil mit Anleitungen More on www.springer.com/978-0-387-96017-3 hend bis zum Niveau von Mathematikvorlesungen im ersten Studienjahr. Die Stoffdarstellung geht vom bietet neben konkreten Beispielen und alternativen Available Aufbau der natürlichen Zahlen aus; der Schwerpunkt Beweisgängen vielfältige Rechenpraxis und Hinweise liegt aber in den exakten Begründungen der Zahlen- auf algorithmische Lösungswege. 1984. XII, 172 p. 9 illus. (Graduate Texts in begriffe, der Geometrie der Ebene und der Funktio- Mathematics, 58) More on www.springer.com/978-3-540-58791-0 nen einer Veränderlichen. Dabei werden alle Sätze bis 978-0-387-96017-3 Available hin zum Hauptsatz der Algebra vollständig bewiesen. Der klare Aufbau des Buches mit Stichwortregister 1996. XII, 354 S. 9 Abb. Mit 1 Falttafel. (Springer- wichtiger Begriffe erleichtert das systematische Ler- Lehrbuch, ) nen und Nachschlagen. Die zweite Auflage enthält 978-3-540-58791-0 teilweise ausführliche Darstellungen für die Lösungen der zahlreichen Übungsaufgaben.Da viele Aspekte 60 Number Theory springer.com

interesting problems throughout. The text is suitable for a graduate course in analytic number theory. More on www.springer.com/978-0-387-98308-0 Available M.R. Murty, J.(. Esmonde 1998. VIII, 78 p. (Graduate Texts in Mathematics, 177) Problems in Algebraic Number 978-0-387-98308-0 Theory The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challeng- R. Schoof ing All problems are elegantly solved Catalan's Conjecture More on www.springer.com/978-0-387-22182-3 Eugène Charles Catalan made his famous conjecture – Available that 8 and 9 are the only two consecutive perfect pow- ers of natural numbers – in 1844 in a letter to the edi- 2005. XVI, 352 p. (Graduate Texts in Mathematics, 190) tor of Crelle’s mathematical journal. One hundred 978-0-387-22182-3 and fifty-eight years later, Preda Mihailescu proved it. Catalan’s Conjecture presents this spectacular result A. Schmidt in a way that is accessible to the advanced undergraduate. The first few sections of the book require lit- Einführung in die algebraische tle more than a basic mathematical background and M.B. Nathanson some knowledge of elementary number theory, while Zahlentheorie later sections involve Galois theory, algebraic number theory and a small amount of commutative alge- Additive Number Theory: Inverse Das vorliegende Buch gibt eine Einführung in die bra. The prerequisites, such as the basic facts from Grundgedanken der modernen algebraischen Zahlen- Problems and the Geometry of the arithmetic of cyclotomic fields, are all discussed theorie, einer der traditionsreichsten und gleichzeitig within the text. The author dissects both Mihailescu’s Sumsets heute besonders aktuellen Grunddisziplinen der proof and the earlier work it made use of, taking great Mathematik. Ausgehend von Themenbereichen, die Many classical problems in additive number theory care to select streamlined and transparent versions üblicherweise der elementaren Zahlentheorie zuge- are direct problems, in which one starts with a set A of the arguments and to keep the text self-contained. ordnet werden, führt es anhand konkreter Prob- of natural numbers and an integer H -> 2, and tries to Only in the proof of Thaine’s theorem is a little class lemstellungen zu den Techniken, die das Herz der describe the structure of the sumset hA consisting of field theory used; it is hoped that this application will modernen Theorie ausmachen. Hierbei wird beson- all sums of h elements of A. By contrast, in an inverse motivate the interested reader to study the theory derer Wert auf Lokal-Global-Prinzipien für diophan- problem, one starts with a sumset hA, and attempts further. Beautifully clear and concise, this book will tische Gleichungen gelegt. Die Dedekindsche Theorie to describe the structure of the underlying set A. In appeal not only to specialists in number theory but der Ideale wird für den Fall quadratischer Zahlkörper recent years there has been ramrkable progress in the to anyone interested in seeing the application of the vollständig entwickelt. Es werden die p-adischen study of inverse problems for finite sets of integers. In ideas of algebraic number theory to a famous mathe- Zahlen eingeführt und der berühmte Satz von Hasse- particular, there are important and beautiful inverse matical problem. theorems due to Freiman, Kneser, Plünnecke, Vosper, Minkowski über rationale quadratische Formen and others. This volume includes their results, and bewiesen. Der technische Apparat wird behutsam More on www.springer.com/978-1-84800-184-8 culminates with an elegant proof by Ruzsa of the deep und nur so weit entwickelt, wie es für die konkreten Available theorem of Freiman that a finite set of integers with Fragestellungen nötig ist. Daher können weite Teile a small sumset must be a large subset of an n-dimen- des Buches ohne Vorwissen gelesen werden. Umfan- 2009. IX, 124 p. 10 illus. (Universitext, ) sional arithmetic progression. greiches Übungsmaterial rundet die Darstellung ab. 978-1-84800-184-8 More on www.springer.com/978-0-387-94655-9 More on www.springer.com/978-3-540-45973-6 Available Available

1996. XIV, 293 p. (Graduate Texts in Mathematics, 2007. XII, 215 S. (Springer-Lehrbuch, ) 165) 978-3-540-45973-6 978-0-387-94655-9

D.J. Newman Analytic Number Theory Some of the central topics in number theory, presnted J. Stillwell in a simple and concise fashion. The author covers an amazing amount of material, despite a leisurely pace Numbers and Geometry and emphasis on readability. His heartfelt enthusiasm enables readers to see what is magical about the sub- A beautiful and relatively elementary account of a ject. All the topics are presented in a refreshingly ele- part of mathematics where three main fields - alge- gant and efficient manner with clever examples and bra, analysis and geometry - meet. The book provides a broad view of these subjects at the level of calculus, without being a calculus book. Its roots are in arithmetic and geometry, the two opposite poles of mathe- springer.com Numerical Analysis 61 matics, and the source of historic conceptual conflict. vation laws by the same authors. While in the earlier The resolution of this conflict, and its role in the publication, the authors concentrate on the mathe- development of mathematics, is one of the main sto- matical theory of multidimensional scalar conserva- ries in the book. Stillwell has chosen an array of excit- tion laws, in this work, they consider systems and the ing and worthwhile topics and elegantly combines theoretical aspects which are needed in the applica- mathematical history with mathematics. He covers tions, such as the solution of the Riemann problem the main ideas of Euclid, but with 2000 years of extra and further insights into more sophisticated prob- insights attached. Presupposing only high school alge- lems. bra, it can be read by any well prepared student enter- More on www.springer.com/978-0-387-94529-3 ing university. Moreover, this book will be popular with graduate students and researchers in mathemat- Available ics due to its attractive and unusual treatment of fundamental topics. A set of well-written exercises at the 1996. VIII, 524 p. 75 illus. (Applied Mathematical J. Stoer, R. Bulirsch end of each section allows new ideas to be instantly Sciences, 118) 978-0-387-94529-3 tested and reinforced. Numerische Mathematik 2 More on www.springer.com/978-0-387-98289-2 Eine Einführung - unter Berücksichtigung von Available Vorlesungen von F.L.Bauer Dieses zweibändige Standardlehrbuch bietet einen 1997. 364 p. 95 illus. (Undergraduate Texts in umfassenden und aktuellen Überblick über die Mathematics, ) Numerische Mathematik. Dabei wird besonderer 978-0-387-98289-2 A. Hohmann, P. Deuflhard Wert auf solche Vorgehensweisen und Methoden gelegt, die sich durch große Wirksamkeit auszeich- Numerical Analysis in Modern nen. Ihr praktischer Nutzen, aber auch die Grenzen ihrer Anwendung werden vergleichend disku- Scientific Computing tiert. Zahlreiche Beispiele runden dieses unent- Numerical Analysis An Introduction behrliche Buch ab.Die Neuauflage des zweiten Bandes wurde vollständig überarbeitet und ergänzt um eine This introductory book directs the reader to a selec- Beschreibung weiterer Techniken im Rahmen der tion of useful elementary numerical algorithms on C. Bernardi, Y. Maday, F. Rapetti Mehrzielmethode zur Lösung von Randwertproble- a reasonably sound theoretical basis, built up within men für Gewöhnliche Differentialgleichungen. "Das the text. The primary aim is to develop algorith- Lehrbuch ... setzt Maßstäbe für eine Numerik-Vor- Discrétisations variationnelles de mic thinking -- emphasizing long living computa- lesung und ist jedem Studenten der angewandten tional concepts over fast changing software issues. problèmes aux limites elliptiques Mathematik zu empfehlen." Die Neue Hochschule The guiding principle is to explain modern numer- L'analyse numérique de deux types de discrétisations ical analysis concepts applicable in complex scien- More on www.springer.com/978-3-540-23777-8 variationnelles est effectuée en détail pour des tific computing at much simpler model problems. For Available problèmes elliptiques: les méthodes spectrales et les example, the two adaptive techniques in numerical méthodes d'éléments finis. Les avantages de chaque quadrature elaborated here carry the germs for either 2005. X, 394 S. 28 Abb. (Springer-Lehrbuch, ) type sont mis en valeur, et leur mise en oeuvre est extrapolation methods or multigrid methods in dif- 978-3-540-23777-8 décrite. L'originalité de cet ouvrage est d'insérer ferential equations, which are not treated here. The ces deux types de discrétisation dans un cadre presentation draws on geometrical intuition wherever abstrait commun, ce qui permet au lecteur d'étendre appropriate, supported by a large number of illus- l'approche à bien d'autres méthodes et problèmes. trations. Numerous exercises are included for fur- Sont présentés également un algorithme pour cou- ther practice and improved understanding. This text pler ces méthodes dans un cadre de décomposition will appeal to undergraduate and graduate students de domaine et une application aux écoulements de as well as researchers in mathematics, computer sci- fluides incompressibles dans des milieux poreux. ence, science, and engineering. At the same time it is L'ouvrage s'adresse aux étudiants de 3ème cycle addressed to practical computational scientists who, en mathématiques appliquées et mécanique, ainsi via self-study, wish to become acquainted with mod- qu'à tous les ingénieurs intéressés par la simulation ern concepts of numerical analysis and scientific com- numérique. puting on an elementary level. Sole prerequisite is More on www.springer.com/978-3-540-21369-7 undergraduate knowledge in Linear Algebra and Cal- Available culus. More on www.springer.com/978-0-387-95410-3 R.S. Varga 2004. XI, 310 p. (Mathématiques et Applications, 45) Available 978-3-540-21369-7 Matrix Iterative Analysis 2003. XVIII, 337 p. 65 illus. (Texts in Applied Mathematics, 43) This is the softcover reprint of a very popular hard- 978-0-387-95410-3 cover edition, a revised version of the first edition, originally published by Prentice Hall in 1962 and E. Godlewski, P. Raviart regarded as a classic in its field. In some places, newer research results, e.g. results on weak regular splittings, Numerical Approximation have been incorporated in the revision, and in other of Hyperbolic Systems of places, new material has been added in the chapters, as well as at the end of chapters, in the form of addi- Conservation Laws tional up-to-date references and some recent the- This work is devoted to the theory and approximation orems to give the reader some newer directions to of nonlinear hyperbolic systems of conservation laws pursue. The material in the new chapters is basically in one or two spaces variables. It follows directly a self-contained and more exercises have been pro- previous publication on hyperbolic systems of conser- vided for the readers. While the original version was 62 Operations Research, Mathematical Programming springer.com more linear algebra oriented, the revision attempts to Operations Research, describes numerical algorithms in a tutorial way. It emphasize tools from other areas, such as approxima- covers fundamental algorithms as well as more spe- tion theory and conformal mapping theory, to access Mathematical Programming cialized and advanced topics for unconstrained and newer results of interest. The book should be of great constrained problems. Most of the algorithms are interest to researchers and graduate students in the explained in a detailed manner, allowing straight- field of numerical analysis. R. Battiti, M. Brunato, F. Mascia forward implementation. Theoretical aspects of the approaches chosen are also addressed with care, often More on www.springer.com/978-3-642-05154-8 Reactive Search and Intelligent using minimal assumptions. This new edition con- Available tains computational exercises in the form of case stud- 2000. X, 358 p. (Springer Series in Computational Optimization ies which help understanding optimization methods Mathematics, 27) Reactive Search integrates sub-symbolic machine beyond their theoretical, description, when coming to 978-3-642-05154-8 learning techniques into search heuristics for solving actual implementation. Besides, the nonsmooth opti- complex optimization problems. By automatically mization part has been substantially reorganized and adjusting the working parameters, a reactive search expanded. self-tunes and adapts, effectively learning by doing More on www.springer.com/978-3-540-35445-1 until a solution is found. Intelligent Optimization, a superset of Reactive Search, concerns online and Available off-line schemes based on the use of memory, adap- tation, incremental development of models, experi- 2006. XIV, 490 p. 52 illus. (Universitext, ) mental algorithms applied to optimization, intelligent 978-3-540-35445-1 tuning and design of heuristics. Reactive Search and Intelligent Optimization is an excellent introduction to the main principles of reactive search, as well as an attempt to develop some fresh intuition for the approaches. The book looks at different optimization possibilities with an emphasis on opportunities P. Wesseling for learning and self-tuning strategies. While focusing more on methods than on problems, problems Principles of Computational Fluid are introduced wherever they help make the discussion more concrete, or when a specific problem has Dynamics been widely studied by reactive search and intelli- The book is aimed at graduate students, researchers, gent optimization heuristics. Individual chapters engineers and physicists involved in flow computa- cover reacting on the neighborhood; reacting on the tions. An up-to-date account is given of the present annealing schedule; reactive prohibitions; model- R.I. Bot, S. Grad, G. Wanka state-of-the-art of numerical methods employed based search; reacting on the objective function; rela- in computational fluid dynamics. The underlying tionships between reactive search and reinforcement numerical principles are treated with a fair amount learning; and much more. Each chapter is structured Duality in Vector Optimization of detail, using elementary mathematical analysis. to show basic issues and algorithms; the parameters This book presents fundamentals and comprehensive Attention is given to difficulties arising from geomet- critical for the success of the different methods dis- results regarding duality for scalar, vector and set-val- ric complexity of the flow domain and of nonuniform cussed; and opportunities and schemes for the auto- ued optimization problems in a general setting. After structured boundary-fitted grids. Uniform accuracy mated tuning of these parameters. Anyone working a preliminary chapter dedicated to convex analysis and efficiency for singular perturbation problems is in decision making in business, engineering, eco- and minimality notions of sets with respect to par- studied, pointing the way to accurate computation nomics or science will find a wealth of information tial orderings induced by convex cones a chapter on of flows at high Reynolds number. Much attention here. scalar conjugate duality follows. Then investigations is given to stability analysis, and useful stability con- More on www.springer.com/978-0-387-09623-0 on vector duality based on scalar conjugacy are made. ditions are provided, some of them new, for many Available Weak, strong and converse duality statements are numerical schemes used in practice. Unified meth- delivered and connections to classical results from the ods for compressible and incompressible flows are 2008. X, 197 p. 74 illus. (Operations Research Computer literature are emphasized. One chapter is exclusively Science Interfaces Series, 45) discussed. Numerical analysis of the shallow-water consecrated to the scalar and vector Wolfe and Mond- 978-0-387-09623-0 equations is included. The theory of hyperbolic con- Weir duality schemes. The monograph is closed with servation laws is treated. Godunov's order barrier extensive considerations concerning conjugate duality and how to overcome it by means of slope-limited for set-valued optimization problems. schemes is discussed. An introduction is given to effi- More on www.springer.com/978-3-642-02885-4 cient iterative solution methods, using Krylov subspace and multigrid acceleration. Many pointers Available are given to current literature, to help the reader to 2009. XV, 400 p. (Vector Optimization, ) quickly reach the current research frontier. 978-3-642-02885-4 More on www.springer.com/978-3-642-05145-6 Available

2001. XII, 644 p. (Springer Series in Computational Mathematics, 29) 978-3-642-05145-6 J. Bonnans, J.C. Gilbert, C. Lemarechal, C.A. Sagastizábal Numerical Optimization Theoretical and Practical Aspects Just as in its 1st edition, this book starts with illustrations of the ubiquitous character of optimization, and springer.com Operations Research, Mathematical Programming 63

and methods based on operations research, artificial intelligence and computer sciences techniques for design of production systems, supply and inventory management, production planning and scheduling, facility location, transportation and logistics, supply flow optimisation via simulation, etc. The content focuses on a wide spectrum of optimisation problems taking into account supply chain paradigms, which create a pivotal idea to increase the productivity of modern production systems. More on www.springer.com/978-0-387-23566-0 E. Cascetta J. Lasserre Available Transportation Systems Analysis 2005. XVI, 289 p. (Applied Optimization, 94) Linear and Integer Programming 978-0-387-23566-0 Models and Applications vs Linear Integration and This book provides a comprehensive and systematic Counting presentation of the mathematical models for the simulation of transportation systems and the method- A Duality Viewpoint ologies for the analysis and design of these systems. In this book the author analyzes and compares four Theoretical and operational aspects are presented in closely related problems, namely linear program- a rigorous and exhaustive framework, addressing a ming, integer programming, linear integration, lin- broad range of applications performed by researchers ear summation (or counting). The focus is on duality and practitioners. Topics are presented with an and the approach is rather novel as it puts integer increasing level of detail and complexity.In this 2nd programming in perspective with three associated edition the author extends and generalizes the con- problems, and permits one to define discrete ana- tents of the previous edition entitled "Transportation logues of well-known continuous duality concepts, Systems Engineering: Theory and Methods" published and the rationale behind them. Also, the approach in 2001. In addition to entirely new material dealing highlights the difference between the discrete and X. Guo, O. Hernández-Lerma with the recent developments in the field, the text has continuous cases. Central in the analysis are the con- been revised to simplify the presentation. The Bibli- tinuous and discrete Brion and Vergne's formulae for ography has also been expanded significantly. All the Continuous-Time Markov Decision linear integration and counting. This approach pro- topics are presented with simple numerical examples Processes vides some new insights on duality concepts for inte- as well as with references to real-life applications.The Theory and Applications ger programs, and also permits to retrieve and shed material is structured so as to offer different levels new light on some well-known results. For instance, of complexity and different reading paths based on Continuous-time Markov decision processes (MDPs), Gomory relaxations and the abstract superadditive the reader’s needs. It is suitable for graduate level also known as controlled Markov chains, are used dual of integer programs are re-interpreted in this courses on transportation analysis and planning. Pre- for modeling decision-making problems that arise in algebraic approach. This book will serve graduate stu- requisites include a basic knowledge of calculus, opti- operations research (for instance, inventory, manu- dents and researchers in applied mathematics, optimization techniques, probability theory and statistics. facturing, and queueing systems), computer science, mization, operations research and computer science. Due to the breadth and depth of topics covered, the communications engineering, control of popula- Due to the substantial practical importance of some book will also serve as an excellent reference guide for tions (such as fisheries and epidemics), and manage- presented problems, researchers in other areas will researchers, teachers and practitioners. ment science, among many other fields. This volume also find this book useful. provides a unified, systematic, self-contained pre- More on www.springer.com/978-0-387-75856-5 sentation of recent developments on the theory and More on www.springer.com/978-0-387-09413-7 Available applications of continuous-time MDPs. The MDPs Available 2009. XVII, 742 p. 100 illus. (Springer Optimization and Its in this volume include most of the cases that arise 2009. XIV, 168 p. 2 illus. (Springer Series in Operations Applications, 29) in applications, because they allow unbounded tran- Research and Financial Engineering, ) 978-0-387-75856-5 sition and reward/cost rates. Much of the material 978-0-387-09413-7 appears for the first time in book form. More on www.springer.com/978-3-642-02546-4 Available 2009. XVII, 231 p. (Stochastic Modelling and Applied Probability, 62) 978-3-642-02546-4

