springer.com/booksellers Springer News 11/12/2008 Mathematics 37
V. Adamyan, Y. Berezansky, I. Gohberg, V. Adamyan, Y. Berezansky, I. Gohberg, V. Adamyan (Ed.) M. L. Gorbachuk, V. Gorbachuk, A. N. Kochubei, M. L. Gorbachuk, V. Gorbachuk, A. N. Kochubei, H. Langer, G. Popov (Eds.) H. Langer,G. Popov (Eds.) Modern Analysis and Modern Analysis and Modern Analysis and Applications Applications Applications The Mark Krein Centenary Conference The Mark Krein Centenary Conference – The Mark Krein Centenary Conference – Volume 1 Volume 2 These two volumes contain peer-reviewed research and survey papers based on invited talks at the This is the first of two volumes containing peer- This is the second of two volumes containing International Conference on Modern Analysis reviewed research and survey papers based on peer-reviewed research and survey papers based and Applications. The conference, which was invited talks at the International Conference on on invited talks at the International Confer- dedicated to the 100th anniversary of the birth of Modern Analysis and Applications. The confer- ence on Modern Analysis and Applications. The Mark Krein, one of the greatest mathematicians ence, which was dedicated to the 100th anni- conference, which was dedicated to the 100th of the 20th century, was held in Odessa, Ukraine, versary of the birth of Mark Krein, one of the anniversary of the birth of Mark Krein, one of the on April 9-14, 2007. The papers describe the greatest mathematicians of the 20th century, was greatest mathematicians of the 20th century, was contemporary development of subjects influenced held in Odessa, Ukraine, on April 9-14, 2007. The held in Odessa, Ukraine, on April 9-14, 2007. The by Krein, such as the theory of operators in Hilbert papers describe the contemporary development of papers describe the contemporary development of and Krein spaces, differential operators, applica- subjects influenced by Krein, such as the theory of subjects influenced by Krein, such as the theory of tions of functional analysis in function theory, operators in Hilbert and Krein spaces, differential operators in Hilbert and Krein spaces, differential theory of networks and systems, mathematical operators, applications of functional analysis in operators, applications of functional analysis in physics and mechanics. function theory, theory of networks and systems, function theory, theory of networks and systems, mathematical physics and mechanics. mathematical physics and mechanics. Features 7 Wide panorama of the development of func- Features Features tional analysis, operator theory, and their applica- 7 Wide panorama of the development of func- 7 Wide panorama of the development of func- tions 7 Many contributions by active members of tional analysis, operator theory, and their applica- tional analysis, operator theory, and their applica- scientific schools founded by Mark Krein tions 7 Many contributions by active members of tions 7 Many contributions by active members of scientific schools founded by Mark Krein scientific schools founded by Mark Krein Fields of interest Analysis; Operator Theory; Functional Analysis Fields of interest Fields of interest Analysis; Operator Theory; Functional Analysis Analysis; Operator Theory; Functional Analysis Target groups Researchers in operator theory, functional analysis, Target groups Target groups and integral equations Researchers in operator theory, functional analysis, Researchers in operator theory, functional analysis, and integral equations and integral equations Type of publication Commemorative publication Type of publication Type of publication Commemorative publication Commemorative publication
Mathematics Mathematics Mathematics
Due April 2009 Due April 2009 Due April 2009
2009. Approx. 500 p. (Operator Theory) Hardcover 2009. Approx. 500 p. (Operator Theory) Hardcover 2009. Approx. 1000 p. (2-volume-set) (Operator Theory) 7 € 169,00 | £133.50 7 € 169,00 | £133.50 7 € 299,00 | £236.50 9
A. Andrianov, Russian Academy of the Sciences, S. Barwick, University of Adelaide, SA, Australia; D. J. Bernstein, J. Buchmann, E. Dahmen (Eds.) St. Petersburg, Russia G. Ebert, University of Delaware, Newark, DE, USA Post Quantum Cryptography Introduction to Siegel Unitals in Projective Planes Modular Forms and Dirichlet Series Quantum computers will break today’s most This book is a monograph on unitals embedded in popular public-key cryptographic systems, finite projective planes. Unitals are key structures including RSA, DSA, and ECDSA. This book This is intended for a graduate course on Siegel in projective planes, and have connections with introduces the reader to the next generation of modular forms, Hecke operators, and related zeta other structures in algebra. They play a signifi- cryptographic algorithms, the systems that resist functions. The author’s aim is to present a concise cant role in the classification of finite planes and quantum-computer attacks: in particular, post- and self-contained introduction to an important provide a link between groups and geometries. quantum public-key encryption systems and post- and developing area of number theory that will There is a considerable number of research articles quantum public-key signature systems. serve to attract young researchers to this beautiful about unitals, and there also exist many open Leading experts have joined forces for the first field. problems. This book is a thorough survey of the time to explain the state of the art in quantum Topics include: -analytical properties of radial research literature on embedded unitals which computing, hash-based cryptography, code-based Dirichlet series attached to modular forms of collects this material in book form for the first cryptography, lattice-based cryptography, and genuses 1 and 2; - the abstract theory of Hecke– time. The book is aimed at graduate students and multivariate cryptography. Mathematical founda- Shimura rings for symplectic and related groups; researchers who want to learn about this topic tions and implementation issues are included. -action of Hecke operators on Siegel modular without reading all the original articles. This book is an essential resource for students and forms; -applications of Hecke operators to a study The primary proof techniques used involve linear researchers who want to contribute to the field of of multiplicative properties of Fourier coeffi- algebraic arguments, finite field arithmetic, some post-quantum cryptography. cients of modular forms; -Hecke zeta functions of elementary number theory, and combinatorial modular forms in one variable and to spinor (or enumeration. Some computer results not previ- Features Andrianov) zeta functions of Siegel modular forms ously found in the literature also are mentioned in 7 Contributors to the book take on the big chal- of genus two; -the proof of analytical continuation the text. lenge in cryptography, namely: what to do when and functional equation (under certain assump- someone will break the crypto-systems of today tions) for Euler products associated with modular Features forms of genus two. 7 No other book on unitals, book will fill that Fields of interest void 7 Text is clear and easy to follow 7 Book is Number Theory; Data Encryption; Mathematics of Features well-structured and comprehensive with excellent Computing 7 Will become a standard reference on the subject diagrams 7 Intended for graduate students and keeps Target groups prerequisites to a minimum 7 Gives provocative Contents Cryptologists in mathematics, computer science, examples in the simplest and most accessible terms Preface.- Preliminaries.- Hermitian curves and engineering, and industry 7 Author is an expert who has originated many unitals.- Translation planes.- Unitals embedded important ideas in the subject in desarguesian planes.- Unitals embedded in Type of publication non-desarguesian planes.- Combinatorial ques- Contributed volume Contents tions and associated configurations.- Character- Preface.- Introduction: The Two Features ization results.- Open problems.- Nomenclature of Arithmetical Zeta Functions.- Modular of unitals.- Group theoretic characterizations of Forms.- Dirichlet Series of Modular Forms.- unitals.- References.- Notation index.- Index. Hecke-Shimura Rings of Double Cosets.- Hecke Operators.- Euler Factorization of Radial Series.- Fields of interest Conclusion: Other Groups, Other Horizons.- Geometry; Combinatorics; Algebra Notes.- Short Bibliography.- Target groups Fields of interest Graduate students and researchers Number Theory; Algebra Type of publication Target groups Monograph Graduate students, researchers
Type of publication Graduate/Advanced undergraduate textbook
Mathematics Mathematics Mathematics Due December 2008 Due December 2008 Due December 2008 2009. XII, 196 p. 29 illus. (Springer Monographs in 2009. Approx. 210 p. (Universitext) Softcover Mathematics) Hardcover 2009. XII, 245 p. Hardcover 7 € 42,95 | £32.50 7 € 54,95 | £43.99 7 approx. € 59,95 | £47.99 9
L. A. Bokut, E. Zelmanov, I. Shestakov, V. Latyshev W. J. Cook, L. Lovász, J. Vygen (Eds.) A. Deitmar, University of Tübingen, Germany; (Eds.) S. Echterhoff, University of Muenster, Germany Research Trends in Selected Works of Combinatorial Optimization Principles of Harmonic A.I. Shirshov Bonn Workshop 2008 Analysis
Translated by: M. Bremner, M. Kotchetov The book is written for graduate students who This book, written by leading experts in combina- have read the first book and like to see the proofs This book presents translations of selected works torial optimization, features in-depth surveys of which were not given there and/or want to see the of the famous Russian mathematician A.I. Shirshov current research areas in combinatorial optimi- full extent of the theory. On the other hand it can (1921-1981). He was a pioneer in several direc- zation in the broad sense, ranging from applied be read independently from the first one, only a tions of associative, Lie, Jordan, and alternative graph theory to mathematical programming. It modest knowledge on Fourier series/tranform is algebras, as well as groups and projective planes. also contains numerous new results and shows required to understand the examples. His name is associated with notions and results many interesting current research directions. This This book fills a major gap in the textbook on Gröbner-Shirshov bases, the Composition- book will be indispensible for any researcher in literature, as a full proof of Pontryagin Duality Diamond Lemma, the Shirshov-Witt Theorem, the combinatorial optimization. and Plancherel Theorem is hard to come by. It is Lazard-Shirshov elimination process, Shirshov’s usually given in books that focus on C*-algebras Height Theorem, Lyndon-Shirshov words, Hall- Fields of interest and thus carry too much technical overload for Shirshov bases, Shirshov’s theorem on the Kurosh Operations Research, Mathematical Programming; the reader who only wants these basic results of problem for alternative algebras, Shirshov’s Computational Mathematics and Numerical Anal- Harmonic Analysis. Other proofs use the structure theorem on Jordan algebras with two generators. ysis; Discrete Mathematics in Computer Science theory which carries the reader away in a different Shirshov’s ideas were used by his student Efim direction. Here the authors consider the Banach- Zelmanov for the solution of the Restricted Burn- Target groups algebra approach more elegant and enlighting. side Problem. Several famous algebraists provide Mathematicians, computer scientists, graduate They provide a streamlined approach that reaches a detailed comment on the impact of Shirshov’s students and researchers in operations research the main results directly, and they also give the work on current algebra. generalizations to the non-Abelian case. Type of publication Features Contributed volume Features 7 English translations of Shirshov’s works, 7 Contains material unavailable elsewhere, which were published only in Russian 7 Due including the full proof of Pontryagin Duality and to Shirshov’s future leading and unique handling the Plancherel Theorem 7 Authors emphasize of algebraic problems, the results are still of high Banach algebras as the cleanest way to get many interest for current research in algebra fundamental results in harmonic analysis 7 Gentle pace, clear exposition, and clean proofs Fields of interest Mathematics, general; History of Mathematics Contents Preface.- Haar Integration.- Banach Algebras.- Target groups Duality for Abelian Groups.- The Structure of Specialists and graduate students in algebra and LCA-Groups.- Operators on Hilbert Spaces.- computer algebra Representations.- Compact Groups.- Direct Integrals.- The Selberg Trace Formula.- The Type of publication Heisenberg Group.- SL2(R).- Wavelets.- Topology.- Collected works Measure and Integration.- Functional Analysis.- Bibliography.- Index.