A. Dolgui, J. Soldek, O. Zaikin D.G. Luenberger, Y. Ye Supply Chain Optimisation Linear and Nonlinear Product/Process Design, Facility Location and Programming Flow Control "Linear and Nonlinear Programming" is considered This volume is a collection of recent key results in a classic textbook in Optimization. While it is a clas- supply chain optimisation. It presents new approaches 64 Operator Theory springer.com sic, it also reflects modern theoretical insights. These experts on the subject. The chapters are organized in insights provide structure to what might otherwise three parts: Theory, Algorithms, and Applications and be simply a collection of techniques and results, and Extensions. this is valuable both as a means for learning existing More on www.springer.com/978-0-7923-7771-9 material and for developing new results. One major insight of this type is the connection between the Available purely analytical character of an optimization prob- 2000. 688 p. (International Series in Operations Research & lem, expressed perhaps by properties of the necessary Management Science, 27) conditions, and the behavior of algorithms used to 978-0-7923-7771-9 solve a problem. This was a major theme of the first and second editions. Now the third edition has been completely updated with recent Optimization Methods. Yinyu Ye has written chapters and chap- R. Vanderbei ter material on a number of these areas including Operator Theory Interior Point Methods. This book is designed for Linear Programming either self-study by professionals or classroom work Foundations and Extensions at the undergraduate or graduate level for technical This Third Edition introduces the latest theory and students. Like the field of optimization itself, which applications in optimization. It emphasizes con- involves many classical disciplines, the book should strained optimization, beginning with a substantial be useful to system analysts, operations researchers, treatment of linear programming and then proceed- numerical analysts, management scientists, and other ing to convex analysis, network flows, integer pro- specialists. gramming, quadratic programming, and convex More on www.springer.com/978-0-387-74502-2 optimization. Readers will discover a host of practical Available business applications as well as non-business applications. Topics are clearly developed with many numer- 2008. XIV, 546 p. 93 illus. (International Series in ical examples worked out in detail. Specific examples Operations Research & Management Science, 116) and concrete algorithms precede more abstract topics. 978-0-387-74502-2 With its focus on solving practical problems, the book K. Engel, R. Nagel features free C programs to implement the major algorithms covered, including the two-phase simplex method, primal-dual simplex method, path-follow- A Short Course on Operator ing interior-point method, and homogeneous self- Semigroups dual methods. In addition, the author provides online JAVA applets that illustrate various pivot rules and The book offers a direct and up-to-date introduction variants of the simplex method, both for linear pro- to the theory of one-parameter semigroups of linear gramming and for network flows. These C programs operators on Banach spaces. It contains the funda- and JAVA tools can be found on the book's website. mental results of the theory such as the Hille-Yoshida The website also includes new online instructional generation theorem, the bounded perturbation theo- tools and exercises. rem, and the Trotter-Kato approximation theorem. It also treats the spectral theory of semigroups and its More on www.springer.com/978-0-387-74387-5 consequences for the qualitative behavior. The book Available is intended for students and researchers who want to 2008. XX, 464 p. 82 illus., 16 in color. (International Series in become acquainted with the concept of semigroups A. Mucherino, P.J. Papajorgji, P.M. Pardalos Operations Research & Management Science, 114) in order to work with it in fields like partial and func- 978-0-387-74387-5 tional differential equations. Exercises are provided at Data Mining in Agriculture the end of the chapters. Data Mining in Agriculture represents a compre- More on www.springer.com/978-0-387-31341-2 hensive effort to provide graduate students and Available researchers with an analytical text on data mining H. Wolkowicz, R. Saigal, L. Vandenberghe techniques applied to agriculture and environmen- 2006. XII, 247 p. 3 illus. (Universitext, ) tal related fields. This book presents both theoretical Handbook of Semidefinite 978-0-387-31341-2 and practical insights with a focus on presenting the context of each data mining technique rather intu- Programming itively with ample concrete examples represented Theory, Algorithms, and Applications graphically and with algorithms written in MATLAB®. Examples and exercises with solutions are provided Semidefinite programming (SDP) is one of the most at the end of each chapter to facilitate the comprehen- exciting and active research areas in optimization. sion of the material. For each data mining technique It has and continues to attract researchers with very described in the book variants and improvements diverse backgrounds, including experts in convex of the basic algorithm are also given. Also by P.J. programming, linear algebra, numerical optimiza- Papajorgji and P.M. Pardalos: Advances in Modeling tion, combinatorial optimization, control theory, and Agricultural Systems, 'Springer Optimization and its statistics. This tremendous research activity has been Applications' vol. 25, ©2009. prompted by the discovery of important applications in combinatorial optimization and control theory, the More on www.springer.com/978-0-387-88614-5 development of efficient interior-point algorithms for Available solving SDP problems, and the depth and elegance of the underlying optimization theory. The Handbook 2009. XVIII, 274 p. 92 illus. (Springer Optimization of Semidefinite Programming offers an advanced and Its Applications, 34) and broad overview of the current state of the field. 978-0-387-88614-5 It contains nineteen chapters written by the leading springer.com Optimization 65

Optimization state of the art and find new applications. The book is of interest to researchers, students, and practitioners across the applied sciences who are working on optimization problems. More on www.springer.com/978-0-387-74931-0 Available 2008. XXII, 274 p. 36 illus. (International Series in Operations Research & Management Science, 118) 978-0-387-74931-0

R.A. Martinez-Avendano, P. Rosenthal An Introduction to Operators on the Hardy-Hilbert Space J.W. Chinneck This book offers an elementary and engaging intro- Feasibility and Infeasibility in duction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of Optimization: all spaces of analytic functions and of the operators Algorithms and Computational Methods on them. Blending techniques from "soft" and "hard" Constrained optimization models are core tools in analysis, the book contains clear and beautiful proofs. business, science, government, and the military with G.B. Dantzig, M.N. Thapa There are numerous exercises at the end of each chap- applications including airline scheduling, control of ter, along with a brief guide for further study which petroleum refining operations, investment decisions, includes references to applications to topics in engi- Linear Programming and many others. Constrained optimization mod- neering. 2: Theory and Extensions els have grown immensely in scale and complexity More on www.springer.com/978-0-387-35418-7 in recent years as inexpensive computing power has Linear programming represents one of the major applications of mathematics to business, industry, and Available become widely available. Models now frequently have many complicated interacting constraints, giving rise economics. It provides a methodology for optimizing an output given that is a linear function of a number 2007. XII, 220 p. (Graduate Texts in Mathematics, to a host of issues related to feasibility and infeasibil- of inputs. George Dantzig is widely regarded as the 237) ity. For example, it is sometimes difficult to find any 978-0-387-35418-7 feasible point at all for a large model, or even to accu- founder of the subject with his invention of the sim- rately determine if one exists, e.g. for nonlinear mod- plex algorithm in the 1940's. This second volume is els. If the model is feasible, how quickly can a solution intended to add to the theory of the items discussed in the first volume. It also includes additional advanced M. Takesaki be found? If the model is infeasible, how can the cause be isolated and diagnosed? Can a repair to restore fea- topics such as variants of the simplex method, interior Theory of Operator Algebras II sibility be carried out automatically? Researchers have point methods (early and current methods), GUB, developed numerous algorithms and computational decomposition, integer programming, and game the- Together with "Theory of Operator Algebras I, methods in recent years to address such issues, with ory. Graduate students in the fields of operations III" (EMS 124 and 127), this book, written by one of a number of surprising spin-off applications in fields research, industrial engineering, and applied mathe- the most prominent researchers in the field of oper- such as artificial intelligence and computational biol- matics will find this volume of particular interest. ator algebras, presents the theory of von Neumann ogy. Over the same time period, related approaches More on www.springer.com/978-0-387-98613-5 algebras and non-commutative integration focus- and techniques relating to feasibility and infeasibility Available ing on the group of automorphisms and the struc- of constrained problems have arisen in the constraint ture analysis. It is part of the recently developed part programming community. Feasibility and Infeasibil- 2003. XXV, 448 p. 45 illus. (Springer Series in of the "Encyclopaedia of Mathematical Sciences" on ity in Optimization is a timely expository book that Operations Research and Financial Engineering, ) operator algebras and non-commutative geometry summarizes the state of the art in both classical and 978-0-387-98613-5 (see http://www.springer.de/math/ems/index.html). recent algorithms related to feasibility and infeasibil- The book provides essential and comprehensive ity in optimization, with a focus on practical methods. information for graduate students and researchers in All model forms are covered, including linear, non- mathematics and mathematical physics. linear, and mixed-integer programs. Connections to More on www.springer.com/978-3-540-42914-2 related work in constraint programming are shown. Part I of the book addresses algorithms for seeking Available feasibility quickly, including new methods for the dif- 2003. XXII, 518 p. (Encyclopaedia of Mathematical Sciences, ficult cases of nonlinear and mixed-integer programs. 125) Part II provides algorithms for analyzing infeasibil- 978-3-540-42914-2 ity by isolating minimal infeasible (or maximum feasible) subsets of constraints, or by finding the best repair for the infeasibility. Infeasibility analysis algorithms have arisen primarily over the last two decades, and the book covers these in depth and detail. Part III describes applications in numerous areas outside of direct infeasibility analysis such as finding deci- J.N. Hooker sion trees for data classification, analyzing protein folding, radiation treatment planning, automated test Integrated Methods for assembly, etc. A main goal of the book is to impart Optimization an understanding of the methods so that practitioners can make immediate use of existing algorithms Integrated Methods for Optimization integrates the and software, and so that researchers can extend the key concepts of Mathematical Programming and 66 Order, Lattices, Ordered Algebraic Structures springer.com

Constraint Programming into a unified framework ologies for general nonlinear integer programming, introduction to linear programming, nonlinear pro- that allows them to be generalized and combined. and at the same time, provides a timely and compre- gramming, numerical optimization algorithms, varia- The unification of MP and CP creates optimization hensive summary of the theoretical and algorithmic tional problems, dynamic programming, and optimal methods that have much greater modeling power, development in the last 30 years on this topic. The control. Prerequisites have been kept to a minimum, increased computational speed, and a sizeable reduc- following are some features of the book: Duality the- although a basic knowledge of calculus, linear algebra, tion computational coding. Hence the benefits of this ory for nonlinear integer programming is thoroughly and differential equations is assumed. discussed. Convergent Lagrangian and cutting meth- integration are substantial, providing the Applied Sci- More on www.springer.com/978-0-387-40398-4 ences with a powerful, high-level modeling solution ods for separable nonlinear integer programming are for optimization problems. As reviewers of the book explained and demonstrated. Convexification scheme Available have noted, this integration along with constraint pro- and the relation between the monotonicity and con- gramming being incorporated into a number of pro- vexity is explored and illustrated. A solution frame- 2004. 248 p. 38 illus. (Texts in Applied Mathematics, gramming languages, brings the field a step closer to work is provided using global descent. Computational 46) 978-0-387-40398-4 being able to simply state a problem and having the implementations for large-scale nonlinear integer computer solve it. John Hooker is a leading researcher programming problems are demonstrated for several in both the Optimization and Constraint Program- efficient solution algorithms presented in the book. ming research communities. He has been an instru- More on www.springer.com/978-0-387-29503-9 mental principal for this integration, and over the years, he has given numerous presentations and tuto- Available rials on the integration of these two areas. It is felt by 2006. XXII, 440 p. 71 illus. (International Series in Operations many in the field that the future Optimization courses Research & Management Science, 84) will increasingly be taught from this integrated frame- 978-0-387-29503-9 work. More on www.springer.com/978-0-387-38272-2 Available Y. Nesterov 2007. XIV, 490 p. 72 illus. (International Series in Operations Research & Management Science, 100) Introductory Lectures on Convex W. Sun, Y. Yuan 978-0-387-38272-2 Optimization Optimization Theory and Methods A Basic Course Nonlinear Programming This is the first elementary exposition of the main ideas of complexity theory for convex optimization. This book, a result of the author's teaching and Up to now, most of the material can be found only in research experience in various universities and insti- special journals and research monographs. The book tutes over the past ten years, can be used as a textbook covers optimal methods and lower complexity bounds for an optimization course for graduates and senior for smooth and non-smooth convex optimization. A undergraduates. It systematically describes optimiza- separate chapter is devoted to polynomial-time inte- tion theory and several powerful methods, including rior-point methods. Audience: The book is suitable recent results. For most methods, the authors discuss for industrial engineers and economists. an idea’s motivation, study the derivation, establish the global and local convergence, describe algorithmic More on www.springer.com/978-1-4020-7553-7 steps, and discuss the numerical performance. The Available book deals with both theory and algorithms of optimization concurrently. It also contains an extensive D. Li, X. Sun 2004. 254 p. (Applied Optimization, 87) 978-1-4020-7553-7 bibliography. Finally, apart from its use for teaching, Optimization Theory and Methods will be very bene- Nonlinear Integer Programming ficial as a research reference. The methodological development of integer program- More on www.springer.com/978-0-387-24975-9 ming has grown by leaps and bounds in the past four Available decades, with its main focus on linear integer programming. However, the past few years have also 2006. XII, 687 p. 25 illus. (Springer Optimization and Its witnessed certain promising theoretical and method- Applications, 1) 978-0-387-24975-9 ological achievements in nonlinear integer programming. These recent developments have produced applications of nonlinear (mixed) integer programming across a variety of various areas of scientific computing, engineering, management science and operations research. Its prominent applications Order, Lattices, Ordered include, for examples, portfolio selection, capital bud- Algebraic Structures geting, production planning, resource allocation, computer networks, reliability networks and chemi- P. Pedregal cal engineering. In recognition of nonlinearity's aca- N. Caspard, B. Leclerc, B. Monjardet demic significance in optimization and its importance Introduction to Optimization in real world applications, NONLINEAR INTEGER This undergraduate textbook introduces students Ensembles ordonnés finis : PROGRAMMING is a comprehensive and systematic of science and engineering to the fascinating field of treatment of the methodology. The book's goal is to optimization. It is a unique book that brings together concepts, résultats et usages bring the state-of-the-art of the theoretical foundation the subfields of mathematical programming, varia- Les notions d'ordre, de classement, de rangement and solution methods for nonlinear integer program- tional calculus, and optimal control, thus giving stu- sont présentés dans de multiples activités et situa- ming to students and researchers in optimization, dents an overall view of all aspects of optimization tions humaines. La formalisation mathématique de operations research, and computer science. This book in a single reference. As a primer on optimization, ces notions a permis d'abord le grand développement systemically investigates theory and solution method- its main goal is to provide a succinct and accessible de la théorie des treillis, puis celui de structures springer.com Ordinary Differential Equations 67 ordonnées plus générales, notamment celles relevant aspects as a thorough study of the center/focus prob- des mathématiques discrètes. Les buts principaux de lem and recent results on integrability. In the last two cet ouvrage qui comble un vide sont donc de: - don- chapters the performant software tool P4 is intro- ner les concepts et résultats fondamentaux sur les duced. From the start, differential systems are rep- ensembles ordonnés finis, - présenter leurs usages resented by vector fields enabling, in full strength, a dans des domaines variés (de la RO ou l’IA à la micro- dynamical systems approach. All essential notions, économie), - signaler un certain nombre de résultats including invariant manifolds, normal forms, desin- et de recherches en cours. Le lecteur sera ainsi à même gularization of singularities, index theory and limit de trouver tout ce qu'il a besoin de connaître sur ces cycles, are introduced and the main results are proved structures sans devoir le rechercher dans de multiples for smooth systems with the necessary specifications revues relevant de disciplines variées. for analytic and polynomial systems. More on www.springer.com/978-3-540-73755-1 More on www.springer.com/978-3-540-32893-3 P. Deuflhard, F. Bornemann Available Available 2007. XVII, 340 p. 62 ill. (Mathématiques et Applications, 60) Scientific Computing with 978-3-540-73755-1 2006. XVI, 302 p. 123 illus. (Universitext, ) Ordinary Differential Equations 978-3-540-32893-3 This text provides an introduction to the numerical solution of initial and boundary value problems in ordinary differential equations on a firm theoretical J. Françoise Ordinary Differential Equations basis. The book strictly presents numerical analysis as part of the more general field of scientific comput- Oscillations en biologie ing. Important algorithmic concepts are explained Analyse qualitative et modèles down to questions of software implementation. For Par sa nature pluridisciplinaire, ce livre s'adresse à initial value problems a dynamical systems approach un large public de mathématiciens, physiciens et is used to develop Runge-Kutta, extrapolation, and ingénieurs s'intéressant aux aspects théoriques des multistep methods. For boundary value problems phénomènes périodiques, de même qu'aux étudi- including optimal control problems both multiple ants en sciences de la vie intéressés par les outils shooting and collocation methods are worked out in mathématiques de la modélisation. Les oscillations detail. Graduate students and researchers in mathe- complexes mises en évidence dans les systèmes matics, computer science, and engineering will find physiologiques s'analysent par des modèles. Cet this book useful. Chapter summaries, detailed illus- ouvrage se propose de présenter et de développer les trations, and exercises are contained throughout the mathématiques nécessaires à leur compréhension. book with many interesting applications taken from On présente en particulier les notions d'excitabilité, a rich variety of areas.Peter Deuflhard is founder and de bistabilité, de synchronisation et d'oscillations en C. Chicone president of the Zuse Institute Berlin (ZIB) and full salves dans le cadre de l'analyse qualitative. professor of scientific computing at the Free Univer- Ordinary Differential Equations sity of Berlin, department of mathematics and com- More on www.springer.com/978-3-540-25152-1 puter science.Folkmar Bornemann is full professor of Available with Applications scientific computing at the Center of Mathematical Based on a one-year course taught by the author to Sciences, Technical University of Munich. 2005. XII, 179 p. (Mathématiques et Applications, 46) 978-3-540-25152-1 graduates at the University of Missouri, this book pro- More on www.springer.com/978-0-387-95462-2 vides a student-friendly account of some of the stan- Available dard topics encountered in an introductory course of ordinary differential equations. In a second semester, 2002. XIX, 485 p. 37 illus. (Texts in Applied these ideas can be expanded by introducing more Mathematics, 42) advanced concepts and applications. A central theme 978-0-387-95462-2 in the book is the use of Implicit Function Theorem, while the latter sections of the book introduce the basic ideas of perturbation theory as applications of this Theorem. The book also contains material differ- ing from standard treatments, for example, the Fiber Contraction Principle is used to prove the smoothness of functions that are obtained as fixed points of con- tractions. The ideas introduced in this section can be extended to infinite dimensions. B. Kruglikov, V. Lychagin, E. Straume More on www.springer.com/978-0-387-30769-5 Available Differential Equations - Geometry, Symmetries and Integrability 2006. XX, 638 p. 73 illus. (Texts in Applied The Abel Symposium 2008 Mathematics, 34) 978-0-387-30769-5 F. Dumortier, J. Llibre, J.C. Artés The Abel Symposium 2008 focused on the modern theory of differential equations and their applications Qualitative Theory of Planar in geometry, mechanics, and mathematical physics. Following the tradition of Monge, Abel and Lie, Differential Systems the scientific program emphasized the role of alge- This book deals with systems of polynomial bro-geometric methods, which nowadays permeate autonomous ordinary differential equations in two all mathematical models in natural and engineering real variables. The emphasis is mainly qualitative, sciences. The ideas of invariance and symmetry are of although attention is also given to more algebraic fundamental importance in the geometric approach 68 Partial Differential Equations springer.com to differential equations, with a serious impact com- journals. Previously, the authors have co-authored/ G. Barles ing from the area of integrable systems and field the- co-edited the following books with Springer: Infinite ories. This volume consists of original contributions Interval Problems for Differential, Difference and Solutions de viscosité des and broad overview lectures of the participants of the Integral Equations; Singular Differential and Inte- Symposium. The papers in this volume present the gral Equations with Applications; Nonlinear Analy- équations de Hamilton-Jacobi modern approach to this classical subject. sis and Applications: To V. Lakshmikanthan on his Le but de ce livre est de présenter la théorie des 80th Birthday; An Introduction to Ordinary Differ- More on www.springer.com/978-3-642-00872-6 solutions de viscosité pour les équations de Hamil- ential Equations. In addition, they have collaborated ton-Jacobi du premier ordre et ses applications aux Available with others on the following titles: Positive Solutions problèmes de contrôle optimal déterministe et de 2009. XIV, 386 p. 1 illus. in color. (Abel Symposia, 5) of Differential, Difference and Integral Equations; perturbations singulières, en particulier du type 978-3-642-00872-6 Oscillation Theory for Difference and Functional Dif- Grandes Déviations. Il est principalement destiné ferential Equations; Oscillation Theory for Second aux étudiants de troisième cycle et aux chercheurs Order Linear, Half-Linear, Superlinear and Sublinear qui souhaitent se familiariser avec cette théorie mais Dynamic Equations. il en fournit également un panorama assez complet More on www.springer.com/978-0-387-79145-6 pour les équations du premier ordre. La première par- Partial Differential Equations tie du texte concerne les solutions continues et les Available propriétés de base de solutions de viscosité (stabilité, unicité, etc.). La deuxième partie décrit les méthodes 2009. XIV, 410 p. 35 illus. (Universitext, ) plus sophistiquées liées aux solutions discontinues 978-0-387-79145-6 (méthode des semi-limites relaxées) et leurs applications. More on www.springer.com/978-3-540-58422-3 Available

1994. IX, 194 p. (Mathématiques et Applications, 17) 978-3-540-58422-3

B. Bidégaray-Fesquet R.P. Agarwal, D. O'Regan Hiérarchie de modèles en optique Ordinary and Partial Differential quantique Equations De Maxwell-Bloch à Schrödinger non-linéaire With Special Functions, Fourier Series, and S. Alinhac Cet ouvrage présente les modèles d'interaction onde- Boundary Value Problems Hyperbolic Partial Differential matière faisant intervenir une description quan- This textbook provides a genuine treatment of ordi- tique de la matière (optique quantique), ainsi que des nary and partial differential equations (ODEs and Equations modèles classiques qui en sont dérivés. L'objectif est PDEs) through 50 class tested lectures. Key Features: Serge Alinhac (1948–) received his PhD from de décrypter pour des lecteurs mathématiciens ces Explains mathematical concepts with clarity and l'Université Paris-Sud XI (Orsay). After teaching at modèles habituellement décrits dans des livres de rigor, using fully worked-out examples and help- l'Université Paris Diderot VII and Purdue University, physique et de donner les résultats mathématiques ful illustrations. Develops ODEs in conjuction with he has been a professor of mathematics at l'Université et les méthodes numériques existants. Ces résultats, PDEs and is aimed mainly toward applications. Cov- Paris-Sud XI (Orsay) since 1978. He is the author reflets de sujets de recherche actuels faisant intervenir ers importat applications-oriented topics such as solu- of Blowup for Nonlinear Hyperbolic Equations des outils mathématiques variés, sont détaillés pour tions of ODEs in the form of power series, special (Birkhäuser, 1995) and Pseudo-differential Opera- être accessibles à des étudiants ayant un niveau DEA. functions, Bessel functions, hypergeometric functors and the Nash–Moser Theorem (with P. Gérard, Les parties numériques de ce livre peuvent également tions, orthogonal functions and polynomicals, Legen- American Mathematical Society, 2007). His primary intéresser des physiciens désirant effectuer des simu- dre, Chebyshev, Hermite, and Laguerre polynomials, areas of research are linear and nonlinear partial dif- lations. and the theory of Fourier series. Provides exercis- ferential equations. This excellent introduction to More on www.springer.com/978-3-540-27238-0 es at the end of each chapter for practice. This book is hyperbolic differential equations is devoted to linear Available ideal for an undergratuate or first year graduate-level equations and symmetric systems, as well as conser- course, depending on the university. Prerequisites vation laws. The book is divided into two parts. The 2006. XIII, 175 p. 21 ill. (Mathématiques et include a course in calculus. About the Authors: Ravi first, which is intuitive and easy to visualize, includes Applications, 49) P. Agarwal received his Ph.D. in mathematics from all aspects of the theory involving vector fields and 978-3-540-27238-0 the Indian Institute of Technology, Madras, India. He integral curves; the second describes the wave equa- is a professor of mathematics at the Florida Institute tion and its perturbations for two- or three-space of Technology. His research interests include numer- dimensions. Over 100 exercises are included, as well ical analysis, inequalities, fixed point theorems, and as "do it yourself" instructions for the proofs of many differential and difference equations. He is the author/ theorems. Only an understanding of differential cal- co-author of over 800 journal articles and more than culus is required. Notes at the end of the self-con- 20 books, and actively contributes to over 40 journals tained chapters, as well as references at the end of the and book series in various capacities. Donal O’Regan book, enable ease-of-use for both the student and the received his Ph.D. in mathematics from Oregon State independent researcher. University, Oregon, U.S.A. He is a professor of math- More on www.springer.com/978-0-387-87822-5 ematics at the National University of Ireland, Galway. He is the author/co-author of 15 books and has pub- Available lished over 650 papers on fixed point theory, operator, integral, differential and difference equations. He 2009. XII, 150 p. (Universitext, ) serves on the editorial board of many mathematical 978-0-387-87822-5 springer.com Partial Differential Equations 69

analytic hypoellipticity and regularity for very low E. Cances, C. Le Bris, Y. Maday regularity coefficients; * Nonlinear evolution equations: Navier–Stokes system, Strichartz estimates Méthodes mathématiques for the wave equation, instability and the Zakharov equation and eikonals; * Local solvability: its con- en chimie quantique. Une nection with subellipticity, local solvability for sys- introduction tems of vector fields in Gevrey classes; * Hyperbolic equations: the Cauchy problem and multiple char- Ce cours est une introduction à la modélisation acteristics, both positive and negative results. Grad- mathématique et à l'analyse numérique pour la uate students at various levels as well as researchers chimie moléculaire quantique, un champ peu connu in PDEs and related fields will find this an excel- des mathématiciens et pourtant riche en sujets lent resource. List of contributors: L. Ambrosio d'investigation. Le point de vue choisi est celui du A. Bonfiglioli, E. Lanconelli, F. Uguzzoni N. Lerner H. Bahouri mathématicien appliqué. Le cours est construit de X. Lu S. Berhanu J. Met- manière auto-consistante. Seules des notions de base Stratified Lie Groups and calfe J.-M. Bony T. Nishi- en analyse fonctionnelle sont requises pour l'aborder. Les outils mathématiques plus élaborés sont intro- Potential Theory for Their Sub- tani N. Dencker V. Petkov S. Ervedoza J. Rauch I. Gallagher duits progressivement et les connaissances nécessaires Laplacians M. Reissig J. Hounie en physique et en théorie spectrale sont regroupées L. Stoyanov E. Jannelli dans des annexes. On présente d'abord les modèles The existence, for every sub-Laplacian, of a homoge- D. S. Tartakoff K. Kajitani les plus utilisés en pratique. Puis, on analyse ces neous fundamental solution smooth out of the origin, D. Tataru A. Kurganov F. modèles d'un point de vue mathématique (ques- plays a crucial role in the book. This makes it possi- Treves G. Zampieri tions d'existence de solutions, d'unicité, ...). On intro- ble to develop an exhaustive Potential Theory, almost E. Zuazua duit ensuite les différentes stratégies numériques completely parallel to that of the classical Laplace employées pour la résolution pratique, et on four- operator. This book provides an extensive treatment More on www.springer.com/978-0-8176-4860-2 nit, quand ceci est possible, des éléments d'analyse of Potential Theory for sub-Laplacians on stratified Available numérique de ces méthodes. Les liens existants entre Lie groups. In recent years, sub-Laplacian operators 2009. XIV, 292 p. 1 illus. (Progress in Nonlinear Differential les modèles de la chimie moléculaire et des sujets con- have received considerable attention due to their spe- Equations and Their Applications, 78) nexes sont aussi explorés : modélisation de la phase cial role in the theory of linear second-order PDE's 978-0-8176-4860-2 liquide, physique de l'état cristallin, biologie, simula- with semidefinite characteristic form. It also provides tion des matériaux, ... Le cours peut aussi intéresser a largely self-contained presentation of stratified Lie le chimiste ou le physicien curieux de comprendre les groups, and of their Lie algebra of left-invariant vector techniques mathématiques dont relèvent les modèles F. Boyer, P. Fabrie fields. The presentation is accessible to graduate stu- qu'il utilise, et de découvrir comment de telles tech- dents and requires no specialized knowledge in alge- niques peuvent améliorer significativement l'efficacité bra nor in differential geometry. It is thus addressed, Eléments d'analyse pour et la qualité des simulations numériques. The book besides PhD students, to junior and senior researchers l'étude de quelques modèles is an introduction to the mathematical modelling in different areas such as: partial differential equa- and the numerical analysis for computational quan- tions; geometric control theory; geometric measure d'écoulements de fluides tum chemistry. The text is self-consistent: no particu- theory and minimal surfaces in stratified Lie groups. visqueux incompressibles lar familiarity with the subject nor the mathematical More on www.springer.com/978-3-540-71896-3 tools is required. Only a basic training in functional Ce tome a pour but premier d'initier le lecteur à analysis is necessary. The models are introduced and Available l'analyse de certaines équations aux dérivées par- discussed. They are analyzed mathematically. The 2007. XXVI, 802 p. 23 illus. (Springer Monographs in tielles issues de la mécanique des fluides. Celles-ci numerical techniques are presented and, when pos- Mathematics, ) sont présentées à partir des principes fondamentaux sible, also analyzed. Topics closely related to molecu- 978-3-540-71896-3 de la mécanique et de la thermodynamique dans le lar simulation are also addressed, such as solid state premier chapitre. Les notions mathématiques fon- physics, liquid state physics, biology, and materials damentales utilisées sont rappelées en détail dans un science. The book canalso be useful for students and chapitre à part ce qui rend l'ouvrage auto-contenu researchers of those fields, curious about the mathe- et utile à un lecteur désireux d'appréhender l'analyse matical techniques and the numerical strategies. de bien d'autres types d'équations aux dérivées par- tielles. Une partie importante du texte est consacrée More on www.springer.com/978-3-540-30996-3 aux résultats "classiques" sur les problèmes de Stokes Available et de Navier-Stokes homogènes incompressibles. Enfin, les trois derniers chapitres traitent de ques- 2006. XVI, 411 p. 34 ill. (Mathématiques et tions plus spécifiques issues de travaux de recherche Applications, 53) récents (toujours dans le but d'illustrer les techniques 978-3-540-30996-3 mathématiques sous-jacentes). More on www.springer.com/978-3-540-29818-2 M. Choulli Available

A. Bove, D. Del Santo, M.V. Murthy 2006. XVI, 400 p. 12 ill. (Mathématiques et Une introduction aux problèmes Applications, 52) inverses elliptiques et Advances in Phase Space Analysis 978-3-540-29818-2 paraboliques of Partial Differential Equations In Honor of Ferruccio Colombini's 60th Birthday Cet ouvrage est consacré à une introduction aux problèmes inverses elliptiques et paraboliques. L’ This collection of original articles and surveys objectif est de présenter quelques méthodes récentes addresses the recent advances in linear and non- pour établir des résultats d’unicité et de stabilité. linear aspects of the theory of partial differential Seront traités quelques problèmes inverses elliptiques equations. Key topics include: * Operators as "sums devenus maintenant classiques, tels que la conduc- of squares" of real and complex vector fields: both tivité inverse, la détection de corrosion ou de fis- 70 Partial Differential Equations springer.com sures et les problèmes spectraux inverses. Parmi les de choc, on met en relief l'importance des espaces problèmes inverses paraboliques considérés figurent de fonctions à variation bornée pour le traitement et le problème classique de retrouver une distribution l'interprétation des modélisations régies par des équa- initiale de la chaleur et la localisation de sources, de tions paraboliques dégénérées ou hyperboliques du chaleur ou de pollution par exemple. Les problèmes premier ordre sur des ouverts bornés. d’identification de non linéarités seront aussi étudiés. More on www.springer.com/978-3-540-60588-1 Cet ouvrage s’adresse à tous ceux qui souhaitent s’ intéresser à l’analyse mathématique des problèmes Available inverses. This volume is devoted to an introduction of elliptic and parabolic inverse problems. The goal 1996. XVII, 187 p. (Mathématiques et Applications, is to present some recent methods for establishing 22) 978-3-540-60588-1 uniqueness and stability results. A number of clas- S.D. Eidelman, S.D. Ivasyshen, A.N. Kochubei sical elliptic inverse problems are studied, e.g. the inverse conductivity problem, the detection of corro- Analytic Methods in the Theory sion or cracks and inverse spectral problems. Among the parabolic inverse problems, the classic problem of Differential and Pseudo- of finding an initial distribution of heat and the loca- Differential Equations of tion of sources is considered. This volume will be of interest to all those who want to learn the mathemati- Parabolic Type cal analysis of inverse problems. The theory of parabolic equations, a well-developed More on www.springer.com/978-3-642-02459-7 part of the contemporary theory of partial differen- Available tial equations and mathematical physics, is the subject of immense research activity. A stable interest 2009. XXII, 252 p. (Mathématiques et Applications, 65) to parabolic equations is caused both by the depth 978-3-642-02459-7 and complexity of mathematical problems emerging here, and by its importance in applied problems of natural science, technology, and economics.This J. Kevorkian book aims at a consistent and, as far as possible, complete exposition of analytic methods of construct- Partial Differential Equations ing, investigating, and using fundamental solutions Analytical Solution Techniques of the Cauchy problem for the following four classes of linear parabolic equations: - 2b-parabolic partial A broad treatment of important partial differential differential equations, in which every spatial vari- equations, particularly emphasizing the analytical able may have its own weight with respect to the time techniques. In each chapter the author raises vari- variable - degenerate partial differential equations ous questions concerning the particular equations of Kolmogorov's structure, which generalize clas- discussed, treats different methods for tackling these sical Kolmogorov equations of diffusion with iner- equations, gives applications and examples, and con- tia- pseudo-differential equations with non-smooth cludes with a list of proposed problems and a relevant bibliography. This new edition has been substantially G. Da Prato quasi-homogeneous symbols- fractional diffusion equations.All of these provide mathematical models updated to take account of the new techniques avail- Kolmogorov Equations for for various diffusion phenomena. In spite of a large able, making it valuable for students and researchers number of research papers on the subject, this is the in mathematics, physics and engineering. Stochastic PDEs first book devoted to this topic. It will be useful both More on www.springer.com/978-0-387-98605-0 The subject of this book is stochastic partial differ- for mathematicians interested in new classes of partial Available ential equations, in particular, reaction-diffusion differential equations, and physicists specializing in equations, Burgers and Navier-Stokes equations and diffusion processes. 2000. XI, 636 p. 128 illus. (Texts in Applied the corresponding Kolmogorov equations. For each More on www.springer.com/978-3-7643-7115-9 Mathematics, 35) case the transition semigroup is considered and irre- 978-0-387-98605-0 Available ducibility, the strong Feller property, and invariant measures are investigated. Moreover, it is proved 2004. IX, 386 p. (Operator Theory: Advances and that the exponential functions provide a core for the Applications, 152) 978-3-7643-7115-9 infinitesimal generator. As a consequence, it is possible to study Sobolev spaces with respect to invariant measures and to prove a basic formula of integration by parts (the so-called "carré du champs iden- G. Gagneux, M. Madaune-Tort tity". Several results were proved by the author and his collaborators and appear in book form for the first Analyse mathématique de time. Presenting the basic elements of the theory in a modèles non linéaires de simple and compact way, the book covers a one-year course directed to graduate students in mathematics l'ingénierie pétrolière or physics. The only prerequisites are basic probabil- Cet ouvrage présente l'analyse mathématique de ity (including finite dimensional stochastic differential systèmes issus de l'industrie pétrolière. Le lecteur y equations), basic functional analysis and some ele- trouvera, avec une présentation d'ensemble du sujet D.A. Kopriva ments of the theory of partial differential equations. et les rappels utiles à l'autonomie du propos, des More on www.springer.com/978-3-7643-7216-3 résultats récents et des méthodes adaptables à d'autres Implementing Spectral Methods Available domaines de la mécanique des fluides (modèles non for Partial Differential Equations linéaires de diffusion-transport en pédologie, simu- 2004. VII, 182 p. (Advanced Courses in Mathematics - CRM Algorithms for Scientists and Engineers Barcelona, ) lation des pollutions, cryogénie industrielle, etc...). This book offers a systematic and self-contained 978-3-7643-7216-3 Par une approche heuristique de la notion de solution entropique et la définition rigoreuse de l'onde approach to solve partial differential equations springer.com Partial Differential Equations 71 numerically using single and multidomain spectral- acting in pairs of spaces of differentiable functions. methods. It contains detailed algorithms in pseu- The theory was essentially developed by the authors docode for the application of spectral approximations during the last thirty years and the present volume to both one and two dimensional PDEs of mathe- is mainly based on their results. Part I is devoted to matical physics describing potentials, transport, and J.D. Logan the theory of multipliers and encloses the following wave propagation. David Kopriva, a well-known topics: trace inequalities, analytic characterization of researcher in the field with extensive practical experi- Applied Partial Differential multipliers, relations between spaces of Sobolev mul- ence, shows how only a few fundamental algorithms tipliers and other function spaces, maximal subal- form the building blocks of any spectral code, even- Equations gebras of multiplier spaces, traces and extensions of for problems with complex geometries. The book This textbook is for the standard, one-semester, multipliers, essential norm and compactness of mul- addresses computational and applications scientists, junior-senior course that often goes by the title "Ele- tipliers, and miscellaneous properties of multipliers. as it emphasizes the practical derivation and imple- mentary Partial Differential Equations" or "Boundary Part II concerns several applications of this theory: mentation of spectral methods over abstract math- Value Problems". The audience consists of students continuity and compactness of differential operators ematics. It is divided into two parts: First comes a in mathematics, engineering, and the physical sci- in pairs of Sobolev spaces, multipliers as solutions to primer on spectral approximation and the basic algo- ences. The topics include derivations of some of the linear and quasilinear elliptic equations, higher regu- rithms, including FFT algorithms, Gauss quadrature standard models of mathematical physics (e.g., the larity in the single and double layer potential theory algorithms, and how to approximate derivatives. The heat equation, the wave equation, and Laplace’s equa- for Lipschitz domains, regularity of the boundary in second part shows how to use those algorithms to tion) and methods for solving those equations on $L_p$-theory of elliptic boundary value problems, solve steady and time dependent PDEs in one and two unbounded and bounded domains (transform meth- and singular integral operators in Sobolev spaces. space dimensions. Exercises and questions at the end ods and eigenfunction expansions). Prerequisites More on www.springer.com/978-3-540-69490-8 of each chapter encourage the reader to experiment include multivariable calculus and elementary differ- Available with the algorithms. ential equations. The text differs from other texts in 2009. XIV, 614 p. 2 illus. (Grundlehren der mathematischen More on www.springer.com/978-90-481-2260-8 that it is a brief treatment; yet it provides coverage of the main topics usually studied in the standard course Wissenschaften, 337) Available 978-3-540-69490-8 as well as an introduction to using computer algebra 2009. XXIV, 411 p. (Scientific Computation, ) packages to solve and understand partial differential 978-90-481-2260-8 equations. The many exercises help students sharpen their computational skills by encouraging them to Q.S. Nguyen think about concepts and derivations. The student who reads this book carefully and solves most of the Stabilité des structures élastiques problems will have a sound knowledge base for a sec- Ce livre résulte des notes de cours sur la stabilité ond-year partial differential equations course where des structures, cours de spécialité offert à l'Ecole careful proofs are constructed or for upper division Nationale des Ponts et Chaussées, à l'Ecole Poly- courses in science and engineering where detailed technique et aux DEA Mécanique. Il s'agit d'une applications of partial differential equations are intro- présentation simple et auto-cohérente des princi- duced. To give this text an even wider appeal, the sec- paux résultats de la théorie de stabilité et de bifur- ond edition has been updated with a new chapter on cation des structures. Si le premier objectif reste partial differential equation models in biology, and l'enseignement et l'initiation, ce livre intéresse aussi with various examples from the life sciences that have les ingénieurs et les lecteurs avertis qui cherchent been added throughout the text. There are more exer- une présentation naturelle et moderne sur la sta- cises, as well as solutions and hints to some of the V.V. Kravchenko bilité faisant le lien entre les traités d'ingénieurs et problems at the end of the book. les ouvrages de recherche plus complets mais aussi Applied Pseudoanalytic Function More on www.springer.com/978-0-387-20953-1 d'accès plus difficile. Theory Available More on www.springer.com/978-3-540-58927-3 Available Pseudoanalytic function theory generalizes and pre- 2004. XII, 212 p. 40 illus. (Undergraduate Texts in serves many crucial features of complex analytic func- Mathematics, ) 1995. XIV, 148 p. (Mathématiques et Applications, tion theory. The Cauchy-Riemann system is replaced 978-0-387-20953-1 by a much more general first-order system with vari- 18) able coefficients which turns out to be closely related 978-3-540-58927-3 to important equations of mathematical physics. This relation supplies powerful tools for studying and solving Schrödinger, Dirac, Maxwell, Klein-Gordon and other equations with the aid of complex-analytic methods. The book is dedicated to these recent developments in pseudoanalytic function theory and their applications as well as to multidimensional generalizations. It is directed to undergraduates, graduate students and researchers interested in complex-analytic methods, solution techniques for equations of mathematical physics, partial and ordinary differential equations. More on www.springer.com/978-3-0346-0003-3 V. Maz'ya, T.O. Shaposhnikova P. Quittner, P. Souplet Available Theory of Sobolev Multipliers 2009. XII, 184 p. (Frontiers in Mathematics, ) Superlinear Parabolic Problems With Applications to Differential and Integral 978-3-0346-0003-3 Blow-up, Global Existence and Steady States Operators This book is devoted to the qualitative study of solu- The purpose of this book is to give a comprehen- tions of superlinear elliptic and parabolic partial sive exposition of the theory of pointwise multipliers 72 Partial Differential Equations springer.com differential equations and systems. This class of prob- Advanced readers may study each chapter indepen- tions of continuum mechanics, and to show the need lems contains, in particular, a number of reaction-dif- dently from the others. for developing new adapted mathematical tools. fusion systems which arise in various mathematical More on www.springer.com/978-3-540-34461-2 More on www.springer.com/978-3-540-35743-8 models, especially in chemistry, physics and biology. The first two chapters introduce to the field Available Available and enable the reader to get acquainted with the main 2006. XXVIII, 247 p. (Lecture Notes of the Unione ideas by studying simple model problems, respec- 2006. XIV, 392 p. 8 illus., 1 in color. (Universitext, ) Matematica Italiana, 1) tively of elliptic and parabolic type. The subsequent 978-3-540-34461-2 978-3-540-35743-8 three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whose study requires new ideas. Many open problems are mentioned and commented. The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate F. Sauvigny C. Villani and postgraduate students and researchers working in the field of partial differential equations and applied Partial Differential Equations Optimal Transport mathematics. Vol. 1 Foundations and Integral Representations Old and New More on www.springer.com/978-3-7643-8441-8 This comprehensive two-volume textbook presents- At the close of the 1980s, the independent contribu- Available the whole area of Partial Differential Equations - of tions of Yann Brenier, Mike Cullen and John Mather the elliptic, parabolic, and hyperbolic type - in two launched a revolution in the venerable field of opti- 2007. XI, 584 p. (Birkhäuser Advanced Texts Basler and several variables. Special emphasis is put on the mal transport founded by G. Monge in the 18th cen- Lehrbücher, ) connection of PDEs and complex variable methods. tury, which has made breathtaking forays into various 978-3-7643-8441-8 In this first volume the following topics are treated: other domains of mathematics ever since. The author Integration and differentiation on manifolds, Func- presents a broad overview of this area, supplying com- tional analytic foundations, Brouwer's degree of map- plete and self-contained proofs of all the fundamen- ping, Generalized analytic functions, Potential theory tal results of the theory of optimal transport at the and spherical harmonics, Linear partial differen- appropriate level of generality. Thus, the book encom- tial equations. While we solve the partial differential passes the broad spectrum ranging from basic theory equations via integral representations in this volume, to the most recent research results. PhD students or we shall present functional analytic solution methods researchers can read the entire book without any prior in the second volume. This textbook can be chosen knowledge of the field. A comprehensive bibliography for a course over several semesters on a medium level. with notes that extensively discuss the existing liter- Advanced readers may study each chapter indepen- ature underlines the book’s value as a most welcome dently from the others. reference text on this subject. More on www.springer.com/978-3-540-34457-5 More on www.springer.com/978-3-540-71049-3 Available Available F. Sauvigny 2009. XXII, 978 p. 33 illus. (Grundlehren der mathematischen 2006. XIV, 437 p. 14 illus., 1 in color. (Universitext, ) Wissenschaften, 338) Partial Differential Equations 2 978-3-540-34457-5 978-3-540-71049-3 Functional Analytic Methods This comprehensive two-volume textbook presents- L. Tartar the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two An Introduction to Navier-Stokes and several variables. Special emphasis is put on the connection of PDEs and complex variable methods. Equation and Oceanography In this second volume the following topics are treated: The Introduction to Navier-Stokes Equation and Solvability of operator equations in Banach spaces, Oceanography corresponds to a graduate course in Linear operators in Hilbert spaces and spectral the- mathematics, taught at Carnegie Mellon University ory, Schauder's theory of linear elliptic differential in the spring of 1999. Comments were added to the equations, Weak solutions of differential equations, lecture notes distributed to the students, as well as Nonlinear partial differential equations and char- short biographical information for all scientists men- acteristics, Nonlinear elliptic systems with differen- tioned in the text, the purpose being to show that the tial-geometric applications. While partial differential creation of scientific knowledge is an international equations are solved via integral representations in enterprise, and who contributed to it, from where, the preceding volume, functional analytic methods and when. The goal of the course is to teach a critical are used in this volume. This textbook can be chosen point of view concerning the partial differential equa- for a course over several semesters on a medium level. springer.com Physiological, Cellular and Medical Topics 73