Fields of interest Abstract Harmonic Analysis; Fourier Analysis
Target groups Graduate students and researchers
Type of publication Graduate/Advanced undergraduate textbook
Mathematics Mathematics Mathematics Due April 2009 Due November 2008 Due February 2009 2009. Approx. 250 p. (Contemporary Mathematicians) Hardcover 2009. XVIII, 562 p. 79 illus. Hardcover 2009. Approx. 345 p. (Universitext) Softcover 7 € 129,00 | £102.00 7 € 89,95 | £71.00 7 € 34,95 | £27.99 9
A. L. Dontchev, Ann Arbor, MI, USA; R. T. Rockafeller, M. Emmer, Università “La Sapienza”, Roma, Italia (Ed.) S. Fournais, University of Aarhus, Denmark; University of Washington, Seattle, WA, USA B. Helffer, Université Paris-Sud and CNRS, France Mathematics and Culture VI Implicit Functions and Spectral Methods in Surface Solution Mappings Superconductivity The latest in the series Mathematics and Culture probes the interplay between mathematics and The book is about the implicit function paradigm the worlds of art, cinema, theatre and history, These two expert researchers in the field present a in the classical framework and beyond, focusing medicine, biology and aeronautics. Series Editor comprehensive treatment of key results concerning largely on properties of solution mappings of Michele Emmer has chosen a new collection of the Ginzburg-Landau (GL) functional. Spectral variational problems. essays illuminating these connections in surprising Methods in Surface Superconductivity examines The purpose of this self-contained work is to and fascinating ways. in detail the two- and three-dimensional cases of provide a reference on the topic and to provide a Mathematics and Culture VI includes: the GL functional as they pertain to supercon- unified collection of a number of results which are An homage to the artist Mario Merz, whose work ductivity. Also, instances of large GL parameter currently scattered throughout the literature. The depicted numbers derived from the Fibonacci in kappa are covered, and a variety of exercises and first chapter of the book treats the classical implicit curving neon arrays open problems are discussed to further the readers function theorem in a way that will be useful for Essays on the relationships of mathematics with understanding of the material. The authors have students and teachers of undergraduate calculus. video and cinema; the complex connections provided a great introduction to the applications of The remaining part becomes gradually more between mathematics and psychoanalysis and the partial differential equations and spectral theory. advanced, and considers implicit mappings defined frontiers of applied mathematics by relations other than equations, e.g., variational Chapters on Mathematics and Cartoon; Math- Features problems. Applications to numerical analysis and ematics and Art; Mathematics and Cinema and 7 Covers groundbreaking results in the fast optimization are also provided. Mathematics and Wine and the journeys of Marco growing field of superconductivity 7 Provides The implicit function theorem is one of the most Polo and the Venice he left and came home to. a concrete introduction to PDEs and spectral important theorems in analysis and its many vari- methods 7 Covers both two and three dimen- ants are basic tools in partial differential equations Features sional cases of Ginzburg-Landau function exten- and numerical analysis. This valuable book is a 7 Book arising from the best international confer- sively 7 Exercises and open problems included major achievement and is sure to become a stan- ence series on mathematics and culture dard reference on the topic. Contents Contents Introduction.- Linear Analysis.- Spectral Theory.- Features Introduction.- Homage to mario merz.- Mathe- 2D Models .- Models in dimension 3.- Magnetic 7 An attractive blend of modern topics and matics and images.- Mathematics and psychoanal- semiclassics.- Main results in dimension 3.- Non- classical results 7 Authors have included a nice ysis.- Mathematics and applications.- Mathematics Linear analysis.- Ginzburg-Landau functional.- selection of exercises for classroom use 7 Ideal and cartoon.- Mathematics and art.- Matematica Optimal elliptic estimates.- On the third critical reference work which contains a large amount of e parole.- Mathematics and cinema.- Mathematics field.- between H_{C_2} and H_{C_3}.- More historical material and references and vine.- Homage to alfred döblin and vincent dimension 3.- On the problems with corners.- On doeblin.- Venice.- Venice and marco polo. other models in superconductivity.- Open prob- Contents lems.- Bibliography. Introduction.- Functions and their Inverses.- Fields of interest Implicit Function Theorems for Variational Prob- Mathematics, general; Visualization; Applications Fields of interest lems.- Regularity Properties of Set-Valued Solution of Mathematics Functional Analysis; Superconductivity, Super- Mappings.- Regularity Properties Through fluidity, Quantum Fluids; Partial Differential Generalized Derivatives.- Regularity in Infinite Target groups Equations Dimensions.- Numerical Variational Analysis. Mathematicians of all kinds, mathematics teachers, lay people interested in mathematics Target groups Fields of interest Graduate students, researchers Analysis; Optimization Type of publication Undergraduate textbook Type of publication Target groups Monograph Graduate students, researchers
Type of publication Monograph
Mathematics Mathematics Due November 2008 Due January 2009 Due August 2009 Only available in print 2009. Approx. 310 p. 12 illus. (Springer Monographs in 2009. Approx. 300 p. (Progress in Nonlinear Differential Mathematics) Hardcover 2009. Approx. 310 p. Hardcover Equations and Their Applications, Volume77) Hardcover 7 approx. € 46,95 | £37.99 7 € 49,95 | £39.99 7 approx. € 61,60 | £63.99 9
A. Geroldinger, University of Graz, Austria; N. Ghoussoub, University of British Columbia, G. Grubb, University of Copenhagen, Denmark I. Z. Ruzsa, Hungarian Academy of Sciences, Vancouver, BC, Canada Budapest, Hungary Distributions and Operators Self-dual Partial Differential Combinatorial Number Theory Systems and Their Variational and Additive Group Theory Principles This book gives an introduction to distribution theory, based on the work of Schwartz and of many other people. Additionally, the aim is to show how Additive Combinatorics is a relatively recent This text is intended for a beginning graduate the theory is combined with the study of operators term coined to comprehend the developments course on convexity methods for PDEs. The in Hilbert space by methods of functional analysis, of the more classical Additive Number Theory, generality chosen by the author puts this under the with applications to ordinary and partial differen- mainly focussed on problems related to the addi- classification of “functional analysis”. The applica- tial equations. In some of the latter chapters, the tion of integers. Some classical problems like the tions, however, require a fair knowledge of clas- author illustrates how distribution theory is used Waring problem on the sum of k-th powers or sical analysis and PDEs which is needed to make to define pseudodifferential operators and how the Goldbach Conjecture are genuine examples judicious choices of function spaces where the self- they are applied in the discussion of solvability of of the original questions addressed in the area. dual variational principles need to be applied, and PDE, with or without boundary conditions. Each One of the features of contemporary Additive these choices necessarily require prior knowledge chapter has been enhanced with many exercises Combinatorics is the interplay of a great variety of of the expected regularity of the (weak) solutions. and examples, and a bibliography of relevant books mathematical techniques, including combinatorics, While this text contains many new results, it is the and papers is collected at the end. harmonic analysis, convex geometry, graph theory, author’s hope that this material will soon become A few of the unique topics include: (1) Boundary probability theory, algebraic geometry or ergodic standard for all graduate students. value problems in a constant-coefficient case; theory. (2) Pseudodifferential Boundary Operators; This book gathers the contributions of many of the Features (3) Families of extensions. Gerd Grubb is Professor leading researchers in the area and is divided into 7 Contains plenty of examples and exercises of Mathematics at University of Copenhagen. three parts. The two first parts correspond to the 7 Includes new results which have not been material of the main courses delivered, Additive previously presented in book form Features Combinatorics and non-unique factorizations, by 7 First book to present distribution theory as a Alfred Geroldinger, and Sumsets and structure, by Contents standard text 7 Contains unique topics Imre Z. Ruzsa. The third part collects the notes of Preface.- Introduction.- Legendre-Fenchel Duality 7 Author has made this easily accessible to most of the seminars which accompanied the main on Phase Space.- Self-dual Lagrangians on Phase advanced undergraduates, as well as graduates courses, and cover a reasonably large part of the Space.- Skew-adjoint Operators and Self-dual methods, techniques and problems of contempo- Lagrangians.- Self-dual Vector Fields and Their From the contents rary additive combinatorics. Calculus.- Variational Principles for Completely Preface.- Motivation and overview.- Func- Self-dual Functionals.- Semigroups of Contrac- tion spaces and approximation.- Distributions: Contents tions Associated to Self-dual Lagrangians.- Itera- Examples and rules of calculus.- Realizations and Foreword.- Preface.- I. Additive Group Theory tion of Self-dual Lagrangians and Multiparameter Sobolev spaces.- Fourier transformation of distri- and Non-unique Factorizations - II. Sumsets Evolutions.- Direct Sum of Completely Self-dual butions.- Applications to differential operators: and structure.- III. Thematic seminars - Contri- Functionals.- Semilinear Evolution with Self-dual The Sobolev theorem.- Pseudodifferential opera- butions by Jean Marc Deshouillers, Christian Boundary Conditions.- The Class of Antisym- tors on open sets.- Pseudodifferential operators on Elsholtz, Gregory A. Freiman, Yahya O. Hami- metric Hamiltonians.- Variational Principles for manifolds, index of elliptic operators.- Boundary doune, Norbert Hegyvári, Gyula Károly, Melvyn Self-dual Functionals and First Applications.- The value problems in a constant-coefficient case.- B. Nathanson, Jaroslav Nešetril, Jozsef Solymosi, Role of the Co-Hamiltonian in Self-dual Varia- Pseudodifferential boundary operators.- Pseudo- Yonutz V. Stanchescu, Gilles Zémor. tional Problems. differential methods for boundary value problems.