Physiological, Cellular and Potential Theory tional and electromagnetic forces and the divergence theorem of the calculus, the author develops meth- Medical Topics ods for constructing solutions of Laplace’s equation on a region with prescribed values on the boundary of the region. The second half addresses more advanced material aimed at those with a background of a senior undergraduate or beginning graduate course in real analysis. For specialized regions, namely spherical chips, solutions of Laplace’s equation are constructed having prescribed normal derivatives on the flat portion of the boundary and prescribed values on the remaining portion of the boundary. By means of transformations known as diffeomorphisms, these solutions are morphed into local solutions on regions with curved boundaries. The Perron-Weiner-Brelot D.R. Adams, L.I. Hedberg method is then used to construct global solutions for elliptic partial differential equations involving a mix- F.C. Hoppensteadt, C.S. Peskin Function Spaces and Potential ture of prescribed values of a boundary differential operator on part of the boundary and prescribed val- Modeling and Simulation in Theory ues on the remainder of the boundary. Medicine and the Life Sciences The subject of this book is the interplay between func- More on www.springer.com/978-1-84882-318-1 tion space theory and potential theory. A crucial step Available Mathematics in Medicine and the Life Sciences grew in classical potential theory is the identification of from lectures given by the authors at New York Uni- the potential energy of a charge with the square of a 2009. XI, 441 p. 2 illus. (Universitext, ) versity, the University of Utah, and Michigan State Hilbert space norm. This leads to the Dirichlet space 978-1-84882-318-1 University. The material is written for students who of locally integrable functions whose gradients are have had but one term of calculus, but it contains square integrable. More recently, a generalized poten- material that can be used in modeling courses in tial theory has been developed, which has an analo- applied mathematics at all levels through early gradu- gous relationship to the standard Banach function ate courses. Numerous exercises are given as well, and spaces, Sobolev spaces, Besov spaces etc., that appear solutions to selected exercises are included. Numer- naturally in the study of partial differential equations. ous illustrations depict physiological processes, pop- A surprisingly large part of classical potential the- ulation biology phenomena, models of them, and the ory has been extended to this nonlinear setting. The results of computer simulations. Mathematical mod- extensions are sometimes surprising, usually they are els and methods are becoming increasingly important nontrivial and have required new methods. in medicine and the life sciences. This book provides an introduction to a wide diversity of problems rang- More on www.springer.com/978-3-540-57060-8 ing from population phenomena to demographics, Available genetics, epidemics and dispersal; in physiological 1996. XI, 366 p. (Grundlehren der mathematischen processes, including the circulation, gas exchange in Wissenschaften, 314) P. Pucci, J.B. Serrin the lungs, control of cell volume, the renal counter- 978-3-540-57060-8 current multiplier mechanism, and muscle mechan- The Maximum Principle ics; to mechanisms of neural control. Each chapter is graded in difficulty, so a reading of the first parts of Maximum principles are bedrock results in the the- each provides an elementary introduction to the pro- ory of second order elliptic equations. This princi- cesses and their models. Materials that deal with the ple, simple enough in essence, lends itself to a quite same topics but in greater depth are included later. remarkable number of subtle uses when combined Finally, exercises and some solutions are given to test appropriately with other notions. Intended for a wide the reader on important parts of the material in the audience, the book provides a clear and comprehen- text, or to lead the reader to the discovery of interest- sive explanation of the various maximum principles ing extensions of that material. available in elliptic theory, from their beginning for linear equations to recent work on nonlinear and sin- More on www.springer.com/978-0-387-95072-3 gular equations. Available More on www.springer.com/978-3-7643-8144-8 2002. XIV, 376 p. 71 illus. (Texts in Applied Available L. Helms Mathematics, 10) 2007. X, 234 p. (Progress in Nonlinear Differential Equations 978-0-387-95072-3 and Their Applications, 73) Potential Theory 978-3-7643-8144-8 Aimed at graduate students and researchers in mathematics, physics, and engineering, this book presents a clear path from calculus to classical potential theory and beyond, moving the reader into a fertile area of mathematical research as quickly as possible. The author revises and updates material from his classic work, Introduction to Potential Theory (1969), to provide a modern text that introduces all the important concepts of classical potential theory. In the first half of the book, the subject matter is developed meticulously from first principles using only calculus. Commencing with the inverse square law for gravita- 74 Probability Theory and Stochastic Processes springer.com

Probability Theory and much updated and expanded second edition of the 1987 original contains an extended treatment of queu- Stochastic Processes ing networks and matrix-analytic methods as well as additional topics like Poisson's equation, the fundamental matrix, insensitivity, rare events and extreme values for regenerative processes, Palm theory, rate conservation, Levy processes, reflection, Skorokhod problems, Loynes' lemma, Siegmund duality, light traffic, heavy tails, the Ross conjecture and ordering, and finite buffer problems. Students and researchers in statistics, probability theory, operations research, and industrial engineering will find this book useful. More on www.springer.com/978-0-387-00211-8 A. Bain, D. Crisan Available Fundamentals of Stochastic 2003. XII, 438 p. 46 illus. (Stochastic Modelling and Applied Probability, 51) Filtering 978-0-387-00211-8 L. Arnold The objective of stochastic filtering is to determine the best estimate for the state of a stochastic dynam- Random Dynamical Systems ical system from partial observations. The solution This book is the first systematic presentation of the of this problem in the linear case is the well known theory of dynamical systems under the influence of Kalman-Bucy filter which has found widespread prac- randomness. It includes products of random map- tical application. The purpose of this book is to pro- pings as well as random and stochastic differential vide a rigorous mathematical treatment of the non- equations. The basic mulitplicative ergodic theorem linear stochastic filtering problem using modern is presented and provides a random substitute for lin- methods. Particular emphasis is placed on the theoret- ear algebra. On its basis random invariant manifolds ical analysis of numerical methods for the solution of are constructed, systems are simplified by smooth the filtering problem via particle methods. The book random coordinate transformations (random nor- should provide sufficient background to enable study mal forms), and qualitative changes in families of ran- of the recent literature. While no prior knowledge of dom systems (random bifurcation theory) are studied. stochastic filtering is required, readers are assumed Numerous instructive examples are treated analyti- to be familiar with measure theory, probability the- cally or numerically. The main intention, however, is K.B. Athreya, S.N. Lahiri ory and the basics of stochastic processes. Most of to present a reliable and rather complete source of ref- the technical results that are required are stated and erence which lays the foundation for future work and Measure Theory and Probability proved in the appendices. The book is intended as a applications. reference for graduate students and researchers inter- Theory ested in the field. It is also suitable for use as a text for More on www.springer.com/978-3-540-63758-5 This is a graduate level textbook on measure theory a graduate level course on stochastic filtering. Suitable Available and probability theory. It presents the main concepts exercises and solutions are included. 1998. XVI, 586 p. 40 illus. (Springer Monographs in and results in measure theory and probability the- More on www.springer.com/978-0-387-76895-3 Mathematics, ) ory in a simple and easy-to-understand way. It fur- Available 978-3-540-63758-5 ther provides heuristic explanations behind the theory to help students see the big picture. The book can be 2009. XIII, 390 p. (Stochastic Modelling and Applied used as a text for a two semester sequence of courses Probability, 60) in measure theory and probability theory, with an 978-0-387-76895-3 option to include supplemental material on stochastic processes and special topics. Prerequisites are kept to the minimal level and the book is intended primarily for first year Ph.D. students in mathematics and statistics. More on www.springer.com/978-0-387-32903-1 Available

2006. XIV, 618 p. (Springer Texts in Statistics, ) 978-0-387-32903-1

S. Asmussen Applied Probability and Queues This book serves as an introduction to queuing the- F. Biagini, Y. Hu, B. Øksendal, T. Zhang ory and provides a thorough treatment of tools like Markov processes, renewal theory, random walks, Stochastic Calculus for Levy processes, matrix-analytic methods and change Fractional Brownian Motion and of measure. It also treats in detail basic structures like GI/G/1 and GI/G/s queues, Markov-modulated mod- Applications els and queuing networks, and gives an introduction Fractional Brownian motion (fBm) has been widely to areas such as storage, inventory, and insurance used to model a number of phenomena in diverse risk. Exercises are included and a survey of mathe- fields from biology to finance. This huge range of matical prerequisites is given in an appendix This potential applications makes fBm an interesting object springer.com Probability Theory and Stochastic Processes 75 of study. fBm represents a natural one-parameter Suitable as a textbook for graduate or advanced extension of classical Brownian motion therefore it is undergraduate courses, the work may also be used natural to ask if a stochastic calculus for fBm can be for self-study or as a reference. Prerequisites include developed. This is not obvious, since fBm is neither a knowledge of calculus and some analysis; exposure to semimartingale (except when H = ½), nor a Markov probability would be helpful but not required since process so the classical mathematical machineries for the necessary fundamentals of measure and integra- stochastic calculus are not available in the fBm case. tion are provided. Several approaches have been used to develop the More on www.springer.com/978-0-8176-3234-2 concept of stochastic calculus for fBm. The purpose of this book is to present a comprehensive account of Available the different definitions of stochastic integration for fBm, and to give applications of the resulting theory. 2005. XI, 343 p. 13 illus. (Modeling and Simulation in Particular emphasis is placed on studying the rela- Science, Engineering and Technology, ) 978-0-8176-3234-2 W. Ching, M.K. Ng tions between the different approaches. Readers are assumed to be familiar with probability theory and Markov Chains: Models, stochastic analysis, although the mathematical techniques used in the book are thoroughly exposed and Algorithms and Applications some of the necessary prerequisites, such as classical MARKOV CHAINS: Models, Algorithms and Appli- white noise theory and fractional calculus, are recalled cations outlines recent developments of Markov chain in the appendices. This book will be a valuable refer- models for modeling queueing sequences, Internet, ence for graduate students and researchers in math- re-manufacturing systems, reverse logistics, inventory ematics, biology, meteorology, physics, engineering systems, bio-informatics, DNA sequences, genetic and finance. Aspects of the book will also be useful networks, data mining, and many other practical sys- in other fields where fBm can be used as a model for tems. The book consists of eight chapters. Chapter 1 applications. is a brief introduction to the classical theory on both More on www.springer.com/978-1-85233-996-8 discrete and continuous time Markov chains. The Available relationship between Markov chains of finite states and matrix theory is also discussed. Chapter 2 dis- 2008. XII, 332 p. (Probability and Its Applications, ) cusses the applications of continuous time Markov 978-1-85233-996-8 M. Chang chains to model queueing systems and discrete time Stochastic Control of Hereditary Markov chains for computing. Chapter 3 studies re- manufacturing systems and presents Markovian mod- Systems and Applications els for reverse manufacturing applications. In Chapter This research monograph develops the Hamil- 4, Hidden Markov models are applied to classify cus- ton-Jacobi-Bellman (HJB) theory through dynamic tomers. Chapter 5 discusses the Markov decision pro- programming principle for a class of optimal con- cess for customer lifetime values. Customer Lifetime trol problems for stochastic hereditary differential Values (CLV) is an important concept and quantity systems. It is driven by a standard Brownian motion in marketing management. Chapter 6 covers higher- and with a bounded memory or an infinite but fading order Markov chain models. Multivariate Markov memory. The optimal control problems treated in this models are discussed in Chapter 7. It presents a class book include optimal classical control and optimal of multivariate Markov chain models with a lower stopping with a bounded memory and over finite time order of model parameters. Chapter 8 studies higher- horizon. This book can be used as an introduction for order hidden Markov models. It proposes a class of researchers and graduate students who have a special higher-order hidden Markov models with an efficient V. Capasso, D. Bakstein interest in learning and entering the research areas algorithm for solving the model parameters. This in stochastic control theory with memories. Each book is aimed at students, professionals, practition- An Introduction to Continuous- chapter contains a summary. Mou-Hsiung Chang is ers, and researchers in applied mathematics, scientific Time Stochastic Processes a program manager at the Division of Mathematical computing, and operational research, who are inter- Sciences for the U.S. Army Research Office. ested in the formulation and computation of queueing Theory, Models, and Applications to Finance, and manufacturing systems. Biology, and Medicine More on www.springer.com/978-0-387-75805-3 More on www.springer.com/978-0-387-29335-6 Available This concisely written book is a rigorous and self- Available contained introduction to the theory of continu- 2008. XVIII, 406 p. (Stochastic Modelling and Applied 2006. XIV, 208 p. 18 illus. (International Series in Operations ous-time stochastic processes. A balance of theory Probability, 59) Research & Management Science, 83) and applications, the work features concrete exam- 978-0-387-75805-3 978-0-387-29335-6 ples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics covered include: * Interacting particles and agent- based models: from polymers to ants * Population dynamics: from birth and death processes to epidemics * Financial market models: the non-arbitrage principle * Contingent claim valuation models: the risk-neutral valuation theory * Risk analysis in insurance An Introduction to Continuous-Time Stochas- tic Processes will be of interest to a broad audience of students, pure and applied mathematicians, and researchers or practitioners in mathematical finance, biomathematics, biotechnology, and engineering. 76 Probability Theory and Stochastic Processes springer.com

zum Anderen wird der Itô-Kalkül in einem ersten father of 39 Ph.D. students and was recently elected to Schritt völlig ohne Martingale entwickelt. Dies erle- the National Academy of Sciences. ichtert (insbesondere für Anwender) den Einstieg in More on www.springer.com/978-0-387-78168-6 die Theorie, da tiefer liegende stochastische Methoden zunächst nicht benötigt werden. Erst in einem zweiten Available Schritt werden die engen Beziehungen zur Martin- 2008. XII, 432 p. (Probability and Its Applications, ) galtheorie und zur Browschen Bewegung entwickelt 978-0-387-78168-6 (Darstellungssätze, Sätze von Lévy, Girsanov, etc.). Anwendungen auf stochastische Differentialgleichun- gen und Optionspreistheorie runden den Text ab. More on www.springer.com/978-3-540-25392-1 Y.S. Chow, H. Teicher Available Probability Theory 2006. VIII, 247 S. (Springer-Lehrbuch Masterclass, ) 978-3-540-25392-1 Independence, Interchangeability, Martingales Comprising the major theorems of probability theory and the measure theoretical foundations of the subject, the main topics treated here are independence, interchangeability, and martingales. Partic- ular emphasis is placed upon stopping times, both as tools in proving theorems and as objects of inter- W.H. Fleming, H.M. Soner est themselves. No prior knowledge of measure theory is assumed and a unique feature of the book is Controlled Markov Processes and the combined presentation of measure and probabil- Viscosity Solutions ity. It is easily adapted for graduate students familiar with measure theory using the guidelines given. Spe- This book is intended as an introduction to optimal cial features include: - A comprehensive treatment stochastic control for continuous time Markov proof the law of the iterated logarithm - The Marcin- cesses and to the theory of viscosity solutions. The klewicz-Zygmund inequality, its extension to mar- authors approach stochastic control problems by tingales and applications thereof - Development and R. Durrett the method of dynamic programming. The text pro- applications of the second moment analogue of Walds vides an introduction to dynamic programming for equation - Limit theorems for martingale arrays; the Probability Models for DNA deterministic optimal control problems, as well as central limit theorem for the interchangeable and Sequence Evolution to the corresponding theory of viscosity solutions. martingale cases; moment convergence in the cen- A new Chapter X gives an introduction to the role tral limit theorem - Complete discussion, including How is genetic variability shaped by natural selec- of stochastic optimal control in portfolio optimiza- central limit theorem, of the random casting of r balls tion, demographic factors, and random genetic drift? tion and in pricing derivatives in incomplete markets. into n cells - Recent martingale inequalities - Cram r- To approach this question, we introduce and analyze Chapter VI of the First Edition has been completely L vy theorem and factor-closed families of distribu- a number of probability models beginning with the rewritten, to emphasize the relationships between log- tions. basics, and ending at the frontiers of current research. arithmic transformations and risk sensitivity. A new Throughout the book, the theory is developed in close Chapter XI gives a concise introduction to two-con- More on www.springer.com/978-0-387-40607-7 connection with examples from the biology litera- troller, zero-sum differential games. Also covered are Available ture that illustrate the use of these results. Along the controlled Markov diffusions and viscosity solutions way, there are many numerical examples and graphs of Hamilton-Jacobi-Bellman equations. The authors 1997. XXII, 488 p. (Springer Texts in Statistics, ) to illustrate the conclusions. This is the second edi- have tried, through illustrative examples and selective 978-0-387-40607-7 tion and is twice the size of the first one. The mate- material, to connect stochastic control theory with rial on recombination and the stepping stone model other mathematical areas (e.g. large deviations theory) have been greatly expanded, there are many results and with applications to engineering, physics, man- form the last five years, and two new chapters on dif- agement, and finance. In this Second Edition, new fusion processes develop that viewpoint. This book is material on applications to mathematical finance has written for mathematicians and for biologists alike. been added. Concise introductions to risk-sensitive No previous knowledge of concepts from biology is control theory, nonlinear H-infinity control and dif- assumed, and only a basic knowledge of probability, ferential games are also included. including some familiarity with Markov chains and More on www.springer.com/978-0-387-26045-7 Poisson processes. The book has been restructured into a large number of subsections and written in a Available theorem-proof style, to more clearly highlight the 2006. XVII, 429 p. (Stochastic Modelling and Applied main results and allow readers to find the results they Probability, 25) need and to skip the proofs if they desire. Rick Dur- 978-0-387-26045-7 rett received his Ph.D. in operations research from T. Deck Stanford University in 1976. He taught in the UCLA mathematics department before coming to Cornell in Der Itô-Kalkül 1985. He is the author of eight books and 160 research Einführung und Anwendungen papers, most of which concern the use of probability models in genetics and ecology. He is the academic Dieses Buch behandelt stochastische Integrale bezüglich der Brownschen Bewegung (Itô-Integrale), den daraus resultierenden Itôschen Differentialkalkül und einige Anwendungen. Das Buch zeichnet sich durch zwei Besonderheiten aus: Zum Einen sind die mathematischen Voraussetzungen minimiert, und springer.com Probability Theory and Stochastic Processes 77

subject that provides them with a foretaste of the subject's many treasures. The present second edition offers updated content, one hundred additional problems for solution, and a new chapter that provides an outlook on further areas and topics, such as stable distributions and domains of attraction, extreme value theory and records, and martingales. The main idea is that this chapter may serve as an appetizer to the more advanced theory. Allan Gut is Professor of Mathematical Statistics at Uppsala University, Uppsala, Sweden. He is a member of the International Statistical Institute, the Bernoulli Soci- G.R. Grimmett ety, the Institute of Mathematical Statistics, and the O. Häggström Swedish Statistical Society. He is an Associate Editor The Random-Cluster Model of the Journal of Statistical Planning and Inference Streifzüge durch die and Sequential Analysis, a former Associate Editor of The random-cluster model has emerged in recent Wahrscheinlichkeitstheorie the Scandinavian Journal of Statistics, and the author years as a key tool in the mathematical study of ferro- of five other books including Probability: A Graduate Dies ist eine Einführung in die Wahrscheinlichkeit- magnetism. It may be viewed as an extension of per- Course (Springer, 2005) and Stopped Random Walks: stheorie - der Mathematik des Zufalls. In einer colation to include Ising and Potts models, and its Limit Theorems and Applications, Second Edition mehr oder weniger losen Folge von Kapiteln wer- analysis is a mix of arguments from probability and (Springer, 2009). den veschiedene Themen angesprochen: Ein Teil geometry. This systematic study includes accounts of behandelt klassische Begriffe, wie Irrfahrten oder die the subcritical and supercritical phases, together with More on www.springer.com/978-1-4419-0161-3 Gesetze der großen Zahlen, während andere Kapitel clear statements of important open problems. There Available zeigen, wie die Mathematik in aktuelle Forschungen, is an extensive treatment of the first-order (discontin- z.B. die der Evolutionsbiologie, eingreift. Anschaulich uous) phase transition, as well as a chapter devoted to 2009. XIV, 302 p. (Springer Texts in Statistics, ) wird der Zusammenhang zur Spieltheorie erläutert. applications of the random-cluster method to other 978-1-4419-0161-3 Der Text widmet sich ausführlich einigen der am models of statistical physics. meisten diskutierten Paradoxa der Wahrschein- More on www.springer.com/978-3-540-32890-2 lichkeitstheorie, deren Betrachtung zu lehrreichen Available Einsichten führt. Einen wichtigen Raum nimmt 2006. XIV, 380 p. 37 illus. (Grundlehren der mathematischen auch die Perkolation und ihre Anwendungen ein, Wissenschaften, 333) so wird zum Beispiel das so genannte "kleine Welt"- 978-3-540-32890-2 Phänomen mathematisch untersucht. Das Buch ist in erster Linie als Zusatzlektüre für Vorlesun- gen zur Stochastik und mathematischen Statistik im Grundstudium an Universität und Hochschule gedacht. Darüber hinaus gibt es Anregungen für Gymnasiallehrer und ihre Schüler. Häggströms Buch leistet für die Wahrscheinlichkeitstheorie das, was Jänichs für die Topologie tut. More on www.springer.com/978-3-540-23050-2 T.S. Han Available Information-Spectrum Methods in 2006. XII, 267 S. 38 Abb. (Springer-Lehrbuch, ) Information Theory 978-3-540-23050-2 This book opens a novel dimension in the 50 year his- A. Gut tory of mathematical theory of "information" since the birth of Shannon theory. First of all, it introduces, in An Intermediate Course in place of the traditional notion of entropy and mutual R. Isaac information, the completely new and highly uncon- Probability ventional approach of "information-spectrum" as a The Pleasures of Probability basic but powerful tool for constructing the general The purpose of this book is to provide the reader theory of information. Reconstructing step-by-step all The purpose of "The Pleasures of Probability" is to with a solid background and understanding of the the essential major topics in information theory from introduce some of the most fundamental ideas in clas- basic results and methods in probability theory before the viewpoint of such an "information-spectrum", this sical probability to a fairly general audience - reach- entering into more advanced courses. The first six comprehensive work provides an accessible introducing from mathematical amateurs to scientists, from chapters focus on some central areas of what might be tion to the new type of mathematical theory of infor- students to professional mathematicians. The only called pure probability theory: multivariate random mation that focuses mainly on general nonstationary prerequisites required are a decent background in ele- variables, conditioning, transforms, order variables, and /or nonergodic sources and channels, in clear mentary algebra and an interest in discussions of a the multivariate normal distribution, and conver- contrast with the traditional theories of information. variety of problems and applications in probability. gence. A final chapter is devoted to the Poisson pro- This book is a new non-traditional theoretical refer- The style is informal, and the chapters are more like cess as a means both to introduce stochastic processes ence for communication professionals and statisti- essays on a particular topic than textbook treatments. and to apply many of the techniques introduced ear- cians specializing in information theory. Even well-known problems are often covered in more lier in the text. Students are assumed to have taken depth than usual in order to illustrate underlying More on www.springer.com/978-3-540-43581-5 a first course in probability, though no knowledge ideas. The book can be used as a text for a first course of measure theory is assumed. Throughout, the pre- Available in probability or as a companion to a text. Each chap- sentation is thorough and includes many examples 2003. XVII, 538 p. 46 illus. (Stochastic Modelling and Applied that are discussed in detail. Thus, students consid- Probability, 50) ering more advanced research in probability the- 978-3-540-43581-5 ory will benefit from this wide-ranging survey of the 78 Probability Theory and Stochastic Processes springer.com ter ends with a few problems, the answers to which Latin Hypercube Sampling, LHS). The data resulting world of probability theory. In addition, plenty of fig- are given at the end of the book. from these modern designs may be analyzed through ures, computer simulations, biographic details of key low-order polynomials for group screening and var- mathematicians, and a wealth of examples support More on www.springer.com/978-0-387-94415-9 ious metamodel types (e.g., Kriging) for LHS. In this and enliven the presentation. Available way, the book provides relatively simple solutions for More on www.springer.com/978-1-84800-047-6 the problem of which scenarios to simulate and how 1995. XV, 268 p. 17 illus. (Undergraduate Texts in to analyze the resulting data. The book also includes Available Mathematics, ) methods for computationally expensive simulations. 978-0-387-94415-9 It discusses only those tactical issues that are closely 2008. XII, 621 p. 23 illus. (Universitext, ) related to strategic issues; i.e., the text briefly discusses 978-1-84800-047-6 run-length and variance reduction techniques. The leading textbooks on discrete-event simulation pay A.F. Karr little attention to the strategic issues of simulation. The author has been working on strategic issues for Probability approximately forty years, in various scientific disci- ples--such as operations research, management sci- This is a textbook which will provide students with ence, industrial engineering, mathematical statistics, a straightforward introduction to the mathemati- economics, nuclear engineering, computer science, cal theory of probability. It is written with the aim of and information systems. The intended audience presenting the central results and techniques of the is comprised of researchers, graduate students, and subject in a complete and self-contained account. As mature practitioners in the simulation area. They are a result, the emphasis is on giving results in simple assumed to have a basic knowledge of simulation and forms with clear proofs and to eschew more powerful mathematical statistics; nevertheless, the book sum- forms of theorems which require technically involved marizes these basics, for the readers' convenience. proofs. Any graduate student who has a familiarity P.E. Kloeden, E. Platen with real analysis will be able to use this text - mea- More on www.springer.com/978-0-387-71812-5 sure theory is used only where necessary and undue Available Numerical Solution of Stochastic abstraction is avoided. Throughout there are a wide 2008. XIV, 218 p. 26 illus. (International Series in Operations Differential Equations variety of exercises to illustrate and to develop ideas in Research & Management Science, 111) the text. 978-0-387-71812-5 The numerical analysis of stochastic differential equa- More on www.springer.com/978-0-387-94071-7 tions differs significantly from that of ordinary differential equations, due to the peculiarities of stochastic Available calculus. The book proposes to the reader whose background knowledge is limited to undergraduate 1993. 312 p. (Springer Texts in Statistics, ) level methods for engineering and physics, and eas- 978-0-387-94071-7 ily accessible introductions to SDE and then applications as well as the numerical methods for dealing with them. To help the reader develop an intuitive understanding and hand-on numerical skills, numerous exercises including PC-exercises are included. More on www.springer.com/978-3-540-54062-5 Available 1992. XXXVI, 636 p. (Stochastic Modelling and Applied A. Klenke Probability, 23) 978-3-540-54062-5 Probability Theory A Comprehensive Course Probabilistic concepts play an increasingly impor- J.P. Kleijnen tant role in mathematics, physics, biology, financial engineering and computer science. They help us to Design and Analysis of Simulation understand magnetism, amorphous media, genetic diversity and the perils of random developments on Experiments the financial markets, and they guide us in construct- This is an advanced expository book on statistical ing more efficient algorithms. This text is a compre- methods for the Design and Analysis of Simulation hensive course in modern probability theory and its Experiments (DASE). Though the book focuses on measure-theoretical foundations. Aimed primarily at DASE for discrete-event simulation (such as queuing graduate students and researchers, the book covers and inventory simulations), it also discusses DASE a wide variety of topics, many of which are not usu- for deterministic simulation (such as engineering ally found in introductory textbooks, such as: limit A. Lasota, M.C. Mackey and physics simulations). The text presents both clas- theorems for sums of random variables; martingales; sic and modern statistical designs. Classic designs percolation; Markov chains and electrical networks; Chaos, Fractals, and Noise construction of stochastic processes; Poisson point (e.g., fractional factorials) assume only a few factors Stochastic Aspects of Dynamics with a few values per factor. The resulting input/out- processes and infinite divisibility; large deviation put data of the simulation experiment are analyzed principles and statistical physics; Brownian motion; This book gives a unified treatment of a variety of through low-order polynomials, which are linear and stochastic integral and stochastic differential mathematical systems generating densities, ranging regression (meta)models. Modern designs allow many equations. The theory is developed rigorously and in a from one-dimensional discrete time transformations more factors, possible with many values per factor. self-contained way, with the chapters on measure the- through continuous time systems described by inte- These designs include group screening (e.g., Sequen- ory interlaced with the probabilistic chapters in order gro-partial-differential equations. Examples have tial Bifurcation, SB) and space filling designs (e.g., to display the power of the abstract concepts in the been drawn from a variety of the sciences to illustrate springer.com Probability Theory and Stochastic Processes 79 the utility of the techniques presented. This material mathematics. In the second edition, the authors have was organized and written to be accessible to scien- made numerous corrections, updating every chapter, tists with knowledge of advanced calculus and differ- adding two new subsections devoted to the Kalman ential equations. In various concepts from measure filter under wrong initial conditions, as well as a new theory, ergodic theory, the geometry of manifolds, chapter devoted to asymptotically optimal filtering partial differential equations, probability theory and under diffusion approximation. Moreover, in each Markov processes, and chastic integrals and differen- chapter a comment is added about the progress of tial equations are introduced. The past few years have recent years. witnessed an explosive growth in interest in physical, More on www.springer.com/978-3-540-63929-9 biological, and economic systems that could be prof- itably studied using densities. Due to the general inac- Available cessibility of the mathematical literature to the non- M. Lefebvre 2001. XV, 427 p. (Stochastic Modelling and Applied mathematician, there has been little diffusion of the Probability, 5) concepts and techniques from ergodic theory into the Basic Probability Theory with 978-3-540-63929-9 study of these "chaotic" systems. This book intends to bridge that gap. Applications More on www.springer.com/978-0-387-94049-6 This book presents elementary probability theory with Available interesting and well-chosen applications that illustrate the theory. An introductory chapter reviews the basic 1994. (Applied Mathematical Sciences, 97) elements of differential calculus which are used in the 978-0-387-94049-6 material to follow. The theory is presented systematically, beginning with the main results in elementary probability theory. This is followed by material on random variables. Random vectors, including the M. Ledoux, M. Talagrand all important central limit theorem, are treated next. The last three chapters concentrate on applications Probability in Banach Spaces of this theory in the areas of reliability theory, basic Isoperimetry and Processes queuing models, and time series. Examples are ele- R.S. Liptser, A.N. Shiryaev New isoperimetric inequalities and random process gantly woven into the text and over 400 exercises rein- techniques have recently appeared at the basis of force the material and provide students with ample the modern understanding of Probability in Banach practice. This textbook can be used by undergraduate Statistics of Random Processes spaces. Based on these tools, the book presents a com- students in pure and applied sciences such as math- II. Applications ematics, engineering, computer science, finance and plete treatment of the main aspects of Probability in The subject of these two volumes is non-linear fil- economics. A separate solutions manual is available to Banach spaces (e.g. boundedness and continuity of tering (prediction and smoothing) theory and its instructors who adopt the text for their course. random processes, integrability and limit theorems application to the problem of optimal estimation, for vector valued random variables) and of some of More on www.springer.com/978-0-387-74994-5 control with incomplete data, information theory, and their links to Geometry of Banach spaces. Its pur- Available sequential testing of hypothesis. The book is not only pose is to present some of the main aspects of this the- addressed to mathematicians but should also serve ory, from the foundations to the latest developments, 2009. XVI, 340 p. 50 illus. (Springer Undergraduate the interests of other scientists who apply probabilis- treated with the most recent and updated tools. In Texts in Mathematics and Technology, ) tic and statistical methods in their work. The theory of particular, the most important features are the sys- 978-0-387-74994-5 martingales presented in the book has an independent tematic use of isoperimetry and related concentra- interest in connection with problems from financial tion of measure phenomena (to study integrability mathematics. In the second edition, the authors have and limit theorems for vector valued random vari- made numerous corrections, updating every chapter, ables), and recent abstract random process techniques adding two new subsections devoted to the Kalman (entropy and majorizing measures). Some examples filter under wrong initial conditions, as well as a new of these probabilistic ideas to classical Banach space chapter devoted to asymptotically optimal filtering theory complete this exposition. under diffusion approximation. Moreover, in each More on www.springer.com/978-3-540-52013-9 chapter a comment is added about the progress of recent years. Available 1991. XII, 480 p. 1 illus. (Ergebnisse der Mathematik und More on www.springer.com/978-3-540-63928-2 ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Available Mathematics, 23) 2001. XV, 402 p. (Stochastic Modelling and Applied 978-3-540-52013-9 Probability, 6) 978-3-540-63928-2 R.S. Liptser, A.N. Shiryaev Statistics of Random Processes I. General Theory P. Malliavin The subject of these two volumes is non-linear filtering (prediction and smoothing) theory and its application to the problem of optimal estimation, Integration and Probability control with incomplete data, information theory, and An introduction to analysis with the right mix of sequential testing of hypothesis. The book is not only abstract theories and concrete problems. Starting addressed to mathematicians but should also serve with general measure theory, the book goes on to the interests of other scientists who apply probabilis- treat Borel and Radon measures and introduces the tic and statistical methods in their work. The theory of reader to Fourier analysis in Euclidean spaces with martingales presented in the book has an independent a treatment of Sobolev spaces, distributions, and the interest in connection with problems from financial corresponding Fourier analysis. It continues with a 80 Probability Theory and Stochastic Processes springer.com

Hilbertian treatment of the basic laws of probability ing particle methods and worked out illustrations of including Doob's martingale convergence theorem the key aspect of the theory. With practical and easy and finishes with Malliavin's "stochastic calculus of to use references as well as deeper and modern math- variations" developed in the context of Gaussian mea- ematics studies, the book will be of use to engineers sure spaces. This invaluable contribution gives a taste and researchers in pure and applied mathematics, of the fact that analysis is not a collection of indepen- statistics, physics, biology, and operation research dent theories, but can be treated as a whole. who have a background in probability and Markov chain theory. From the reviews: "I also recommend More on www.springer.com/978-0-387-94409-8 this book as informal reading for anyone intersted Available in the subject, preferably with a strong background in Markov processes; in particular, for someone also 1995. XXI, 322 p. 1 illus. (Graduate Texts in familiar with one of the many fields to which the book Mathematics, 157) I. Molchanov applies Feynman-Kac models. The book is entertain- 978-0-387-94409-8 ing and informative." Journal of the American Statisti- Theory of Random Sets cal Association, December 2005 This is the first systematic exposition of random More on www.springer.com/978-0-387-20268-6 sets theory since Matheron (1975), with full proofs, Available exhaustive bibliographies and literature notes Inter- 2004. XVIII, 555 p. 15 illus. (Probability and Its Applications, ) disciplinary connections and applications of ran- 978-0-387-20268-6 dom sets are emphasized throughout the bookAn extensive bibliography in the book is available on the Web at http://liinwww.ira.uka.de/bibliography/math/ random.closed.sets.html, and is accompanied by a search engine More on www.springer.com/978-1-85233-892-3 Available

D. Meintrup, S. Schäffler 2005. XVI, 488 p. 33 illus. (Probability and Its Applications, ) 978-1-85233-892-3 Stochastik Theorie und Anwendungen Stochastische Methoden besitzen in vielen Teilen der Technik und Informatik eine hohe Relevanz. So beruhen z.B. die meisten modernen Verfahren der G. Nunno, B. Øksendal, F. Proske digitalen Nachrichtenübertragung, der Schaltkreis- simulation aber auch der Verfahrenstechnik und des Malliavin Calculus for Lévy Financial Engineering auf stochastischen Prinzipien. Processes with Applications to Das Buch bietet eine fundierte und anwendungsbe- zogene Einführung in die Wahrscheinlichkeitsthe- Finance orie und Statistik. Im Zentrum stehen nach einer While the original works on Malliavin calculus aimed grundlegenden Behandlung der Maß- und Integra- to study the smoothness of densities of solutions tionstheorie sowie der Grundlagen der Wahrschein- to stochastic differential equations, this book has lichkeitstheorie stochastische Prozesse, insbesonders P. Moral another goal. It portrays the most important and Poisson-Prozesse, Martingale und Brownsche Bewe- innovative applications in stochastic control and gungen. Alle Resultate werden ausführlich motiviert Feynman-Kac Formulae finance, such as hedging in complete and incomplete und exakt bewiesen. Dadurch eignet sich das Buch markets, optimisation in the presence of asymmetric hervorragend zum Selbststudium und als vorlesungs- Genealogical and Interacting Particle Systems with Applications information and also pricing and sensitivity analysis. begleitende Literatur. In a self-contained fashion, both the Malliavin calcu- More on www.springer.com/978-3-540-21676-6 This book contains a systematic and self-contained lus with respect to Brownian motion and general Lévy Available treatment of Feynman-Kac path measures, their type of noise are treated. Besides, forward integra- genealogical and interacting particle interpretations, tion is included and indeed extended to general Lévy 2005. XIV, 609 S. (Statistik und ihre Anwendungen, ) and their applications to a variety of problems aris- processes. The forward integration is a recent devel- 978-3-540-21676-6 ing in statistical physics, biology, and advanced engi- opment within anticipative stochastic calculus that, neering sciences. Topics include spectral analysis together with the Malliavin calculus, provides new of Feynman-Kac-Schrödinger operators, Dirichlet methods for the study of insider trading problems. To problems with boundary conditions, finance, molec- allow more flexibility in the treatment of the mathe- ular analysis, rare events and directed polymers sim- matical tools, the generalization of Malliavin calculus ulation, genetic algorithms, Metropolis-Hastings to the white noise framework is also discussed. This type models, as well as filtering problems and hid- book is a valuable resource for graduate students, lec- den Markov chains. This text takes readers in a clear turers in stochastic analysis and applied researchers. and progressive format from simple to recent and More on www.springer.com/978-3-540-78571-2 advanced topics in pure and applied probability such as contraction and annealed properties of non-linear Available semi-groups, functional entropy inequalities, empirical process convergence, increasing propagations 2009. XIV, 418 p. (Universitext, ) of chaos, central limit, and Berry Esseen type theo- 978-3-540-78571-2 rems as well as large deviations principles for strong topologies on path-distribution spaces. Topics also include a body of powerful branching and interact- springer.com Probability Theory and Stochastic Processes 81

models under the usual invariance assumptions. A statistics, operations research, computer science, engi- characteristic of the book is the interplay between neering, and business. stochastic and geometric arguments, leading to var- More on www.springer.com/978-3-540-89331-8 ious major results. Its main theme, once the foundations have been laid, is the quantitative investigation Available of the basic models. This comprises the introduc- 2009. XIV, 443 p. 11 illus. (Probability and Its Applications, ) tion of suitable parameters, in the form of functional 978-3-540-89331-8 densities, relations between them, and approaches to their estimation. Much additional information on stochastic geometry is collected in the section notes. As a combination of probability theory and geometry, the volume is intended for readers from either field. G.d. Prato Probabilists with interest in random spatial structures, or motivated by the prospect of applications, An Introduction to Infinite- will find an in-depth presentation of the geometric Dimensional Analysis background. Geometers can see integral geometry "at work" and may be surprised to learn how classical In this revised and extended version of his course results from convex geometry have elegant applica- notes from a 1-year course at Scuola Normale Supe- tions in a stochastic setting. riore, Pisa, the author provides an introduction – More on www.springer.com/978-3-540-78858-4 for an audience knowing basic functional analysis Available and measure theory but not necessarily probabil- A.N. Shiryaev ity theory – to analysis in a separable Hilbert space 2008. XII, 694 p. (Probability and Its Applications, ) of infinite dimension. Starting from the definition 978-3-540-78858-4 Optimal Stopping Rules of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian Although three decades have passed since first publi- motion and Wiener integral are introduced in a sim- cation of this book reprinted now as a result of pop- ple way. These concepts are then used to illustrate ular demand, the content remains up-to-date and some basic stochastic dynamical systems (includ- interesting for many researchers as is shown by the ing dissipative nonlinearities) and Markov semi- many references to it in current publications. The groups, paying special attention to their long-time "ground floor" of Optimal Stopping Theory was con- behavior: ergodicity, invariant measure. Here funda- structed by A.Wald in his sequential analysis in con- mental results like the theorems of Prokhorov, Von nection with the testing of statistical hypotheses by Neumann, Krylov-Bogoliubov and Khas'minski are non-traditional (sequential) methods. It was later proved. The last chapter is devoted to gradient sys- discovered that these methods have, in idea, a close tems and their asymptotic behavior. connection to the general theory of stochastic optimization for random processes. The area of applica- More on www.springer.com/978-3-540-29020-9 tion of the Optimal Stopping Theory is very broad. It Available R. Serfozo is sufficient at this point to emphasise that its methods are well tailored to the study of American (-type) 2006. X, 214 p. (Universitext, ) Basics of Applied Stochastic options (in mathematics of finance and financial 978-3-540-29020-9 engineering), where a buyer has the freedom to exer- Processes cise an option at any stopping time. In this book, the general theory of the construction of optimal stop- Stochastic processes are mathematical models of ran- ping policies is developed for the case of Markov pro- dom phenomena that evolve according to prescribed cesses in discrete and continuous time. One chapter dynamics. Processes commonly used in applications is devoted specially to the applications that address are Markov chains in discrete and continuous time, problems of the testing of statistical hypotheses, and renewal and regenerative processes, Poisson pro- quickest detection of the time of change of the proba- cesses, and Brownian motion. This volume gives an bility characteristics of the observable processes. The in-depth description of the structure and basic prop- author, A.N.Shiryaev, is one of the leading experts erties of these stochastic processes. A main focus is on of the field and gives an authoritative treatment of a equilibrium distributions, strong laws of large num- subject that, 30 years after original publication of this bers, and ordinary and functional central limit theo- book, is proving increasingly important. rems for cost and performance parameters. Although these results differ for various processes, they have a More on www.springer.com/978-3-540-74010-0 common trait of being limit theorems for processes Available R. Schneider, W. Weil with regenerative increments. Extensive examples 2008. XII, 220 p. 7 illus. (Stochastic Modelling and Applied and exercises show how to formulate stochastic mod- Stochastic and Integral Geometry Probability, 8) els of systems as functions of a system’s data and 978-3-540-74010-0 Stochastic geometry has in recent years experienced dynamics, and how to represent and analyze cost and considerable progress, both in its applications to other performance measures. Topics include stochastic sciences and engineering, and in its theoretical foun- networks, spatial and space-time Poisson processes, dations and mathematical expansion. This book, queueing, reversible processes, simulation, Brown- by two eminent specialists of the subject, provides a ian approximations, and varied Markovian models. solid mathematical treatment of the basic models of The technical level of the volume is between that of stochastic geometry -- random sets, point processes introductory texts that focus on highlights of applied of geometric objects (particles, flats), and random stochastic processes, and advanced texts that focus on mosaics. It develops, in a measure-theoretic setting, theoretical aspects of processes. Intended readers are the integral geometry for the motion and the trans- researchers and graduate students in mathematics, lation group, as needed for the investigation of these 82 Quantitative Finance springer.com

ture of the subject and avoiding sophisticated measure strate that the viscosity solution theory provides the theory Leads the reader to a rigorous understanding framework to unify them. of basic theory More on www.springer.com/978-0-387-98723-1 More on www.springer.com/978-3-540-23451-7 Available Available 1999. XXII, 438 p. (Stochastic Modelling and Applied Probability, 43) 2005. XIV, 171 p. (Graduate Texts in Mathematics, 978-0-387-98723-1 230) 978-3-540-23451-7