Fields of interest Fields of interest Fields of interest Combinatorics Functional Analysis; Partial Differential Equations Functional Analysis; Partial Differential Equations
Target groups Target groups Target groups Graduate students and lecturers in combinatorics Graduate students and researchers Advanced undergraduates, graduate students
Type of publication Type of publication Type of publication Graduate/Advanced undergraduate textbook Undergraduate textbook Graduate/Advanced undergraduate textbook
Mathematics Mathematics Mathematics
Due January 2009 Due February 2009 Due February 2009
2009. Approx. 400 p. (Advanced Courses in 2009. Approx. 370 p. (Springer Monographs in 2009. XII, 464 p. 8 illus. (Graduate Texts in Mathematics, Mathematics – CRM Barcelona) Softcover Mathematics) Hardcover Volume 252) Hardcover 7 € 39,90 | £31.99 7 € 46,95 | £37.99 7 approx. € 46,95 | £37.99 9
A. Guionnet, CNRS UMR 5669, Lyon, France A. Gut, Uppsala University, Uppsala, Sweden H. Hege, K. Polthier, G. Scheuermann (Eds.) Random Matrices: Lectures on Stopped Random Walks Topology-Based Methods in Macroscopic Asymptotics Limit Theorems and Applications Visualization II École d’Été des Probabilités de Saint-Flour XXXVI – 2006 Classical probability theory provides information Visualization research aims at providing insight about random walks after a fixed number of steps. into large, complicated data. Topological methods For applications, however, it is more natural to stand out by their solid mathematical ground Random matrix theory has developed in the last consider random walks evaluated after a random guiding the algorithmic analysis and its presenta- few years, in connection with various fields of number of steps. Examples are sequential analysis, tion among the various visualization techniques. mathematics and physics. These notes emphasize queueing theory, storage and inventory theory, This book contains 13 peer-reviewed papers the relation with the problem of enumerating insurance risk theory, reliability theory, and the resulting from the second workshop on complicated graphs, and the related large devia- theory of counters. Stopped Random Walks: Limit “Topology-Based Methods in Visualization”, tions questions. Such questions are also closely Theorems and Applications shows how this theory held 2007 in Grimma near Leipzig, Germany. All related with the asymptotic distribution of can be used to prove limit theorems for renewal articles present new original work from leading matrices, which is naturally defined in the context counting processes, first passage time processes, experts that has not been published before. of free probability and operator algebra. and certain two-dimensional random walks, and to Together, these articles present the state of the art how these results are useful in various applications. of topology-based visualization research. Contents This second edition offers updated content and Notation.- Introduction.- Part I Wigner matrices an outlook on further results, extensions and Features and moments estimates.- Part II Wigner matrices generalizations. A new chapter examines nonlinear 7 Book on core topic in visualization and concentration inequalities.- Part III Matrix renewal processes in order to present the anala- models.- Part IV Eigenvalues of Gaussian Wigner gous theory for perturbed random walks, modeled From the contents matrices and large deviations.- Part V Stochastic as a random walk plus “noise”. Visualization of Coherent Structures in Transient Calculus.- Part VI Free probability.- Part VII 2D Flows: C.Garth et al.- Visualizing Lagrangian Appendix.- References.- Index. Features Coherent Structures and Comparison to Vector 7 Second edition features a new chapter on Field Topology: F. Sadlo et al.- Extraction of Fields of interest perturbed random walks, which are modeled as Separation Manifolds using Topological Structures Linear and Multilinear Algebras, Matrix Theory; random walks plus “noise” 7 Presents updates to in Flow Cross Sections: A. Wiebel et al.-Topology Probability Theory and Stochastic Processes; the first edition, including an outlook on further Based Selection and Curation of Level Sets: C.Bajaj Functional Analysis results, extensions, and generalizations on the et al.- Representing Interpolant Topology for subject 7 Close to 100 additional bibliographic Contour Tree Computation: H. Carr et al.- Path Target groups references added to some 200 original ones Line Attributes - an Information Visualization Researchers and graduate students 7 Concise blend of material useful for both the Approach to Analyzing the Dynamic Behavior researcher and student of probability theory of 3D Time-Dependent Flow Fields: K. Shi et Type of publication al.- Flow Structure based 3D Streamline Place- Monograph Fields of interest ment: T.Salzbrunn et al.- Critical Points of the Probability Theory and Stochastic Processes; Electric Field from a Collection of Point Charges: Operations Research, Mathematical Programming N. Max et al.- Visualizing global manifolds during the transition to chaos in the Lorenz system: Target groups B.Krauskopf et al.- Streamline and Vortex Line For classroom use or self-study Analysis of the Vortex Breakdown in a Confined Cylinder Flow: M.Rütten et al. Type of publication Graduate/Advanced undergraduate textbook Fields of interest Visualization; Topology; Geometry
Target groups Graduate students, researchers, and professionals in visualization, mathematics, and computer science
Type of publication Mathematics Contributed volume
Mathematics Due February 2009 Mathematics Due November 2008 Originally published as volume 5 in the series: Applied Probability Due December 2008 2009. Approx. 325 p. (Lecture Notes in Mathematics / Ecole d’Eté Probabilit.Saint-Flour, Volume 1957) 2nd ed. 2009. Approx. 270 p. (Springer Series in Opera- 2009. Approx. 200 p. (Mathematics and Visualization) Softcover tions Research and Financial Engineering) Hardcover Hardcover 7 approx. € 39,95 | £30.00 7 approx. € 42,95 | £33.99 7 € 69,95 | £55.99 9
E. Hurst, M. Gould M. J. Jacobson, Jr., H. C. Williams, University of J. Kallrath, P. M. Pardalos, S. Rebennack, M. Scheidt Calgary, AB, Canada (Eds.) Bridging the Gap to University Mathematics Solving the Pell Equation Optimization in the Energy Industry
Designed as an introduction to higher-educa- Pell’s Equation is a very simple Diophantine equa- tion mathematics, Bridging the Gap is the only tion that has been known to mathematicians for Today, the optimization of production planning book of this sort written for students by students. over 2000 years. Even today research involving this processes using IT and quantitative methods is The authors, Martin Gould and Edward Hurst, equation continues to be very active, as can be seen a de-facto standard in the energy industry. The wrote this book as second-year undergraduates at by the publication of at least 150 articles related energy problem is challenging and one of the most Warwick University. Their experiences as students to this equation over the past decade. However, important political and economical issues in the have helped them create an approachable and very few modern books have been published on world. Governments face the problem how to comprehensive introductory text that will be of Pell’s Equation, and this will be the first to give adopt the system of `Cap and Trade.’ Especially, benefit to anyone looking to make the step-up to a historical development of the equation, as well energy consuming industries, like steel, power, university education. This book contains chapters as to develop the necessary tools for solving the oil and chemical, are seriously confronted with rich with worked examples and exercises covering equation. this problem. The book offers a broad in-depth all the key subject-areas that a first-year under- The authors provide a friendly introduction for overview reflecting the requirements, possibili- graduate will encounter, such as Inequalities, advanced undergraduates to the delights of alge- ties and limits of mathematical optimization and, Complex Numbers, Probability, Matrices and braic number theory via Pell’s Equation. The only especially, stochastic optimization in the energy many more. The authors have also included a “Test prerequisites are a basic knowledge of elementary industry. 22 chapters with world-wide origins illu- Yourself” exercise at the beginning of each chapter number theory and abstract algebra. There are also minate the mathematical requirements based on so that students will know straightaway which numerous references and notes for those who wish practical experiences and provide an ideal insight chapters will be of most use to them. Every topic to follow up on various topics. into the energy world – from integration of wind concludes with a “Where Now?” section that helps energy, chain of errors in nuclear power plants the reader find out exactly how and where they can Features and scheduling of hydroelectric power stations, apply their newly-learned skills. 7 Describes modern (and surprising) applica- over risk assessment in trading activities to various tions to cryptography 7 Includes the most recent mathematical approaches. Features advances, with a deeper approach than any other 7 Covers a wider area of subjects than any other book 7 Hugh Williams is Canada’s most famous Features book aimed at A-Level-to-undergraduate students computational number theorist who has published 7 Provides a broad introduction into the field of 7 A “down-to-earth” style makes it more acces- close to 200 articles in top journals 7 Michael energy production and trading by discussion about sible to readers 7 The “Test Yourself” exercise at Jacobson is the known expert on subexponential 20 real world cases 7 Besides the overview the the beginning of each chapter makes it easier for methods, and a former student of Hugh Williams reader learns about mathematical optimization the reader to find out exactly what material they 7 Both authors are known as outstanding exposi- methods used to solve these problems aren’t familiar with tors Fields of interest Contents From the contents Calculus of Variations and Optimal Control; Opti- 1. Inequalities.- 2. Trigonometry, Differentiation Early History of the Pell Equation.- Continued mization; Operations Research/Decision Theory; and Exponents.- 3. Polar Co-Ordinates.- Fractions.- Quadratic Number Fields.- Ideals and Power Engineering 4. Complex Numbers.- 5. Vectors.- 6. Matrices.- Continued Fractions.- Quadratic Number Fields.- 7. Matrices as Maps.- 8. Separable Differential Ideals and Continued Fractions.- Some Special Pell Target groups Equations.- 9. Integrating Factors.- 10. Mechanics. Equations.- The Ideal Class Group.- The Analytic Scientists/researchers, practitioners/professionals, Class Number Formula.- Some Additional graduates/undergraduates; academic/corporate Fields of interest Analytic Results. libraries; lecturers/tutors Mathematics, general; Engineering, general; Physics, general Fields of interest Type of publication Number Theory Contributed volume Target groups School-leavers, teachers; education colleges; first- Target groups year undergraduate students in the mathematical Advanced undergraduates, number theorists - sciences; lecturers professional and amateur
Type of publication Type of publication Undergraduate textbook Graduate/Advanced undergraduate textbook
Mathematics Mathematics Mathematics Due February 2009 Due November 2008 Due December 2008 2009. Approx. 515 p. 20 illus. (CMS Books in 2009. Approx. 370 p. 97 illus. Softcover Mathematics) Hardcover 2009. Approx. 550 p. (Energy Systems) Hardcover 7 approx. € 32,95 | £15.95 7 approx. € 54,95 | £43.99 7 approx. € 129,95 | £103.00 9
A. Kanamori, Boston University, Boston, MA, USA E. Kaniuth, Paderborn University, Paderborn, Y. Kosmann-Schwarzbach, École Polytechnique, Germany Palaiseau, France The Higher Infinite Large Cardinals in Set Theory from Their A Course in Commutative The Noether Theorems Beginnings Banach Algebras Invariance and Conservation Laws in the 20th Century
This is the softcover reprint of the very popular This book provides a thorough and self-contained hardcover edition. The theory of large cardinals introduction to the theory of commutative Banach In 1915 and 1916 Emmy Noether was asked by is currently a broad mainstream of modern set algebras, aimed at graduate students with a basic Felix Klein and David Hilbert to assist them in theory, the main area of investigation for the knowledge of functional analysis, topology, understanding issues involved in any attempt to analysis of the relative consistency of math- complex analysis, measure theory, and group formulate a general theory of relativity, in partic- ematical propositions and possible new axioms for theory. At the core of this text are the chapters on ular the new ideas of Einstein. She was consulted mathematics. The first of a projected multi-volume Gelfand’s theory, regularity and spectral synthesis. particularly over the difficult issue of the form a series, this book provides a comprehensive account Special emphasis is placed on applications in law of conservation of energy could take in the of the theory of large cardinals from its beginnings abstract harmonic analysis and on treating many new theory, and she succeeded brilliantly, finding and some of the direct outgrowths leading to the special classes of commutative Banach algebras, two deep theorems. frontiers of contemporary research. A “genetic” such as uniform algebras, group algebras and But between 1916 and 1950, the theorem was approach is taken, presenting the subject in the Beurling algebras, and tensor products. Detailed poorly understood and Noether’s name disap- context of its historical development. With hind- proofs and a variety of exercises are given. The peared almost entirely. People like Klein and sight the consequential avenues are pursued and book is intended for graduate students taking a Einstein did little more then mention her name the most elegant or accessible expositions given. course on Banach algebras, with various possible in the various popular or historical accounts they With open questions and speculations provided specializations, or a Gelfand theory based course wrote. Worse, earlier attempts which had been throughout the reader should not only come to in harmonic analysis. eclipsed by Noether’s achievements were remem- appreciate the scope and coherence of the overall bered, and sometimes figure in quick ‘historical’ enterprise but also become prepared to pursue Features accounts of the time. research in several specific areas by studying the 7 Author has carefully chosen the most important This book carries a translation of Noether’s relevant sections. topics within Banach algebra theory 7 Incorpo- original paper into English, and then describes the rates recent advances concerning so-called spectral strange history of its reception and the responses Features extension properties and the unique uniform norm to her work. 7 Has become a standard reference and guide in property 7 Investigates projective tensor prod- the set theory community ucts under all aspects of the book 7 Exercises are From the contents plentiful throughout the text 7 Class-tested at Emmy Noether’s Paper, Invariant Variational Prob- Fields of interest the University of Heidelberg, Technical University lems.- Introduction.- The Circumstances of the Mathematical Logic and Foundations; Topology of Munich, and University of Paderborn Composition of Noether’s Paper.- The Theorems of Noether.- The Appreciation of her Theorems Target groups Contents by her Contemporaries and by Historians.- The Researchers and graduate students in set theory, Preface.- General Theory of Banach Algebras.- Transmission of her Ideas, 1918-1951.- The Fortu- including set-theoretic topology Gelfand Theory.- Functional Calculus, Shilov nate of the 2nd Theorem after 1950. Boundary, and Applications.- Regularity and Type of publication Related Properties.- Spectral Synthesis and Ideal Fields of interest Monograph Theory.- Appendix.- References.- Index. History of Mathematics; Calculus of Variations and Optimal Control; Optimization; Dynamical Fields of interest Systems and Ergodic Theory Functional Analysis; Operator Theory Target groups Target groups Historians of mathematics and physics, graduate Graduate students, advanced undergraduates students; anyone interested in the history and philosophy of mathematics and physics Type of publication Graduate/Advanced undergraduate textbook Type of publication Monograph
Mathematics Mathematics
Due December 2008 Due January 2009 Mathematics Originally published in the series: Perspectives Original French edition published by Editions de l’École Mathematical Logic Due December 2008 Polytechnique, 2004
2nd ed. 2003. Corr. 2nd printing 2009. XXII, 564 p. 2009. Approx. 370 p. (Graduate Texts in Mathematics, 2009. Approx. 220 p. 10 illus. (Sources and Studies in the (Springer Monographs in Mathematics) Softcover Volume 246) Hardcover History of Mathematics and Physical Sciences) Softcover 7 approx. € 49,95 | £39.99 7 € 46,95 | £37.99 7 approx. € 34,95 | £27.99 9