Quantitative Finance R.W. Shonkwiler, F. Mendivil Explorations in Monte Carlo Methods Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems. Applications covered in this book include optimization, finance, statistical mechanics, birth and death processes, and gambling systems. Explorations in K. Waldmann, U.M. Stocker Monte Carlo Methods provides a hands-on approach to learning this subject. Each new idea is carefully Stochastische Modelle motivated by a realistic problem, thus leading from Eine anwendungsorientierte Einführung questions to theory via examples and numerical N.H. Bingham, R. Kiesel Das vorliegende Buch führt den Leser in die Welt simulations. Programming exercises are integrated der stochastischen Modellbildung ein. Im Vorder- throughout the text as the primary vehicle for learn- Risk-Neutral Valuation grund steht dabei eine anschauliche Darstellung zeit- ing the material. Each chapter ends with a large col- Pricing and Hedging of Financial Derivatives diskreter Modelle, die auf einer klaren Formulierung lection of problems illustrating and directing the der mathematischen Grundlagen basiert. Der Begriff This second edition - completely up to date with new material. This book is suitable as a textbook for stu- der Markov-Kette zieht sich wie ein roter Leitfaden exercises - provides a comprehensive and self-con- dents of engineering and the sciences, as well as math- durch die einzelnen Kapitel. Markov-Ketten sind tained treatment of the probabilistic theory behind ematics. The problem-oriented approach makes it von Interesse bei der Analyse zeit-diskreter dynamis- the risk-neutral valuation principle and its application ideal for an applied course in basic probability and for cher Systeme, die zufälligen Einflüssen unterliegen. to the pricing and hedging of financial derivatives. a more specialized course in Monte Carlo methods. Sie beeindrucken durch ihre klare Struktur und ihre On the probabilistic side, both discrete- and continu- Topics include probability distributions, counting Einfachheit in der Darstellung und Lösung. Markov- ous-time stochastic processes are treated, with special combinatorial objects, simulated annealing, genetic Ketten sind, zusammen mit den Poisson-Prozessen emphasis on martingale theory, stochastic integration algorithms, option pricing, gamblers ruin, statistical und ihren Verallgemeinerungen, zudem ein wichtiger and change-of-measure techniques. Based on firm mechanics, sampling, and random number genera- Baustein zum Verständnis und zur Analyse zeit- probabilistic foundations, general properties of dis- tion. stetiger Systeme. Die vorgestellten Methoden wer- crete- and continuous-time financial market models More on www.springer.com/978-0-387-87836-2 den durch ausführliche Beispiele veranschaulicht und are discussed. Available durch gezielte Aufgaben mit Lösungen vertieft. Dabei More on www.springer.com/978-1-85233-458-1 kommt den multimedialen Elementen der e-stat- Available 2009. XII, 244 p. 50 illus. (Undergraduate Texts in Umgebung eine zentrale Bedeutung zu, da sie neue Mathematics, ) Möglichkeiten der Veranschaulichung stochastischer 978-0-387-87836-2 Systeme eröffnet. Mehrere Fallstudien runden diese 2004. XVIII, 437 p. 8 illus. (Springer Finance, ) 978-1-85233-458-1 anwendungsorientierte Einführung ab. More on www.springer.com/978-3-540-03241-0 Available

2004. VIII, 188 S. (EMIL@A-stat, ) 978-3-540-03241-0

J. Yong, X.Y. Zhou Stochastic Controls Hamiltonian Systems and HJB Equations D.W. Stroock The maximum principle and dynamic programming An Introduction to Markov are the two most commonly used approaches in solving optimal control problems. These approaches have Processes been developed independently. The theme of this Provides a more accessible introduction than other book is to unify these two approaches, and to demon- books on Markov processes by emphasizing the struc- springer.com Quantitative Finance 83

text for students, teachers and users in the industry of extremal event methodology. More on www.springer.com/978-3-540-60931-5 Available 1997. XVI, 648 p. 100 illus. (Stochastic Modelling and Applied Probability, 33) 978-3-540-60931-5

R. . Carmona, M. Tehranchi G. Fusai, A. Roncoroni Interest Rate Models: an Infinite Implementing Models in Dimensional Stochastic Analysis Quantitative Finance: Methods Perspective and Cases Interest Rate Models: an Infinite Dimensional This book puts numerical methods into action for the Stochastic Analysis Perspective studies the mathemat- purpose of solving concrete problems arising in quan- ical issues that arise in modeling the interest rate term titative finance. Part one develops a comprehensive structure. These issues are approached by casting the D. Filipovic toolkit including Monte Carlo simulation, numerical interest rate models as stochastic evolution equations schemes for partial differential equations, stochastic in infinite dimensional function spaces. The book is Term-Structure Models optimization in discrete time, copula functions, trans- comprised of three parts. Part I is a crash course on form-based methods and quadrature techniques. The interest rates, including a statistical analysis of the A Graduate Course content originates from class notes written for courses data and an introduction to some popular interest Changing interest rates constitute one of the major on numerical methods for finance and exotic deriva- rate models. Part II is a self-contained introduction risk sources for banks, insurance companies, and tive pricing held by the authors at Bocconi University to infinite dimensional stochastic analysis, including other financial institutions. Modeling the term-struc- since the year 2000. Part two proposes eighteen self- SDE in Hilbert spaces and Malliavin calculus. Part ture movements of interest rates is a challenging task. contained cases covering model simulation, derivative III presents some recent results in interest rate the- This volume gives an introduction to the mathemat- valuation, dynamic hedging, portfolio selection, risk ory, including finite dimensional realizations of HJM ics of term-structure models in continuous time. It management, statistical estimation and model cali- models, generalized bond portfolios, and the ergodic- includes practical aspects for fixed-income markets bration. It encompasses a wide variety of problems ity of HJM models. such as day-count conventions, duration of coupon- arising in markets for equity, interest rates, credit More on www.springer.com/978-3-540-27065-2 paying bonds and yield curve construction; arbitrage risk, energy and exotic derivatives. Each case intro- theory; short-rate models; the Heath-Jarrow-Morton duces a problem, develops a detailed solution and Available methodology; consistent term-structure parametriza- illustrates empirical results. Proposed algorithms are 2006. XIV, 235 p. (Springer Finance, ) tions; affine diffusion processes and option pricing implemented using either Matlab® or Visual Basic for 978-3-540-27065-2 with Fourier transform; LIBOR market models; and Applications® in collaboration with contributors. credit risk. The focus is on a mathematically straight- More on www.springer.com/978-3-540-22348-1 forward but rigorous development of the theory. Stu- dents, researchers and practitioners will find this Available volume very useful. Each chapter ends with a set of 2008. XXIII, 608 p. 150 illus., 5 in color. (Springer Finance, ) exercises, that provides source for homework and 978-3-540-22348-1 exam questions. Readers are expected to be familiar with elementary Itô calculus, basic probability theory, and real and complex analysis. More on www.springer.com/978-3-540-09726-6 Available

2009. XII, 256 p. (Springer Finance, ) 978-3-540-09726-6 P. Embrechts, C. Klüppelberg, T. Mikosch Modelling Extremal Events for Insurance and Finance Both in insurance and in finance applications, ques- M. Gundlach, F. Lehrbass tions involving extremal events (such as large insurance claims, large fluctuations in financial data, stock market shocks, risk management, ...) play an increas- CreditRisk+ in the Banking ingly important role. This book sets out to bridge the Industry gap between the existing theory and practical applica- CreditRisk+ is an important and widely implemented tions both from a probabilistic as well as from a statis- default-mode model of portfolio credit risk, based tical point of view. Whatever new theory is presented on a methodology borrowed from actuarial mathe- is always motivated by relevant real-life examples. The matics. This book gives an account of the status quo numerous illustrations and examples, and the exten- as well as of new and recent developments of the sive bibliography make this book an ideal reference credit risk model CreditRisk+, which is widely used in the banking industry. It gives an introduction to 84 Quantitative Finance springer.com the model itself and to its ability to describe, man- the aspects of pricing, hedging and their risk manage and price credit risk. The book is intended for an agement. Starting from the renowned Black-Scholes- audience of practitioners in banking and finance, as Merton formulation of option pricing model, read- well as for graduate students and researchers in the ers are guided through the text on the new advances field of financial mathematics and banking. It con- on the state-of-the-art derivative pricing models tains carefully refereed contributions from experts in and interest rate models. Both analytic techniques the field, selected for mutual consistency and edited and numerical methods for solving various types of for homogeneity of style, notation, etc. The discussion derivative pricing models are emphasized. The sec- ranges from computational methods and extensions ond edition presents a substantial revision of the first for special forms of credit business to statistical cali- edition. The continuous-time martingale pricing the- brations and practical implementations. This unique ory is motivated through analysis of the underlying and timely book constitutes an indispensable tool for financial economics principles within a discrete-time both practitioners and academics working in the eval- J. Kremer framework. A large collection of closed-form formu- uation of credit risk. las of various forms of exotic equity and fixed income derivatives are documented. The most recent research More on www.springer.com/978-3-540-20738-2 Einführung in die Diskrete Finanzmathematik results and methodologies are made accessible to Available readers through the extensive set of exercises at the 2004. XII, 369 p. (Springer Finance, ) Im vorliegenden Buch werden die wichtigsten end of each chapter. Yue-Kuen Kwok is Professor 978-3-540-20738-2 Grundlagen der modernen Finanzmathematik of Mathematics at Hong Kong University of Science im Rahmen endlicher Wahrscheinlichkeitsräume and Technology. He is the author of over 80 research und unter Berücksichtigung endlich vieler Zeit- papers and several books, including Applied Complex punkte dargestellt. Behandelte Themen sind unter Variables. He is an associate editor of Journal of Eco- anderem Ein- und Mehr-Perioden-Modelle, Port- nomic Dynamics and Control and Asia-Pacific Finan- foliotheorie, CAPM, Binomialbaum-Verfahren für cial Markets. europäische und amerikanische Standard-Optio- More on www.springer.com/978-3-540-42288-4 nen, Berücksichtigung von Dividendenzahlungen, ausgewählte exotische Optionen, Black-Scholes- Available Formeln, Value at Risk, diskrete Stochastische Anal- ysis sowie diskrete Stochastische Finanzmathematik. 2008. XVI, 530 p. 49 illus. (Springer Finance, ) Zu allen Bewertungsverfahren werden Algorith- 978-3-540-42288-4 men angegeben, die leicht implementiert werden können. Das Buch kann damit im Rahmen eines Bachelor- oder Diplom-Studiengangs Finanz- oder M. Jeanblanc, M. Yor, M. Chesney Wirtschaftsmathematik verwendet werden, es möchte aber auch den Einstieg in die stetige Finanzmathe- Mathematical Methods for matik erleichtern. Dank vieler Beispiele, Aufgaben mit Lösungen sowie einem Kapitel mit mathematischen Financial Markets Grundlagen sind die dargestellten Inhalte auch zum Mathematical finance has grown into a huge area of Selbststudium geeignet. research which requires a lot of care and a large num- More on www.springer.com/978-3-540-25394-5 ber of sophisticated mathematical tools. The subject Available draws upon quite difficult results from the theory of stochastic processes, stochastic calculus and differen- 2006. XVI, 500 S. 37 Abb. (Springer-Lehrbuch, ) tial equations, among others, which can be daunting 978-3-540-25394-5 for the beginning researcher. This book simultane- P. Malliavin, A. Thalmaier ously introduces the financial methodology and the relevant mathematical tools in a style that is math- Stochastic Calculus of Variations ematically rigorous and yet accessible to practition- in Mathematical Finance ers and mathematicians alike. It interlaces financial concepts such as arbitrage opportunities, admissi- Highly esteemed author Topics covered ble strategies, contingent claims, option pricing and are relevan- default risk with the mathematical theory of Brownian More on www.springer.com/978-3-540-43431-3 motion, diffusion processes, and Lévy processes. The Available authors proceed by successive generalisations with increasing complexity assuming some basic knowl- 2006. XII, 142 p. (Springer Finance, ) edge of probability theory. The first half of the book 978-3-540-43431-3 is devoted to continuous path processes whereas the second half deals with discontinuous processes. The extensive bibliography comprises a wealth of important references and the author index enables readers Y. Kwok quickly to locate where the reference is cited within the book, making this volume an invaluable tool both Mathematical Models of Financial for students and for those at the forefront of research Derivatives and practice. Mathematical Models of Financial Derivatives is a More on www.springer.com/978-1-85233-376-8 textbook on the theory behind modeling derivatives Available using the financial engineering approach, focussing on the martingale pricing principles that are common 2009. XXVI, 732 p. 9 illus. (Springer Finance, ) to most derivative securities. A wide range of finan- 978-1-85233-376-8 cial derivatives commonly traded in the equity and fixed income markets are analyzed, emphasizing on springer.com Quantitative Finance 85

titude of applied stochastic processes. It includes detailed discussions of the fundamental models regarding claim sizes, claim arrivals, the total claim amount, and their probabilistic properties. Through- out the volume the language of stochastic processes is used for describing the dynamics of an insurance portfolio in claim size, space and time. Special emphasis is given to the phenomena which are caused by large claims in these models. The reader learns how the underlying probabilistic structures allow determining premiums in a portfolio or in an individual policy. The second edition contains various new chap- H. Pham A. Meucci ters that illustrate the use of point process techniques in non-life insurance mathematics. Poisson processes Risk and Asset Allocation Continuous-time Stochastic play a central role. Detailed discussions show how Control and Optimization with This encyclopedic, self-contained, detailed exposi- Poisson processes can be used to describe complex tion spans all the steps of one-period allocation from aspects in an insurance business such as delays in Financial Applications the basics to the most advanced and recent develop- reporting, the settlement of claims and claims reserv- Stochastic optimization problems arise in deci- ments. A variety of multivariate estimation meth- ing. Also the chain ladder method is explained in sion-making problems under uncertainty, and find ods are analyzed in depth, including non-parametric, detail. More than 150 figures and tables illustrate and various applications in economics and finance. On maximum-likelihood under non-normal hypothe- visualize the theory. Every section ends with numer- the other hand, problems in finance have recently ses, shrinkage, robust, etc., in addition to very general ous exercises. An extensive bibliography, annotated led to new developments in the theory of stochas- multivariate Bayesian techniques. Evaluation methods with various comments sections with references to tic control. This volume provides a systematic treat- such as stochastic dominance, expected utility, value more advanced relevant literature, makes the volume ment of stochastic optimization problems applied to at risk and coherent measures are thoroughly ana- broadly and easily accessible. finance by presenting the different existing methods: lyzed in a unified setting and applied in a variety of More on www.springer.com/978-3-540-88232-9 dynamic programming, viscosity solutions, backward contexts, including total return and benchmark allo- Available stochastic differential equations, and martingale dual- cation, prospect theory, etc. Portfolio optimization is ity methods. The theory is discussed in the context of presented with emphasis on estimation risk, which is 2009. XV, 432 p. 55 illus. (Universitext, ) recent developments in this field, with complete and tackled by means of Bayesian, resampling and robust 978-3-540-88232-9 detailed proofs, and is illustrated by means of concrete optimization techniques. This work is both a refer- examples from the world of finance: portfolio allo- ence for practitioners and a textbook for students. cation, option hedging, real options, optimal invest- The only prerequisites are linear algebra and multi- ment, etc. This book is directed towards graduate variate calculus. All the statistical tools, such as copu- students and researchers in mathematical finance, and las, location-dispersion ellipsoids and matrix-variate will also benefit applied mathematicians interested distribution theory, are introduced from the basics. in financial applications and practitioners wishing to The same holds for the mathematical machinery, know more about the use of stochastic optimization such as computational results from cone program- methods in finance. ming and heuristic arguments from functional analysis. Comprehension is supported by a large number More on www.springer.com/978-3-540-89499-5 of practical examples, real trading and asset manage- Available ment case studies, figures, geometrical arguments and MATLAB® applications, which can be freely down- 2009. XVII, 232 p. (Stochastic Modelling and Applied loaded from symmys.com. Probability, 61) 978-3-540-89499-5 More on www.springer.com/978-3-642-00964-8 M. Musiela, M. Rutkowski Available Martingale Methods in Financial 2005. XXVI, 532 p. (Springer Finance, ) Modelling 978-3-642-00964-8 A new edition of a successful, well-established book that provides the reader with a text focused on practical rather than theoretical aspects of financial modelling Includes a new chapter devoted to volatility risk The theme of stochastic volatility reappears systematically and has been revised fundamentally, presenting a much more detailed analyses of interest-rate models More on www.springer.com/978-3-540-20966-9 Available 2005. XX, 718 p. (Stochastic Modelling and Applied E. Platen, D. Heath Probability, 36) 978-3-540-20966-9 A Benchmark Approach to Quantitative Finance T. Mikosch The benchmark approach provides a general framework for financial market modeling, which extends Non-Life Insurance Mathematics beyond the standard risk-neutral pricing theory. It An Introduction with the Poisson Process permits a unified treatment of portfolio optimization, The volume offers a mathematical introduction to derivative pricing, integrated risk management and non-life insurance and, at the same time, to a mul- insurance risk modeling. The existence of an equiv- 86 Real Functions springer.com alent risk-neutral pricing measure is not required. Instead, it leads to pricing formulae with respect to the real-world probability measure. This yields important modeling freedom which turns out to be necessary for the derivation of realistic, parsimonious market models. The first part of the book describes the necessary tools from probability theory, statistics, stochastic calculus and the theory of stochastic differential equations with jumps. The second part is devoted to financial modeling by the benchmark approach. Various quantitative methods for the real-world pricing and hedging of derivatives are P. Bullen explained. The general framework is used to provide Y. Zhu, X. Wu, I. Chern an understanding of the nature of stochastic volatility. The book is intended for a wide audience that Derivative Securities and Handbook of Means and Their includes quantitative analysts, postgraduate students Inequalities and practitioners in finance, economics and insur- Difference Methods ance. It aims to be a self-contained, accessible but This is a revision of an earlier Means and Their mathematically rigorous introduction to quantita- More on www.springer.com/978-0-387-20842-8 Inequalities by the present author and Professors tive finance for readers that have a reasonable mathe- Available Mitrinovic and Vasic. Not only does this book bring matical or quantitative background. Finally, the book 2004. XVIII, 518 p. 92 illus. (Springer Finance, ) the earlier version up to date but enlarges the scope should stimulate interest in the benchmark approach 978-0-387-20842-8 considerably to give a full and in-depth treatment of by describing some of its power and wide applicabil- all aspects of the field. While the mention of means ity. occurs in many books this is the only full treatment of the subject. Outstanding features of the book are the More on www.springer.com/978-3-540-26212-1 variety of proofs given for many of the basic results, Available over seventy for the inequality between the arith- Real Functions metic and geometric means for instance, an exhaus- 2006. XVI, 700 p. 199 illus. (Springer Finance, ) tive bibliography and a list of mathematicians who 978-3-540-26212-1 have contributed to this field from the time of Euclid to the present day. Audience: This book is written A. Browder in a language that not only the expert on the subject will understand and appreciate, but graduate students Mathematical Analysis worldwide as well. Any person with an interest in An Introduction means and their inequalities should find this book within their comprehension although to fully appreci- This is a textbook containing more than enough ate all the topics covered a knowledge of calculus and material for a year-long course in analysis at the of elementary real analysis is required. advanced undergraduate or beginning graduate level. The book begins with a brief discussion of sets and More on www.springer.com/978-1-4020-1522-9 mappings, describes the real number field, and pro- Available ceeds to a treatment of real-valued functions of a real 2003. 537 p. (Mathematics and Its Applications, 560) variable. Separate chapters are devoted to the ideas 978-1-4020-1522-9 of convergent sequences and series, continuous func- R. Seydel tions, differentiation, and the Riemann integral. The middle chapters cover general topology and a mis- Tools for Computational Finance cellany of applications: the Weierstrass and Stone- Weierstrass approximation theorems, the existence This book is very easy to read and one can gain a of geodesics in compact metric spaces, elements of quick snapshot of computational issues arising in Fourier analysis, and the Weyl equidistribution the- financial mathematics. Researchers or students of orem. Next comes a discussion of differentiation of the mathematical sciences with an interest in finance vector-valued functions of several real variables, fol- will find this book a very helpful and gentle guide to lowed by a brief treatment of measure and integration the world of financial engineering. SIAM review (46, (in a general setting, but with emphasis on Lebesgue 2004). The fourth edition is thoroughly revised and theory in Euclidean space). The final part of the book extended. Major revisions concern topics like calibra- deals with manifolds, differential forms, and Stokes' tion, Monte Carlo Methods, American options, exotic theorem, which is applied to prove Brouwer's fixed options and Algorithms for Bermuda Options. New point theorem and to derive the basic properties of figures, more exercises, more background material harmonic functions, such as the Dirichlet principle. M. Carter, B.v. Brunt make this guide to the world of financial engineering More on www.springer.com/978-0-387-94614-6 a real must-to-have for everyone working in FE. The Lebesgue-Stieltjes Integral Available More on www.springer.com/978-3-540-92928-4 A Practical Introduction Available 1996. XIV, 356 p. 5 illus. (Undergraduate Texts in While mathematics students generally meet the Rie- Mathematics, ) mann integral early in their undergraduate studies, 2009. XXI, 336 p. 85 illus. (Universitext, ) 978-0-387-94614-6 those whose interests lie more in the direction of 978-3-540-92928-4 applied mathematics will probably find themselves needing to use the Lebesgue or Lebesgue-Stieltjes Integral before they have acquired the necessary theoretical background. This book is aimed at exactly this group of readers. The authors introduce the springer.com Real Functions 87