A. Kox, University of Amsterdam, The Netherlands D. Laidlaw, Brown University, Providence, RI, USA; S. Larsson, V. Thomée, Goeteborg University, (Ed.) J. Weickert, Saarland University, Saarbruecken, Goeteborg, Sweden Germany (Eds.) The Scientific Correspondence Partial Differential Equations of H. A. Lorentz Visualization and Processing with Numerical Methods Volume I of Tensor Fields Advances and Perspectives This is the softcover reprint of the very popular This volume presents a selection of more than hardcover edition. The book is suitable for 400 letters from and to the Dutch physicist and Visualisation and Processing of Tensor Fieldspro- advanced undergraduate and beginning graduate Nobel Prize winner Hendrik Antoon Lorentz vides researchers an inspirational look at how students of applied mathematics and engineering. (1853–1928), covering the period from 1883 until to process and visualize complicated 2D and 3D The main theme is the integration of the theory a few months before his death. The letters included images known as tensor fields. Tensor fields are the of linear PDEs and the numerical solution of such in this volume have been selected according to natural representation for many physical quanti- equations. For each type of PDE, elliptic, parabolic, various criteria, the most important of which is ties; they can describe how water moves around in and hyperbolic, the text contains one chapter on scientific interest. A second criterion has been the the brain, how gravity varies around the earth, or the mathematical theory of the differential equa- availability of letters both from and to Lorentz, so how materials are stressed and deformed. With its tion, followed by one chapter on finite difference that the reader can follow the scientific exchange numerous color figures, this book helps the reader methods and one on finite element methods. between Lorentz and his correspondent. Of such understand both the underlying mathematics and As preparation, the two-point boundary value correspondences only a few unimportant items the applications of tensor fields. The reader also problem and the initial-value problem for ODEs have been omitted, the emphasis always being on will learn about the most recent research topics are discussed in separate chapters. There is also scientific interest. The letters are presented in their and open research questions. one chapter on the elliptic eigenvalue problem and original language (which for this volume is mainly eigenfunction expansion. The presentation does German, with a few French and English items); Features not presume a deep knowledge of mathematical a few Dutch drafts are accompanied by English 7 Major workshop in core field of visualization and functional analysis. Some background on translations. The book’s editor, Anne Kox, has linear functional analysis and Sobolev spaces, and prepared a biography of Lorentz, as well as annota- Contents also on numerical linear algebra, is reviewed in tions of selected letters. Part i models for diffusion mri.- Part ii higher-level two appendices. analysis of diffusion images.- Part iii tensor field Features visualization.- Part iv tensor field analysis in the Features 7 Unique insight into the minds of the 19th–20th physical sciences.- Part v tensor image structure 7 Very well-written 7 Elementary introduction century’s most important physicists 7 Preface models.- Part vi filtering with tensors. contains a biography of Lorentz, with details which Fields of interest cannot be found elsewhere 7 Contains previ- Fields of interest Numerical Analysis; Partial Differential Equations ously unpublished letters from Einstein, Planck Computational Mathematics and Numerical and others Analysis; Mathematics of Computing; Computer Target groups Imaging, Graphics and Computer Vision Advanced undergraduate and beginning graduate Contents students of applied mathematics and engineering Preface.- Letters.- General bibliography.- Lorentz Target groups bibliography.- Index. Researchers in visualization (mathematics and Type of publication computer science) Graduate/Advanced undergraduate textbook Fields of interest History of Mathematics; History of Physics; Rela- Type of publication tivity and Cosmology Contributed volume
Target groups Physicists, historians of science
Type of publication Monograph
Mathematics Mathematics Mathematics
Due December 2008 Due November 2008 Due December 2008
2009. Approx. 805 p. 35 illus. (Sources and Studies in the 2009. Approx. 465 p. (Mathematics and Visualization) 1st ed. 2003. 2nd printing 2009. Approx. 200 p. (Texts in History of Mathematics and Physical Sciences) Hardcover Hardcover Applied Mathematics, Volume 45) Softcover 7 € 94,95 | £71.50 7 € 94,95 | £75.00 7 approx. € 29,95 | £23.99 9
T. Li, L. Wang, Fudan University, Shanghai, China F. Linares, G. Ponce S. Lipscomb, University of Mary Washington, Fredericksburg, VA, USA Global Propagation of Regular Introduction to Nonlinear Nonlinear Hyperbolic Waves Dispersive Equations Fractals and Universal Spaces in Dimension Theory
This monograph describes global propagation of The aim of this textbook is to introduce the theory regular nonlinear hyperbolic waves described by of nonlinear dispersive equations to graduate Historically, for metric spaces the quest for first-order quasilinear hyperbolic systems in one students in a constructive way. The first three universal spaces in dimension theory spanned dimension. The exposition is clear, concise, and chapters are dedicated to preliminary material, approximately a century of mathematical research. unfolds systematically beginning with introduc- such as Fourier transform, interpolation theory The history breaks naturally into two periods - the tory material and leading to the original research and Sobolev spaces. The authors then proceed to classical (separable metric) and the modern (not- of the authors. A systematic theory is established use the linear Schrodinger equation to describe necessarily separable metric). - by means of the concept of weak linear degen- properties enjoyed by general dispersive equations. The classical theory is now well documented in eracy and the method of (generalized) normalized This information is then used to treat local and several books. This monograph is the first book to coordinates - for the global existence and blow-up global well-posedness for the semi-linear Schro- unify the modern theory from 1960-2007. Like the mechanism of regular nonlinear hyperbolic waves dinger equations. The end of each chapter contains classical theory, the modern theory fundamentally with small amplitude for the Cauchy problem and recent developments and open problems, as well involves the unit interval. many other problems. as exercises. Unique features include: - The use of graphics to Topics are motivated with a number of physical illustrate the fractal view of these spaces; - Lucid examples from the areas of elastic materials, one- Features coverage of a range of topics including point-set dimensional gas dynamics, and waves. Aimed at 7 Includes a nice selection of topics 7 Contains topology and mapping theory, fractal geometry, researchers and graduate students in partial differ- a large selection of non-standard exercises and algebraic topology; - A final chapter contains ential equations and related topics, this book will 7 Accessible presentation of key tools in surveys and provides historical context for related stimulate further research and help readers further harmonic and Fourier analysis research that includes other imbedding theorems, understand important aspects and recent progress graph theory, and closed imbeddings; - Each of regular nonlinear hyperbolic waves. Contents chapter contains a comment section that provides Preface.- The Fourier Transform.- Interpolation historical context with references that serve as a Features of Operators: A Multiplier Theorem.- Sobolev bridge to the literature. 7 Provides a complete theory for waves with Spaces and Pseudo-differential Operators.- The general system conditions and boundary condi- Linear Schrödinger Equation.- The Nonlinear Features tions 7 Features many related applications to Schrödinger Equation, Local theory.- Asymptotic 7 Author includes more than 60 bw illustra- mechanics and physics 7 Contains much mate- Behavior for NLS Equation.- Korteweg-de Vries tions and 15 in color 7 Each chapter contains rial based on the results obtained by the authors is Equation.- Asymptotic Behavior of Solutions for comments that provide historical context 7 This recent years the k-gKdV Equations.- Other Nonlinear Disper- is the first time most of this material has appeared sive Models.- General Quasilinear Schrödinger in book form From the contents Equation.- Appendix.- References.- Index. Cauchy problem.- Cauchy problem (Continued).- From the contents Cauchy Problem on a semi-bounded initial axis.- Fields of interest Construction of JA=j alpha.- Self-Similarity One-sided mixed initial-boundary value problem.- Partial Differential Equations and Jn+1 for Finite n.- No-Carry Property of Generalized Riemann problem.- Generalized wA.- Imbedding Ja in Hilbert Space.- Infinite IFS nonlinear initial-boundary Riemann problem. Target groups with Attractor wA.- Infinite IFS with Attractor Advanced undergrads, graduate students wA.- Dimension Zero.- Decompositions.- The Fields of interest Jn+1 Imbedding Theorem.- Minimal-Exponent Partial Differential Equations; Ordinary Differen- Type of publication Question.- The JA Imbedding Theorem. tial Equations; Applications of Mathematics Graduate/Advanced undergraduate textbook Fields of interest Target groups Topology; Analysis; Functions of a Complex Researchers and grad students in math and physics Variable
Type of publication Target groups Monograph Advanced graduate students, researchers
Type of publication Monograph