Lebesgue-Stieltjes integral on the real line as a natural stimulating and enjoyable reading for students, teach- extension of the Riemann integral, making the treat- ers, as well as researchers. ment as practical as possible. They discuss the evalu- More on www.springer.com/978-0-387-94551-4 ation of Lebesgue-Stieltjes integrals in detail, as well as the standard convergence theorems, and conclude Available with a brief discussion of multivariate integrals and surveys of L spaces plus some applications. The whole 1996. X, 377 p. 192 illus. (Undergraduate Texts in is rounded off with exercises that extend and illustrate Mathematics, ) 978-0-387-94551-4 the theory, as well as providing practice in the techniques. More on www.springer.com/978-0-387-95012-9 Available R. Goldblatt 2000. IX, 228 p. 45 illus. (Undergraduate Texts in Mathematics, ) Lectures on the Hyperreals 978-0-387-95012-9 An Introduction to Nonstandard Analysis An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study J. Doob by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory Measure Theory about infinitely small and large numbers, but as a radically different way of viewing many standard math- J. Heinonen This book is different from other books on mea- ematical concepts and constructions. It is a source of sure theory in that it accepts probability theory as new ideas, objects and proofs, and a wealth of pow- Lectures on Analysis on Metric an essential part of measure theory. This means that erful new principles of reasoning. The book begins many examples are taken from probability; that prob- Spaces with the ultrapower construction of hyperreal number abilistic concepts such as independence, Markov systems, and proceeds to develop one-variable calcu- Analysis in spaces with no a priori smooth struc- processes, and conditional expectations are inte- lus, analysis and topology from the nonstandard per- ture has progressed to include concepts from the grated into the text rather than being relegate to an spective. It then sets out the theory of enlargements of first order calculus. In particular, there have been appendix; that more attention is paid to the role of fragments of the mathematical universe, providing a important advances in understanding the infinitesi- algebras than is customary; and that the metric defin- foundation for the full-scale development of the non- mal versus global behavior of Lipschitz functions and ing the distance between sets as the measure of their standard methodology. The final chapters apply this quasiconformal mappings in rather general settings; symmetric difference is exploited more than is cus- to a number of topics, including Loeb measure the- abstract Sobolev space theories have been instrumen- tomary. ory and its relation to Lebesgue measure on the real tal in this development. The purpose of this book is More on www.springer.com/978-0-387-94055-7 line. Highlights include an early introduction of the to communicate some of the recent work in the area Available ideas of internal, external and hyperfinite sets, and while preparing the reader to study more substantial, a more axiomatic set-theoretic approach to enlarge- related articles. The material can be roughly divided 1994. 228 p. (Graduate Texts in Mathematics, 143) ments than is usual. into three different types: classical, standard but sometimes with a new twist, and recent. The author 978-0-387-94055-7 More on www.springer.com/978-0-387-98464-3 first studies basic covering theorems and their appli- Available cations to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasiz- 1998. XIV, 312 p. (Graduate Texts in Mathematics, ing principles that are valid in larger contexts. The last B.R. Gelbaum 188) few sections of the book present a basic theory of qua- 978-0-387-98464-3 sisymmetric maps between metric spaces. Much of the Problems in Real and Complex material is relatively recent and appears for the first time in book format. There are plenty of exercises. Analysis The book is well suited for self-study, or as a text in a This book builds upon the earlier volume Problems in E. Hairer, G. Wanner graduate course or seminar. The material is relevant Analysis, more than doubling it with a new section of to anyone who is interested in analysis and geometry problems on complex analysis. The problems on real Analysis by Its History in nonsmooth settings. analysis from the earlier book have all been checked, More on www.springer.com/978-0-387-95104-1 and stylistic, typographical, and mathematical errors This book presents first-year calculus roughly in the have been corrected. The problems in complex analy- order in which it was first discovered. The first two Available sis cover most of the principal topics in the theory of chapters show how the ancient calculations of prac- functions of a complex variable. The problems in the tical problems led to infinite series, differential and 2001. X, 140 p. (Universitext, ) 978-0-387-95104-1 book cover, in real analysis: set algebra, measure and integral calculus and to differential equations. The topology, real- and complex-valued functions, and establishment of mathematical rigour for these sub- topological vector spaces; in complex analysis: poly- jects in the 19th century for one and several variables nomials and power series, functions holomorphic in a is treated in chapters III and IV. Many quotations are region, entire functions, analytic continuation, singu- included to give the flavor of the history. The text is larities, harmonic functions, families of functions, and complemented by a large number of examples, calcu- convexity theorems. lations and mathematical pictures and will provide More on www.springer.com/978-0-387-97766-9 Available 1992. X, 504 p. 18 illus. (Problem Books in Mathematics, ) 978-0-387-97766-9 88 Science springer.com

Science mathematics. —Zentralblatt MATH (Review of the original hardcover edition) More on www.springer.com/978-0-8176-4926-5 Available 1980. X, 248 p. 67 illus. (Modern Birkhäuser Classics, ) 978-0-8176-4926-5

Sequences, Series, Summability S. Lang Calculus of Several Variables This is a new, revised edition of this widely known P. Collet, J. Eckmann text. All of the basic topics in calculus of several variables are covered, including vectors, curves, functions Iterated Maps on the Interval as of several variables, gradient, tangent plane, max- Dynamical Systems ima and minima, potential functions, curve integrals, Green's theorem, multiple integrals, surface integrals, Iterations of continuous maps of an interval to itself Stokes' theorem, and the inverse mapping theorem serve as the simplest examples of models for dynam- and its consequences. The presentation is self-con- ical systems. These models present an interesting tained, assuming only a knowledge of basic calculus in mathematical structure going far beyond the simple one variable. Many completely worked-out problems equilibrium solutions one might expect. If, in addition, the dynamical system depends on an experimen- have been included. J. Korevaar tally controllable parameter, there is a corresponding More on www.springer.com/978-0-387-96405-8 mathematical structure revealing a great deal about Tauberian Theory Available interrelations between the behavior for different parameter values. This work explains some of the A Century of Developments 1987. XII, 636 p. 298 illus. (Undergraduate Texts in early results of this theory to mathematicians and the- Tauberian theory compares summability methods Mathematics, ) oretical physicists, with the additional hope of stim- for series and integrals, helps to decide when there is 978-0-387-96405-8 ulating experimentalists to look for more of these convergence, and provides asymptotic and remain- general phenomena of beautiful regularity, which der estimates. The author shows the development of oftentimes seem to appear near the much less under- the theory from the beginning and his expert com- stood chaotic systems. Although continuous maps of mentary evokes the excitement surrounding the C.C. Pugh an interval to itself seem to have been first introduced early results. He shows the fascination of the difficult to model biological systems, they can be found as Hardy-Littlewood theorems and of an unexpected Real Mathematical Analysis models in most natural sciences as well as economics. simple proof, and extolls Wiener's breakthrough Iterated Maps on the Interval as Dynamical Systems based on Fourier theory. There are the spectacu- In this new introduction to undergraduate real anal- is a classic reference used widely by researchers and lar "high-indices" theorems and Karamata's "regu- ysis the author takes a different approach from past graduate students in mathematics and physics, open- lar variation", which permeates probability theory. presentations of the subject, by stressing the impor- ing up some new perspectives on the study of dynam- The author presents Gelfand's elegant algebraic treat- tance of pictures in mathematics and hard problems. ical systems . This book is a thorough and readable ment of Wiener theory and his own distributional The exposition is informal and relaxed, with many introduction to some aspects of the theory of one- approach. There is also a new unified theory for Borel helpful asides, examples and occasional comments dimensional dynamical systems…The kneading cal- and "circle" methods. The text describes many Taube- from mathematicians such as Dieudonne, Littlewood, culus of Milnor—Thurston receives its most accessi- rian ways to the prime number theorem. A large bibli- and Osserman. This book is based on the honors ver- ble treatment to date in print…This is an important ography and a substantial index round out the book. sion of a course which the author has taught many and beautiful exposition, both as an orientation for More on www.springer.com/978-3-540-21058-0 times over the last 35 years at Berkeley. The book con- the reader unfamiliar with this theory and as a prelude tains an excellent selection of more than 500 exercises. to studying in greater depth some of the hard papers Available More on www.springer.com/978-0-387-95297-0 on the subject. —Mathematical Reviews (Review of 2004. XV, 483 p. (Grundlehren der mathematischen the original hardcover edition) This book provides a Wissenschaften, 329) Available good survey of recent developments in the study of 978-3-540-21058-0 the dynamics of smooth self-maps on the interval. 2002. XI, 437 p. 133 illus. (Undergraduate Texts in It…deals with a subject whose literature often appears Mathematics, ) in physics journals. This literature suffers in general 978-0-387-95297-0 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 springer.com Several Complex Variables and Analytic Spaces 89

Several Complex Variables and Some 500 references are cited, including many new results of the authors. Basic tools in this field (orthog- Analytic Spaces onal polynomials, moduli of smoothness, K-functionals, etc.) as well as some selected applications in numerical integration, integral equations, moment- preserving approximation and summation of slowly convergent series are also given. Beside the basic properties of the classical orthogonal polynomials the book provides new results on nonclassical orthogonal polynomials including methods for their numerical construction. More on www.springer.com/978-3-540-68346-9 J. Aubin, H. Frankowska Available 2008. XIV, 446 p. 42 illus. (Springer Monographs in Set-Valued Analysis Mathematics, ) 978-3-540-68346-9 "An elegantly written, introductory overview of the field, with a near perfect choice of what to include S. Kobayashi and what not, enlivened in places by historical tid- bits and made eminently readable throughout by crisp Hyperbolic Complex Space language. It has succeeded in doing the near-impossible—it has made a subject which is generally inhos- In the three decades since the introduction of the Systems Theory, Control pitable to nonspecialists because of its ‘family jargon’ Kobayashi distance, the subject of hyperbolic com- appear nonintimidating even to a beginning grad- plex spaces and holomorphic mappings has grown uate student." —The Journal of the Indian Institute to be a big industry. This book gives a comprehen- A.A. Agrachev, Y. Sachkov of Science "The book under review gives a compre- sive and systematic account on the Carathéodory and hensive treatment of basically everything in math- Kobayashi distances, hyperbolic complex spaces and Control Theory from the ematics that can be named multivalued/set-valued holomorphic mappings with geometric methods. A analysis. It includes…results with many historical very complete list of references should be useful for Geometric Viewpoint comments giving the reader a sound perspective to prospective researchers in this area. This book presents some facts and methods of Math- look at the subject…The book is highly recommended ematical Control Theory treated from the geomet- More on www.springer.com/978-3-540-63534-5 for mathematicians and graduate students who will ric viewpoint. It is devoted to finite-dimensional find here a very comprehensive treatment of set-val- Available deterministic control systems governed by smooth ued analysis." —Mathematical Reviews "I recommend 1998. XIII, 472 p. 8 illus. (Grundlehren der mathematischen ordinary differential equations. The problems of con- this book as one to dig into with considerable plea- Wissenschaften, 318) trollability, state and feedback equivalence, and opti- sure when one already knows the subject...'Set-Val- 978-3-540-63534-5 mal control are studied. Some of the topics treated by ued Analysis’ goes a long way toward providing a the authors are covered in monographic or textbook much needed basic resource on the subject." —Bul- literature for the first time while others are presented letin of the American Mathematical Society "This in a more general and flexible setting than elsewhere. book provides a thorough introduction to multivalued Although being fundamentally written for mathe- or set-valued analysis...Examples in many branches maticians, the authors make an attempt to reach both Special Functions of mathematics, given in the introduction, prevail the practitioner and the theoretician by blending the [upon] the reader the indispensability [of dealing] theory with applications. They maintain a good bal- with sequences of sets and set-valued maps…The style ance between the mathematical integrity of the text is lively and vigorous, the relevant historical com- and the conceptual simplicity that might be required ments and suggestive overviews increase the interest by engineers. It can be used as a text for graduate for this work...Graduate students and mathematicians courses and will become most valuable as a reference of every persuasion will welcome this unparalleled work for graduate students and researchers. guide to set-valued analysis." —Zentralblatt Math More on www.springer.com/978-3-540-21019-1 More on www.springer.com/978-0-8176-4847-3 Available Available 2004. XIV, 412 p. 35 illus. (Encyclopaedia of Mathematical 1990. XIX, 461 p. 11 illus. (Modern Birkhäuser Classics, ) Sciences, 87) 978-0-8176-4847-3 978-3-540-21019-1

G. Mastroianni, G. Milovanovic Interpolation Processes Basic Theory and Applications The classical books on interpolation address numerous negative results, i.e., results on divergent interpolation processes, usually constructed over some equidistant systems of nodes. The authors present, with complete proofs, recent results on convergent interpolation processes, for trigonometric and algebraic polynomials of one real variable, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. In this special, but fundamental and important field of real analysis the authors present the state of art. 90 Systems Theory, Control springer.com

première partie est consacrée à une introduction à control in quantum physics and the study of Lie semi- la mécanique céleste, et la seconde au contrôle des groups. The first half of the book is based upon matrix véhicules spatiaux. Un dernier chapitre concerne les analysis, introducing Lie algebras and the Camp- méthodes numériques dites indirectes, développées à bell-Baker-Hausdorff Theorem. Individual chapters partir des études des auteurs: méthode de tir et algo- are dedicated to topics such as discrete-time systems, rithmes de calcul des points conjugués. observability and realization, examples from science More on www.springer.com/978-3-540-28373-7 and engineering, linearization of nonlinear systems, and input-output analysis. Written by one of the lead- Available ing researchers in the field in a clear and comprehen- sible manner and laden with proofs, exercises and 2006. XIV, 276 p. 11 ill. (Mathématiques et Mathematica scripts, this involving text will be a vital Applications, 51) and thorough introduction to the subject for first- 978-3-540-28373-7 J. Aubin year graduate students of control theory. It will also be of great value to academics and researchers with Viability Theory an interest in matrix analysis, Lie algebra, and semigroups. This work examines viability theory and its applications to control theory and differential games. The More on www.springer.com/978-1-4020-9612-9 emphasis is on the construction of feedbacks and Available dynamical systems by myopic optimization meth- 2009. X, 281 p. 8 illus., 2 in color. (Applied Mathematical ods. Systems of first-order partial differential inclu- Sciences, 169) sions, whose solutions are feedbacks, are constructed 978-1-4020-9612-9 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 mathematicians, both pure and applied, this book offers specialists in control and nonlinear systems F. Bullo, A.D. Lewis tools to take into account general state constraints. Viability theory also allows researchers in other dis- Geometric Control of Mechanical ciplines—artificial intelligence, economics, game theory, theoretical biology, population genetics, cog- Systems nitive sciences—to go beyond deterministic mod- Modeling, Analysis, and Design for Simple els by studying them in a dynamical or evolutionary Mechanical Control Systems perspective in an uncertain environment. The book is a compendium of the state of knowledge about The area of analysis and control of mechanical sys- viability...Mathematically, the book should be acces- tems using differential geometry is flourishing. This T. Gross, H. Sayama sible to anyone who has had basic graduate courses book collects many results over the last decade and in modern analysis and functional analysis…The provides a comprehensive introduction to the area. Adaptive Networks concepts are defined and many proofs of the requi- More on www.springer.com/978-0-387-22195-3 Theory, Models and Applications site results are reproduced here, making the present Available book essentially self-contained. —Bulletin of the AMS With adaptive, complex networks, the evolution of Because of the wide scope, the book is an ideal ref- 2004. XVIII, 726 p. 102 illus. (Texts in Applied the network topology and the dynamical processes erence for people encountering problems related Mathematics, 49) on the network are equally important and often fun- to viability theory in their research…It gives a very 978-0-387-22195-3 damentally entangled. Recent research has shown thorough mathematical presentation. Very useful that such networks can exhibit a plethora of new phe- for anybody confronted with viability constraints. — nomena which are ultimately required to describe Mededelingen van het Wiskundig Genootschap many real-world networks. Some of those phenom- More on www.springer.com/978-0-8176-4909-8 ena include robust self-organization towards dynamical criticality, formation of complex global topologies Available based on simple, local rules, and the spontaneous 1992. XXVIII, 544 p. 10 illus. (Modern Birkhäuser Classics, ) division of "labor" in which an initially homogenous 978-0-8176-4909-8 population of network nodes self-organizes into func- tionally distinct classes. These are just a few. This book is a state-of-the-art survey of those unique net- B. Bonnard, L. Faubourg, E. Trélat works. In it, leading researchers set out to define the future scope and direction of some of the most Mécanique céleste et contrôle des advanced developments in the vast field of complex network science and its applications. véhicules spatiaux D. Elliott More on www.springer.com/978-3-642-01283-9 Le but de ce livre est de présenter les développements Available récents du contrôle géométrique orienté vers la com- Bilinear Control Systems mande (notamment optimale) des véhicules spati- Matrices in Action 2009. XIX, 332 p. 162 illus., 15 in color. (Understanding aux. Il est principalement destiné aux étudiants de Complex Systems, ) A control system is called bilinear if it is described 978-3-642-01283-9 3e cycle et aux chercheurs, et son contenu a servi de by linear differential equations in which the con- base à une série de cours de contrôle et d'automatique trol inputs appear as coefficients. The study of bilin- enseignés à des étudiants de 3e cycle. Il s'appuie sur ear control systems began in the 1960s and has since des projets de recherche avec l'ESTEC et le CNES, developed into a fascinating field, vital for the solu- sur le contrôle d'attitude d'un satellite, le problème tion of many challenging practical control problems. de transfert orbital en temps minimal, et le problème Its methods and applications cross inter-disciplinary de rentrée atmosphérique d'une navette spatiale. Une boundaries, proving useful in areas as diverse as spin springer.com Topological Groups, Lie Groups 91

algebra and analysis. Although the formal prerequisites are kept as low level as possible, the subject matter is sophisticated and contains many of the key themes of the fully developed theory, preparing students for a more standard and abstract course in Lie theory and differential geometry. More on www.springer.com/978-1-85233-470-3 Available