Mathematics Mathematics Mathematics Due June 2009 Due February 2009 Due February 2009 2009. Approx. 365 p. (Progress in Nonlinear Differential 2009. XVIII, 242 p. 101 illus., 15 in color. (Springer Mono- Equations and Their Applications, Volume 76) Hardcover 2009. Approx. 265 p. (Universitext) Softcover graphs in Mathematics) Hardcover 7 approx. € 69,30 | £71.00 7 € 34,95 | £27.99 7 € 54,95 | £43.99 9
S. Lynch, Manchester Metropolitan University, B. D. MacCluer, University of Virginia, Charlottesville, O. Martio, V. Ryazanov, U. Srebro,E. Yakubov Manchester, UK VA, USA Moduli in Modern Mapping Dynamical Systems with Elementary Functional Theory Applications using MAPLE Analysis
The purpose of this book is to present a modern From the reviews This nicely written manuscript takes a gentler account of mapping theory with emphasis on 7 The book will be useful for all kinds of dynamical approach than other functional analysis graduate quasiconformal mapping and its generaliza- systems courses…. [It] shows the power of using texts, and includes an improved approach along tions. The modulus method was initiated by Arne a computer algebra program to study dynamical with a better choice of topics. The concise treat- Beurling and Lars Ahlfors to study conformal systems, and, by giving so many worked examples, ment makes this ideal for a one-semester course. mappings, and later this method was extended and provides ample opportunity for experiments. … The exercises in this manuscript are numerous and enhanced by several others. The techniques are [It] is well written and a pleasure to read, which is of a very high quality. Interesting historical tidbits geometric and they have turned out to be an indis- helped by its attention to historical background are scattered throughout the text, many of which pensable tool in the study of quasiconformal and 7 Mathematical Reviews (Review of First Edition) will be new to most readers. The main prereq- quasiregular mappings as well as their generaliza- uisites are basic undergraduate courses in real tions. The book is based on recent research papers “Dynamical Systems with Applications using analysis, linear algebra, and point set topology. and extends the modulus method beyond the Maple” provides an introduction to the theory classical applications of the modulus techniques of dynamical systems with the aid of the Maple Features presented in many monographs. algebraic manipulation package. This new edition 7 Large number of high quality exercises has been thoroughly updated and expanded to 7 Concise and gentle approach with a unique Features include more applications, examples, and exercises, set of topics 7 Historical details are spread 7 Contains new results from leading researchers all with solutions; two new chapters on neural throughout the book 7 This book has been thor- in the field 7 Authors have included an extensive networks and Maplets have also been added. A oughly class-tested bibliography supplementary e-book with interactive exercises, examples, and solutions will also be published. Contents Contents Preface.- Hilbert Space Preliminaries.- Operator Introduction and notation.- Moduli and capacity.- Features Theory Basics.- The Big Three.- Compact Opera- Moduli and domains.- Q-Homeomorphisms.- Q- 7 Excellent reviews of the first edition (Math- tors.- Banach and C+- Algebras.- The Spectral Homeomorphisms with Q in BMO.- More General ematical Reviews, SIAM, Reviews, UK Nonlinear Theorem.- Real Analysis Topics.- References.- Q-Homeomorphisms.- Ring Q-Homeomor- News, The Maple Reporter) 7 New edition has Index. phisms.- Mappings With Finite Length Distortions been thoroughly updated and expanded to include (FLD).- Lower Q-Homeomorphisms.- Mappings more applications, examples, and exercises, all Fields of interest With Finite Area Distortions (FAD).- On Ring with solutions 7 Two new chapters on neural Functional Analysis Solutions of the Beltrami Equation.- Homeo- networks and Maplets have also been added morphisms with Finite Means Dilatations.- On 7 Supplementary e-book with interactive Target groups the Mapping Theory in Metric Spaces.- Moduli exercises, examples, and solutions will also be Advanced undergrads, grad students Theory.- BMO Functions by John-Nirenberg.- published References.- Index. Type of publication Fields of interest Graduate/Advanced undergraduate textbook Fields of interest Applications of Mathematics; Appl.Mathematics/ Analysis; Functional Analysis Computational Methods of Engineering; Ordinary Differential Equations Target groups Graduate students and researchers Target groups Senior undergraduates, graduate students, and Type of publication working scientists in various branches of applied Monograph mathematics, the natural sciences, and engineering
Type of publication Undergraduate textbook
Mathematics Mathematics Mathematics Due February 2009 Due February 2009 Due April 2009 2009. X, 208 p. 5 illus. (Graduate Texts in Mathematics, 2009. Approx. 375 p. 15 illus. (Springer Monographs in 2nd ed. 2009. Approx. 500 p. 350 illus. Softcover Volume 253) Hardcover Mathematics) Hardcover 7 approx. € 44,95 | £47.99 7 € 34,95 | £27.99 7 € 66,95 | £52.99 9
T. Mikosch, University of Copenhagen, Denmark S. K. Mishra, S. Wang, K. K. Lai M. Muresan, Babes-Bolyai University, Cluj-Napoca, Romania Non-Life Insurance Generalized Convexity and Mathematics Vector Optimization A Concrete Approach to An Introduction with Stochastic Processes Classical Analysis
The present book discusses the Kuhn-Tucker This book offers a mathematical introduction Optimality, Karush-Kuhn-Tucker Necessary Mathematical analysis offers a solid basis for many to non-life insurance and, at the same time, to a and Sufficient Optimality Conditions in pres- achievements in applied mathematics and discrete multitude of applied stochastic processes. It gives ence of various types of generalized convexity mathematics. This new textbook is focused on detailed discussions of the fundamental models for assumptions. Wolfe-type Duality, Mond-Weir differential and integral calculus, and includes a claim sizes, claim arrivals, the total claim amount, type Duality, Mixed type Duality for Multiobjec- wealth of useful and relevant examples, exercises, and their probabilistic properties. Throughout tive optimization problems such as Nonlinear and results enlightening the reader to the power the book the language of stochastic processes is programming problems, Fractional programming of mathematical tools. The intended audience used for describing the dynamics of an insurance problems, Nonsmooth programming problems, consists of advanced undergraduates studying portfolio in claim size space and time. In addition Nondifferentiable programming problems, Varia- mathematics or computer science. to the standard actuarial notions, the reader learns tional and Control problems under various types The author provides excursions from the standard about the basic models of modern non-life insur- of generalized convexity assumptions. topics to modern and exciting topics, to illustrate ance mathematics: the Poisson, compound Poisson the fact that even first or second year students can and renewal processes in collective risk theory and Features understand certain research problems. heterogeneity and Bühlmann models in experience 7 Reader will come to know about the present rating. The reader gets to know how the underlying status of the research in this hot area of research Features probabilistic structures allow one to determine field 7 Reader does not have to consult various 7 Includes research topics which can be under- premiums in a portfolio or in an individual policy. research papers from different journals 7 Will stood by undergraduates 7 Author provides Special emphasis is given to the phenomena which provide the reader the present state of knowledge numerous exercises and examples are caused by large claims in these models. on research done in this area so far What makes this book special are more than 100 Contents figures and tables illustrating and visualizing the Contents Preface.- Sets and Numbers.- Vector Spaces and theory. Every section ends with extensive exercises. Introduction and Motivation.- Generalized Metric Spaces.- Sequences and Series.- Limits and They are an integral part of this course since they Convex Functions.- Type I and Related Functions.- Continuity.- Differential Calculus on R.- Integral support the access to the theory. Optimality Conditions.- Duality Theory.- Second Calculus on R.- Differential Calculus on Rn.- and Higher Order Duality.- Symmetric Duality.- Double Integrals, Triple Integrals, and Line Inte- Features Vector Variational-like Inequality Problems. grals.- Constants.- Asymptotic and Combinatorial 7 Rigorous mathematical introduction and as Estimates.- References.- List of Symbols.- Author such quite a unique textbook which can be used Fields of interest Index.- Subject Index. not only by a specialised audience 7 More than Calculus of Variations and Optimal Control; Opti- 100 figures and tables illustrating and visualizing mization; Operations Research/Decision Theory Fields of interest the theory 7 Every section ends with extensive Analysis exercises 7 Book’s content is in agreement with Target groups the European “Group Consultatif” standards Researchers Target groups Advanced undergraduates; beginning graduate Fields of interest Type of publication students Quantitative Finance Monograph Type of publication Target groups Undergraduate textbook Students and lecturers of actuarial mathematics, mathematics, economics, physics, statistics, econometrics
Type of publication Graduate/Advanced undergraduate textbook
Mathematics Mathematics Mathematics Due December 2008 Due December 2008 Due January 2009 2009. Approx. 450 p. (Nonconvex Optimization and Its 2009. Approx. 455 p. 29 illus. (CMS Books in 2nd ed. 2009. Approx. 455 p. (Universitext) Softcover Applications, Volume 90) Hardcover Mathematics) Hardcover 7 € 49,95 | £39.99 7 € 99,95 | £79.00 7 € 46,95 | £37.99 9
K. B. Oldham, J. Myland, Trent University, Peter- C. Parikh, Brookline, MA, USA L. Pronzato, Université Nice, Sophia Antipolis, borough, ON, Canada; J. Spanier, University of France; A. Zhigljavsky, Cardiff University, Cardiff, UK California, Irvine, CA, USA The Unreal Life of (Eds.) Equator Oscar Zariski Optimal Design and Related A Function Calculator Areas in Optimization and Oscar Zariski’s work in mathematics permanently Statistics altered the foundations of algebraic geometry. Equator is a software package designed to generate The powerful tools he forged from the ideas of numerical values of nearly 200 mathematical modern algebra allowed him to penetrate clas- This edited volume, dedicated to Henry P. Wynn, functions and function families used by engineers, sical problems with an unaccustomed depth, and reflects his broad range of research interests, scientists and others. Among the functions made brought new rigor to the intuitive proofs of the focusing in particular on the applications of available by Equator are such simples as cosines Italian School. The students he trained at Hopkins, optimal design theory in optimization and statis- and binomial coefficients as well as more elaborate and later at Harvard, are among the foremost tics. It covers algorithms for constructing optimal examlpes such as Bessel functions and elliptic mathematicians of our time. experimental designs, general gradient-type algo- integrals. While what he called his “real life” is recorded in rithms for convex optimization, majorization and Equator is designed to complement the second almost a hundred books and papers, this story of stochastic ordering, algebraic statistics, Bayesian edition of An Atlas of Functions (Keith B. Oldham, his “unreal life” is based upon Parikh’s interviews networks and nonlinear regression. Written Jan C. Myland, and Jerome Spanier, Springer, with his family, colleagues, and students, and on by leading specialists in the field, each chapter 2008), which is available in both print and elec- his own memories from a series of tape-recorded contains a survey of the existing literature along tronic formats. Full information about this book interviews made a few years before his death in with substantial new material. can be found at www.springerlink.com. 1986. This work will appeal to both the specialist and the Equator is easy to use and its operation will soon First published in 1991, The Unreal Life of Oscar non-expert in the areas covered. By attracting the become as intuitive as using your calculator. We Zariski was highly successful and widely praised, attention of experts in optimization to important hope that you will find it useful. but has been out of print for many years. Springer interconnected areas, it should help stimulate is proud to make this book available again, further research with a potential impact on appli- Features introducing Oscar Zariski to a new generation of cations. 7 Uses the language of mathematics that is mathematicians. common to all branches of science and engi- Features neering 7 This software obviates the need for Features 7 Devoted to applications of the optimal design tables or programming to find numerical values 7 The only biography of the personal life of this theory in optimization and statistics 7 Provides (once installed onto your Windows XP based PC, important mathematician 7 Engaging look at comprehensive surveys written by leading gener- this unique function calculator instantly generates the development of algebraic geometry in the 20th alists 7 Each chapter reviews, analyzes, and precise function values on demand) 7 Easy and century extends the statistical literature with rigor and intuitive to use clarity 7 Contents Fields of interest A Foreword for Non-Mathematicians, by David From the contents Applications of Mathematics; Special Functions; Mumford.- That Darling Old Lady Kobrin and B. Torsney: W-iterations and Ripples Therefrom.- Real Functions Chernigov 1899-1918.- Birds Whirling like R. Haycroft, L. Pronzato, H.P. Wynn, Numbers, Kiev 1918-1920.- Three Great Mathema- A. Zhigljavsky: Studying Convergence of Gradient Target groups ticians, Rome 1921-1926.- Reading Pushkin and Algorithms via Optimal Experimental Design All researchers and students in the science, Dante.- “Oscar, you are not one of us”.- Walking Theory.- L. Pronzato, H.P. Wynn, A. Zhigljavsky: technology and mathematics disciplines, from with Lefschets, Baltimore 1927-1928.- A Voyage of A Dynamical-System Analysis of the Optimum mathematics to chemistry, biology, physics, and Discovery, 1928-1932.- “The Algebra Which Sheds S-Gradient Algorithm. computer science Light on Geometry”, 1932-1935.- A Citizen of the World of Mathematics, 1935-1937. Fields of interest Type of publication Operations Research, Mathematical Programming; Application software Fields of interest Statistics, general; Optimization History of Mathematics; Algebraic Geometry Target groups Target groups Researchers, graduate students Mathematicians, students Type of publication Type of publication Monograph Biography
Mathematics Mathematics Mathematics Due December 2008 Due December 2008 Due December 2008 2009. Approx. 230 p. 23 illus. (Springer Optimization and 2009. 28 illus. in color. CD-ROM. CD special packaging 2009. Approx. 265 p. 46 illus. Softcover Its Applications, Volume 28) Hardcover 7 € 16,95 | £13.99 7 € 26,95 | £21.99 7 € 79,95 | £63.99 9
M. Putinar, S. Sullivant (Eds.) A. M. Quarteroni, Politecnico di Milano, Italia L. Rodino, Università di Torino, Italia; M. W. Wong, York University, Toronto, ON, Canada (Eds.) Emerging Applications of Numerical Models of Algebraic Geometry Differential Problems New Developments in Pseudo- Differential Operators
Recent advances in both the theory and imple- In this text, we introduce the basic concepts for mentation of computational algebraic geometry the numerical modelling of partial equation This volume consists of seventeen peer-reviewed have led to new, striking applications to a variety differential equations. We consider the classical papers related to lectures on pseudodifferential of fields of research. The articles in this volume elliptic, parabolic and hyperbolic linear equations, operators presented at the meeting of the ISAAC highlight a range of these applications and provide but also others, such as the diffusion, transport, Group in Pseudo-Differential Operators (IGPDO) introductory material for topics covered in the and Navier-Stokes equations, as well as equa- held at the Middle East Technical University in IMA workshops on “Optimization and Control” tions representing conservation laws. Further- Ankara,Turkey on August 13-19, 2007, and invited and “Applications in Biology, Dynamics, and more, we provide numerous physical examples papers by experts in the field. Included in this Statistics” held during the IMA year on Applica- which underlie such equations. We then analyze volume are such topics as analysis and partial tions of Algebraic Geometry. The articles related numerical solution methods based on finite differential equations related to the Heisenberg to optimization and control focus on burgeoning elements, finite differences, finite volumes, spectral group; global analysis and pseudo-differential use of semidefinite programming and moment methods and domain decomposition methods. analysis on non-compact manifolds and manifolds matrix techniques in computational real algebraic In particular, we discuss the algorithmic and with singularities; Fourier integral operators and geometry. The new direction towards a systematic computer implementation aspects and provide a Colombeau algebras with applications to partial study of non-commutative real algebraic geometry number of easy-to-use programs. It is suitable for differential equations; exotic pseudo-differential is well represented in the volume. Other articles students of bachelor and master courses in scien- operators and regularity results on quasi-elliptic provide an overview of the way computational tific disciplines, and recommendable to researchers operators and hypoelliptic operators; Stockwell algebra is useful for analysis of contingency who want to approach this interesting branch of transforms in time-frequency analysis; and tables, reconstruction of phylogenetic trees, and applied mathematics. pseudo-differential operators on Lie groups with in systems biology. The contributions collected related results to sampling. This volume is a useful in this volume are accessible to non-experts, Features complement to the volumes “Advances in Pseudo- self-contained and informative; they quickly move 7 Author faces here the basic concepts for the Differential Operators”, “Pseudo-Differential Oper- towards cutting edge research in these areas, and numerical modelling of partial differential equa- ators and Related Topics” and “Modern Trends in provide a wealth of open problems for future tions 7 Outstanding reference work in this Pseudo-Differential Operators” published in the research. branch of applied mathematics same series in, respectively, 2004, 2006 and 2007.