2002. XI, 330 p. 16 illus. (Springer Undergraduate Mathematics Series, ) 978-1-85233-470-3 N.V. Krylov M. Krstic Delay Compensation for Controlled Diffusion Processes Nonlinear, Adaptive, and PDE This book deals with the optimal control of solutions of fully observable Itô-type stochastic differen- Systems tial equations. The validity of the Bellman differential equation for payoff functions is proved and rules Some of the most common dynamic phenomena for optimal control strategies are developed. Topics that arise in engineering practice—actuator and sen- include optimal stopping; one dimensional controlled sor delays—fall outside the scope of standard finite- diffusion; the Lp-estimates of stochastic integral dis- dimensional system theory. The first attempt at infi- tributions; the existence theorem for stochastic equa- nite-dimensional feedback design in the field of con- tions; the Itô formula for functions; and the Bellman trol systems—the Smith predictor—has remained principle, equation, and normalized equation. limited to linear finite-dimensional plants over the last five decades. Shedding light on new opportunities More on www.springer.com/978-3-540-70913-8 A. Bjorner, F. Brenti in predictor feedback, this book significantly broad- Available ens the set of techniques available to a mathematician 2009. XII, 310 p. (Stochastic Modelling and Applied Combinatorics of Coxeter Groups or engineer working on delay systems. The book is a Probability, 14) collection of tools and techniques that make predictor 978-3-540-70913-8 Includes a rich variety of exercises to accompany the feedback ideas applicable to nonlinear systems, sys- exposition of Coxeter groups Coxeter groups have tems modeled by PDEs, systems with highly uncer- already been exposited from algebraic and geometric tain or completely unknown input/output delays, and perspectives, but this book will be presenting the com- systems whose actuator or sensor dynamics are mod- binatorial aspects of Coxeter groups eled by more general hyperbolic or parabolic PDEs, Topological Groups, Lie Groups rather than by pure delay. Specific features and topics More on www.springer.com/978-3-540-44238-7 include: * A construction of explicit Lyapunov func- Available tionals, which can be used in control design or stability analysis, leading to a resolution of several long- 2005. XIV, 370 p. 81 illus. (Graduate Texts in standing problems in predictor feedback. * A detailed Mathematics, 231) treatment of individual classes of problems—non- 978-3-540-44238-7 linear ODEs, parabolic PDEs, first-order hyperbolic PDEs, second-order hyperbolic PDEs, known time- varying delays, unknown constant delays—will help the reader master the techniques presented. * Numer- ous examples ease a student new to delay systems into the topic. * Minimal prerequisites: the basics of function spaces and Lyapunov theory for ODEs. * The basics of Poincaré and Agmon inequalities, Lyapunov A. Baker and input-to-state stability, parameter projection for adaptive control, and Bessel functions are sum- Matrix Groups marized in appendices for the reader’s convenience. Delay Compensation for Nonlinear, Adaptive, and An Introduction to Lie Group Theory PDE Systems is an excellent reference for graduate Aimed at advanced undergraduate and beginning students, researchers, and practitioners in mathemat- graduate students, this book provides a first taste of ics, systems control, as well as chemical, mechanical, the theory of Lie groups as an appetiser for a more A. Borel, L. Ji electrical, computer, aerospace, and civil/structural substantial further course. Lie theoretic ideas lie at engineering. Parts of the book may be used in gradu- the heart of much of standard undergraduate linear Compactifications of Symmetric ate courses on general distributed parameter systems, algebra and exposure to them can inform or motivate linear delay systems, PDEs, nonlinear control, state the study of the latter.The main focus is on matrix and Locally Symmetric Spaces estimator and observers, adaptive control, robust con- groups, i.e., closed subgroups of real and complex Noncompact symmetric and locally symmetric spaces trol, or linear time-varying systems. general linear groups. The first part studies exam- naturally appear in many mathematical theories, More on www.springer.com/978-0-8176-4876-3 ples and describes the classical families of simply including analysis (representation theory, nonabelian connected compact groups. The second part intro- Available harmonic analysis), number theory (automorphic duces the idea of a lie group and studies the asso- forms), algebraic geometry (modulae) and algebraic 2009. XIV, 468 p. 52 illus. (Systems & Control: Foundations & ciated notion of a homogeneous space using orbits topology (cohomology of discrete groups). In most Applications, ) of smooth actions.Throughout, the emphasis is on applications it is necessary to form an appropriate 978-0-8176-4876-3 providing an approach that is accessible to readers compactification of the space. The literature dealing equipped with a standard undergraduate toolkit of with such compactifications is vast. The main purpose 92 Topological Groups, Lie Groups springer.com of this book is to introduce uniform constructions of ily learn the necessary algebra (which is clearly sum- related areas, it is essentially self-contained and there- most of the known compactifications with empha- marized) but wants to see the topology done in detail. fore is also of great interest for advanced students. Apart from the introductory material, most of the sis on their geometric and topological structures. The More on www.springer.com/978-3-540-12179-4 book is divided into three parts. Part I studies com- mathematics presented here has not appeared in book pactifications of Riemannian symmetric spaces and form before. Available 1991. X, 388 p. 14 illus. (Ergebnisse der Mathematik und their arithmetic quotients. Part II is a study of com- More on www.springer.com/978-0-387-74611-1 pact smooth manifolds. Part III studies the compacti- ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in fication of locally symmetric spaces. Familiarity with Available Mathematics, 17) the theory of semisimple Lie groups is assumed, as 978-3-540-12179-4 is familiarity with algebraic groups defined over the 2008. XVI, 473 p. 41 illus. (Graduate Texts in rational numbers in later parts of the book, although Mathematics, 243) 978-0-387-74611-1 most of the pertinent material is recalled as presented. Otherwise, the book is a self-contained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and B. Khesin, R. Wendt representation theory to diverse fields of mathematics. The Geometry of Infinite- More on www.springer.com/978-0-8176-3247-2 Available Dimensional Groups 2006. XIII, 479 p. (Mathematics: Theory & Applications, ) This monograph gives an overview of various classes 978-0-8176-3247-2 of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. While infinite-dimensional groups often exhibit very M.R. Sepanski peculiar features, this book describes unifying geometric ideas of the theory and gives numerous illus- Compact Lie Groups trations and examples, ranging from the classification of the Virasoro coadjoint orbits to knot theory, from Blending algebra, analysis, and topology, the study of optimal mass transport to moduli spaces of flat con- compact Lie groups is one of the most beautiful areas nections on surfaces. The text includes many exer- of mathematics and a key stepping stone to the the- cises and open questions, and it is accessible to both ory of general Lie groups. Assuming no prior knowl- students and researchers in Lie theory, geometry, and edge of Lie groups, this book covers the structure and Hamiltonian systems. representation theory of compact Lie groups. Cov- erage includes the construction of the Spin groups, More on www.springer.com/978-3-540-77262-0 Schur Orthogonality, the Peter-Weyl Theorem, the Available Plancherel Theorem, the Maximal Torus Theorem, R. Geoghegan 2009. XII, 304 p. (Ergebnisse der Mathematik und ihrer the Commutator Theorem, the Weyl Integration and Grenzgebiete. 3. Folge A Series of Modern Surveys in Character Formulas, the Highest Weight Classifica- Topological Methods in Group Mathematics, 51) tion, and the Borel-Weil Theorem. The book develops 978-3-540-77262-0 the necessary Lie algebra theory with a streamlined Theory approach focusing on linear Lie groups. Topological Methods in Group Theory is about the More on www.springer.com/978-0-387-30263-8 interplay between algebraic topology and the the- G.A. Margulis Available ory of infinite discrete groups. The author has kept three kinds of readers in mind: graduate students who Discrete Subgroups of Semisimple 2007. XII, 198 p. (Graduate Texts in Mathematics, have had an introductory course in algebraic topol- Lie Groups 235) ogy and who need a bridge from common knowl- 978-0-387-30263-8 edge to the current research literature in geometric, Discrete subgroups have played a central role combinatorial and homological group theory; group throughout the development of numerous mathemat- theorists who would like to know more about the ical disciplines. Discontinuous group actions and the topological side of their subject but who have been study of fundamental regions are of utmost impor- too long away from topology; and manifold topol- tance to modern geometry. Flows and dynamical ogists, both high- and low-dimensional, since the systems on homogeneous spaces have found a wide book contains much basic material on proper homo- range of applications, and of course number theory topy and locally finite homology not easily found without discrete groups is unthinkable. This book, J. Stillwell elsewhere. The book focuses on two main themes: 1. written by a master of the subject, is primarily devoted Topological Finiteness Properties of groups (general- to discrete subgroups of finite covolume in semi-sim- Classical Topology and izing the classical notions of "finitely generated" and ple Lie groups. Since the notion of "Lie group" is suffi- Combinatorial Group Theory "finitely presented"); 2. Asymptotic Aspects of Infinite ciently general, the author not only proves results in Groups (generalizing the classical notion of "the num- the classical geometry setting, but also obtains theo- This is a well-balanced introduction to topology that ber of ends of a group"). Illustrative examples treated rems of an algebraic nature, e.g. classification results stresses geometric aspects. Focusing on historical in some detail include: Bass-Serre theory, Coxeter on abstract homomorphisms of semi-simple alge- background and visual interpretation of results, it groups, Thompson groups, Whitehead's contractible braic groups over global fields. The treatise of course emphasizes spaces with few dimensions, where visu- 3-manifold, Davis's exotic contractible manifolds in contains a presentation of the author's fundamental alization is possible, and interaction with combinato- dimensions greater than three, the Bestvina-Brady rigidity and arithmeticity theorems. The work in this rial group theory via the fundamental group. It also Theorem, and the Bieri-Neumann-Strebel invariant. monograph requires the language and basic results present algorithms for topological problems. Most of The book also includes a highly geometrical treat- from fields such as algebraic groups, ergodic theory, the results and proofs are known, but some have been ment of Poincaré duality (via cells and dual cells) to the theory of unitary representatons, and the theory of simplified or placed in a new perspective. Over 300 bring out the topological meaning of Poincaré duality amenable groups. The author develops the necessary illustrations, many interesting exercises, and challeng- groups. To keep the length reasonable and the focus material from these subjects; so that, while the book ing open problems are included. New in this edition is clear, it is assumed that the reader knows or can eas- is of obvious importance for researchers working in a chapter on unsolvable problems, which includes the springer.com Topology 93 first textbook proof that the main problem of topol- Topology uate students and researchers in mathematics and ogy, the homeomorphism problem, is unsolvable. physics. More on www.springer.com/978-0-387-97970-0 More on www.springer.com/978-3-540-21040-5 Available Available 2004. XIII, 213 p. (Encyclopaedia of Mathematical Sciences, 1993. XII, 334 p. 312 illus. (Graduate Texts in 142) Mathematics, 72) 978-3-540-21040-5 978-0-387-97970-0

M. Banagl Topological Invariants of Stratified Spaces The central theme of this book is the restoration of Poincaré duality on stratified singular spaces by using J. Stillwell Verdier-self-dual sheaves such as the prototypical A. Granas, J. Dugundji intersection chain sheaf on a complex variety. After Naive Lie Theory carefully introducing sheaf theory, derived categories, Fixed Point Theory Verdier duality, stratification theories, intersection In this new textbook, acclaimed author John Stillwell "Granas-Dugundji's book is an encyclopedic sur- homology, t-structures and perverse sheaves, the ulti- presents a lucid introduction to Lie theory suitable vey of the classical fixed point theory of continuous mate objective is to explain the construction as well for junior and senior level undergraduates. In order mappings (the work of Poincaré, Brouwer, Lef- as algebraic and geometric properties of invariants to achieve this, he focuses on the so-called "classical schetz-Hopf, Leray-Schauder) and all its various mod- such as the signature and characteristic classes effec- groups'' that capture the symmetries of real, complex, ern extensions. This is certainly the most learned tuated by self-dual sheaves. Highlights never before and quaternion spaces. These symmetry groups may book ever likely to be published on this subject." -Felix presented in book form include complete and very be represented by matrices, which allows them to be Browder, Rutgers University "The theory of Fixed detailed proofs of decomposition theorems for self- studied by elementary methods from calculus and lin- Points is one of the most powerful tools of modern dual sheaves, explanation of methods for comput- ear algebra. This naive approach to Lie theory is orig- mathematics. Not only is it used on a daily basis in ing twisted characteristic classes and an introduc- inally due to von Neumann, and it is now possible to pure and applied mathematics, but it also serves as a tion to the author's theory of non-Witt spaces and streamline it by using standard results of undergradu- bridge between Analysis and Topology, and provides Lagrangian structures. ate mathematics. To compensate for the limitations of a very fruitful area of interaction between the two. the naive approach, end of chapter discussions intro- More on www.springer.com/978-3-540-38585-1 This book contains a clear, detailed and well-orga- duce important results beyond those proved in the Available nized presentation of the major results, together with book, as part of an informal sketch of Lie theory and an entertaining set of historical notes and an exten- 2007. XII, 259 p. 14 illus. (Springer Monographs in its history. John Stillwell is Professor of Mathematics sive bibliography describing further developments at the University of San Francisco. He is the author of Mathematics, ) 978-3-540-38585-1 and applications." -Haïm Brézis, Université Pierre et several highly regarded books published by Springer, Marie Curie "In this monograph, no effort has been including The Four Pillars of Geometry (2005), Ele- spared, even to the smallest detail, be it mathemat- ments of Number Theory (2003), Mathematics and Its ical, historical or bibliographical. In particular, the History (Second Edition, 2002), Numbers and Geom- S. Carter, S. Kamada, M. Saito necessary background materials are generously pro- etry (1998) and Elements of Algebra (1994). vided for non-specialists. In fact, the book could even More on www.springer.com/978-0-387-78214-0 Surfaces in 4-Space serve as an introduction to algebraic topology among Available Surfaces in 4-Space, written by leading specialists others. It is certain that the book will be a standard in the field, discusses knotted surfaces in 4-dimen- work on Fixed Point Theory for many years to come." 2008. XIII, 218 p. 25 illus. (Undergraduate Texts in sional space and surveys many of the known results -Isaac Namioka, University of Washington This Mathematics, ) in the area. Results on knotted surface diagrams, con- monograph gives a carefully worked out account of 978-0-387-78214-0 structions of knotted surfaces, classically defined the most basic principles and applications of the the- invariants, and new invariants defined via quandle ory of fixed points. Until now, a treatment of many homology theory are presented. The last chapter com- of the discussed topics has been unavailable in book prises many recent results, and techniques for com- form. The presentation is self-contained and is acces- putation are presented. New tables of quandles with sible to a broad spectrum of readers. The main text is a few elements and the homology groups thereof are complemented by numerous exercises, detailed com- included. This book contains many new illustrations ments, and a comprehensive bibliography. Andrzej of knotted surface diagrams. The reader of the book Granas studied in Warsaw and then Moscow, where will become intimately aware of the subtleties in going he earned his Ph.D. in 1958 under Lazar Lusternik. from the classical case of knotted circles in 3-space to Since 1958, he has held various research and teaching this higher dimensional case. As a survey, the book posts in Poland, USA, Canada and elsewhere. During is a guide book to the extensive literature on knotted the Spring of 1970, he occupied a special chair at the surfaces and will become a useful reference for grad- Collège de France. In the early nineties, Dr. Granas founded and edited the journal Topological Methods of Nonlinear Analysis, and since 1992, he has served on the editorial board of the Zentralblatt. He is an Honorary Member of the Gdansk Scientific Society. The first part of this book is based on "Fixed Point 94 Visualization springer.com

Theory I" which was published by PWN, Warsaw in R. Gamkrelidze, S.K. Lando, V. Vassiliev, A.K. Zvonkin students and researchers". R. Piergallini, Zentralblatt 1982. The second part follows the outline conceived für Mathematik 1048 (2004) For this 2nd edition, new by Andrzej Granas and the late James Dugundji. Graphs on Surfaces and Their results, new proofs, and commentaries for a better orientation of the reader have been added. More on www.springer.com/978-0-387-00173-9 Applications More on www.springer.com/978-3-540-45898-2 Available Graphs drawn on two-dimensional surfaces have 2003. XVI, 696 p. 13 illus. (Springer Monographs in always attracted researchers by their beauty and by Available Mathematics, ) the variety of difficult questions to which they give 978-0-387-00173-9 rise. The theory of such embedded graphs, which long 2007. XIV, 492 p. 264 illus. (Algorithms and Computation in Mathematics, 9) seemed rather isolated, has witnessed the appearance 978-3-540-45898-2 of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group Visualization action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous fig- M. Kapovich ures, examples (including computer calculations) and exercises, and should appeal to both graduate students Hyperbolic Manifolds and and researchers. Discrete Groups More on www.springer.com/978-3-540-00203-1 Available This classic book is at the crossroads of several branches of mathematics: hyperbolic geometry, dis- 2004. XVI, 456 p. (Encyclopaedia of Mathematical Sciences, G. Farin, D. Hansford crete groups, 3-dimensional topology, geometric 141) 978-3-540-00203-1 group theory, and complex analysis. The main focus throughout the text is on Thurston’s hyperbolization Lineare Algebra: Ein theorem, one of the central results of 3-dimensional geometrischer Zugang topology that has completely changed the landscape Dieses Buch bietet Studenten mit Nebenfach Mathe- of the field. The book contains a number of open matik eine praktische Einführung in die lineare Alge- problems and conjectures related to the hyperboliza- bra. Großer Wert wird auf geometrische Erklärungen tion theorem as well as rich discussions on related und numerische Anwendungen gelegt. Zahlreiche topics including geometric structures on 3-manifolds, Beispiele bringen Praxisnähe; auf detaillierte Beweise higher dimensional negatively curved manifolds, and wird verzichtet. Beide Autoren sind Experten auf dem hyperbolic groups. Featuring beautiful illustrations, Gebiet des computergestützten Modellierens; viele a rich set of examples, numerous exercises, and an Anwendungen kommen aus diesem Gebiet. extensive bibliography and index, Hyperbolic Man- ifolds and Discrete Groups continues to serve as an More on www.springer.com/978-3-540-41854-2 ideal graduate text and comprehensive reference. The Available book is very clearly written and fairly self-contained. S. Matveev It will be useful to researchers and advanced gradu- 2003. XIV, 322 S. (Springer-Lehrbuch, ) ate students in the field and can serve as an ideal guide 978-3-540-41854-2 to Thurston's work and its recent developments. --- Algorithmic Topology and Mathematical Reviews Beyond the hyperbolization Classification of 3-Manifolds theorem, this is an important book which had to be written; some parts are still technical and will cer- From the reviews of the 1st edition: "This book pro- tainly be streamlined and shortened in the next years, vides a comprehensive and detailed account of dif- but together with Otal's work a complete published ferent topics in algorithmic 3-dimensional topology, proof of the hyperbolization theorem is finally avail- culminating with the recognition procedure for able. Apart from the proof itself, the book contains a Haken manifolds and including the up-to-date results lot of material which will be useful for various other in computer enumeration of 3-manifolds. Originat- directions of research. ---Zentralbatt MATH This ing from lecture notes of various courses given by the book can act as source material for a postgraduate author over a decade, the book is intended to com- course and as a reference text on the topic as the ref- bine the pedagogical approach of a graduate textbook erences are full and extensive. ... The text is self-con- (without exercises) with the completeness and reli- tained and very well illustrated. ---ASLIB Book Guide ability of a research monograph… All the material, with few exceptions, is presented from the peculiar More on www.springer.com/978-0-8176-4912-8 L.d. Floriani, M. Spagnuolo point of view of special polyhedra and special spines Available of 3-manifolds. This choice contributes to keep the 2001. XXVIII, 468 p. 78 illus. (Modern Birkhäuser Classics, ) level of the exposition really elementary. In conclu- Shape Analysis and Structuring 978-0-8176-4912-8 sion, the reviewer subscribes to the quotation from Several techniques have been developed in the litera- the back cover: "the book fills a gap in the existing lit- ture for processing different aspects of the geometry erature and will become a standard reference for algo- of shapes, for representing and manipulating a shape rithmic 3-dimensional topology both for graduate at different levels of detail, and for describing a shape springer.com Visualization 95 at a structural level as a concise, part-based, or iconic model. Such techniques are used in many different contexts, such as industrial design, biomedical applications, entertainment, environmental monitoring, or cultural heritage. This book covers a variety of topics related to preserving and enhancing shape information at a geometric level, and to effectively capturing the structure of a shape by identifying relevant shape components and their mutual relationships. More on www.springer.com/978-3-540-33264-0 Available 2008. XVI, 296 p. 185 illus., 29 in color. (Mathematics and Visualization, ) 978-3-540-33264-0

L. Younes Invariance, déformations et reconnaissance de formes Cet ouvrage introduit un certain nombre de techniques disponibles pour la reconnaissance de formes planes, en mettant l'accent sur l'importance de la prise en compte des deux notions essentielles que sont l'invariance et l'analyse des déformations. En con- ciliant autant qu'il se peut les aspects théoriques fondamentaux et les techniques algorithmiques réalistes, il revisite les différentes méthodes de représentation de formes, allant des représentations paramétriques invariantes aux axes médians, décrit, sous un éclairage original un certain nombre de techniques de détection de formes, et développe des résultats récents sur l'analyse des déformations et la mise en correspon- dance de formes et d'images. Il est susceptible de servir à la fois de référence pour le chercheur que d'ouvrage d'introduction à la théorie pour l'étudiant de troisième cycle. More on www.springer.com/978-3-540-40868-0 Available

2004. XVII, 248 p. (Mathématiques et Applications, 44) 978-3-540-40868-0