Contents Contents Features Polynomial optimization on odd-dimensional Introduction.- 1 A brief survey on partial 7 Representation of latest trends in pseudo- spheres.- Engineering systems and free semi-alge- differential equations.- 2 Elliptic equations.- differential operators 7 Emphasis of the role braic geometry.- Algebraic statistics and contin- 3 The Galerkin finite element method for elliptic of pseudo-differential operators in analysis, gency table problems: Log-linear models, likeli- problems.- 4 Spectral methods.- 5 Diffusion- applications and computation 7 Presentation of hood estimation, and disclosure limitation.- Using transport-reaction equations.- 6 Parabolic a diversity of topics related to pseudo-differential invariants for phylogenetic tree construction.- On equations.- 7 Finite differences for hyperbolic operators 7 Not perceived to be a conference the algebraic geometry of polynomial dynamical equations.- 8 Finite elements and spectral methods proceedings systems.- A unified approach to computing real for hyperbolic equations.- 9 Nonlinear hyperbolic and complex zeros of zero-dimensional ideals.- problems.- 10 The Navier-Stokes equations.- Fields of interest Sums of squares, moment matrices and optimiza- 11 Finite element programming.- 12 Generation Operator Theory; Partial Differential Equations; tion over polynomials. of 1D and 2D grids. Global Analysis and Analysis on Manifolds
Fields of interest Fields of interest Target groups Algebraic Geometry; General Algebraic Systems; Mathematics, general; Analysis; Numerical Graduate students and researchers in analysis, Applications of Mathematics Analysis mathematical physics, and mathematical sciences
Target groups Target groups Type of publication Researchers Students of bachelor and master courses in scien- Professional book tific disciplines: engineering, mathematics, physics, Type of publication computational sciences, and information science Reference work Type of publication Undergraduate textbook
Mathematics Mathematics Mathematics Due December 2008 Due December 2008 Due February 2009 2009. Approx. 375 p. (The IMA Volumes in Mathematics 2009. Approx. 340 p. (Operator Theory, Volume 189) and its Applications, Volume 149) Hardcover 2009. XX, 450 p. Softcover Hardcover 7 € 66,95 | £50.50 7 € 40,95 | £32.99 7 € 139,00 | £110.00 9
S. Roman, Irvine, CA, USA A. Saracco, Università di Milano-Bicocca, Italia K. Sarma, K. Ramasubramanian, M. Srinivas, M. S. Sriram Lattices and Ordered Sets Extension problems in complex and CR-geometry Ganita-Yukti-Bhasa (Rationales in Mathematical This book is intended to be a thorough introduc- Astronomy) of Jyesthadeva tion to the subject of order and lattices and can This book is both a survey of some aspects of Volume I: Mathematics be used for a course at the graduate or advanced extension problems in Complex Analysis and Volume II: Astronomy undergraduate level or for independent study. Geometry and a collection of results by the author. Prerequisites consist mostly of a bit of math- After recalling the preliminary and necessary ematical maturity, such as that provided by a basic notions of complex analysis, the survey focuses on undergraduate course in abstract algebra. extension of holomorphic functions (filling both Ganita-yukti-bhasa (Rationales in Mathematical compact and non-compact holes), on the reflection Astronomy) of Jyesthadeva (c.1530) is a seminal Features principle, on extension results via cohomology text of the Kerala school of astronomy. It is 7 Written in an appealing style 7 Will become a vanishing, and on the boundary problem. The last composed in the Malayalam language and presents standard text and an invaluable guide 7 Contains two subjects include detailed results by the author detailed yuktis or explanations and demonstra- a plethora of exercises, examples, and illustrations on non-compact extension: the cohomology of tions for the results and processes of mathematical semi q-coronae and the unbounded boundary astronomy. The text, comprising fifteen chapters, Contents problem. is naturally divided into two parts, mathematics Preface.- Partially Ordered Sets.- Well-Ordered and astronomy, and purports to give an exposi- Sets.- Lattices.- Modular and Distributive Features tion of the techniques and theories employed in Lattices.- Boolean Algebras.- The Representation 7 Presents a large survey on the broad subject of the computation of planetary motions as set forth of Distributive Lattices.- Algebraic Lattices.- Prime extension in complex analysis and CR geometry in the great treatise Tantrasangraha (c.1500) of and Maximal Ideals: Separation Theorems.- 7 Endowed with a very extensive bibliography Nilakantha Somayaji. Congruence Relations on Lattices.- Duality for Distributive Lattices: The Priestley Topology.- Free Contents Features Lattices.- Fixed-Point Theorems.- Appendix A: A 1. Introduction.- 2. Classical extension theorems 7 A long-awaited translation of one of the most Bit of Topology.- Appendix B: A Bit of Category in one and several complex variables.- 3. Extension important – and hitherto least accessible – works Theory.- References.- Index of Symbols.- Index. of CR-functions up to a Levi-flat boundary and in Indian mathematics, supplemented by detailed of holomorphic maps.- 4. Cohomology vanishing explanatory notes and commentary Fields of interest and extension problems for semi q-coronae.- 5. Order, Lattices, Ordered Algebraic Structures; Cohomology of semi 1-coronae and extension of Fields of interest Algebra analytic subsets.- 6. The boundary problem.- 7. History of Mathematics; Astronomy Non-compact boundaries of complex analytic Target groups varieties.- 8. Semi-local extension of maximally Target groups Advanced undergrads, graduate students complex submanifolds. Historians of mathematics and astronomy; philosophers of science; indologists Type of publication Fields of interest Graduate/Advanced undergraduate textbook Functions of a Complex Variable; Differential Type of publication Geometry; Global Analysis and Analysis on Monograph Manifolds
Target groups PhD students and researchers in the field of complex and CR geometry
Type of publication Monograph
Due December 2008
Only available in print
For distribution outside India only. Distribution rights in India belong to Hindustan Book Agency (HBA), New Delhi, India
Due November 2008 Co-published with Hindustan Book Agency (HBA), Mathematics New Delhi, India Only available in print Due December 2008 2009. Approx. 1085 p. (Sources and Studies in the 2009. Approx. 150 p. (Publications of the Scuola Normale History of Mathematics and Physical Sciences) 2009. Approx. 330 p. 43 illus. Hardcover Superiore / Theses, Volume 9) Softcover (In 2 volumes, not available separately) Hardcover 7 € 46,95 | £35.50 7 € 18,00 | £14.99 7 approx. € 152,00 | £120.00 9
G. Shimura, Princeton University, Princeton, NJ, USA N. Sivin, University of Pennsylvania, Philadelphia, M. Sofonea, Université de Perpignan, France; PA, USA A. Matei, University of Craiova, Romania The Map of My Life Granting the Seasons Variational Inequalities with The Chinese Astronomical Reform of 1280, Applications The purpose of this book is manifold and includes With a Study of Its Many Dimensions and an A Study of Antiplane Frictional Contact more than just the author’s strict recollections. Annotated Translation of Its Records Problems Shimura not only writes about himself, but also about the atmosphere of the time. As a result, the author includes many things that are completely China’s most sophisticated system of compu- This book is motivated by stimulating problems ordinary and known to almost everyone of my tational astronomy was created for a Mongol in contact mechanics, emphasizing antiplane fric- generation. I do so because since they are so emperor who could neither read nor write tional contact with linearly elastic and viscoelastic ordinary, they will never be written, and as a Chinese, to celebrate victory over China after forty materials. It focuses on the essentials with respect consequence, will be forgotten. years of devastating war. This book explains how to the qualitative aspects of several classes of varia- He has also included his opinions on various and why, and reconstructs the observatory and the tional inequalities (VIs). Clearly presented, easy to historical events and thoughts about human science that made it possible. follow, and well-referenced, this work treats almost nature. In the latter part of the book, he writes For two thousand years, a fundamental ritual entirely VIs of the second kind, with much of the about mathematics, and inevitably he uses of government was the emperor’s “granting the material being state-of-the-art. technical terms. The reader who is not familiar seasons” to his people at the New Year by issuing Applied mathematicians and advanced graduate with these terms should simply read through an almanac containing an accurate lunisolar students wishing to enter the field of VIs would the passages in question without trying too hard calendar. The high point of this tradition was benefit from this work as it sets out in detail basic to understand them. After all, this book is not the “Season-granting system” (Shou-shih li, features and results in the mathematical theory about mathematics, but about how Shimura’s life 1280). Its treatise records detailed instructions of contact mechanics. Researchers interested in is related to the development of mathematics. To for computing eclipses of the sun and moon and applications of numerical analysis pertaining to understand that interaction, it is not necessary to motions of the planets, based on a rich archive of VIs would also find the work useful. Assuming a have any special knowledge of mathematics. observations, some ancient and some new. reasonable knowledge of functional analysis, this volume is a must for graduate students, practitio- Features Features ners, and engineers engaged in contact mechanics. 7 Illustrates what it was like to grow up in Japan 7 Introductory chapters provide a very acces- during World War II 7 Details the life of one of sible overview of the history of Chinese astronomy Features the greatest mathematicians of the 20th century 7 Provides a detailed commentary along with a 7 Organization of the book into 4 parts makes it 7 Provides a rare insider’s glimpse into the math- complete translation 7 Nathan Sivin is the West’s easy to concentrate on the topics 7 Presentation ematical community leading scholar of Chinese science, and this book is very clear, easy to follow, and well-referenced is the result of 30 years of research 7 Presents the essentials of the theory of VIs and Contents its applications to a class of interesting problems in Preface.- Childhood.- As a student.- As a math- From the contents contact mechanics ematician.- A long epilogue.- Appendix.- After- Astonomical reform and occupation politics.- word. Orientation.- The Project: origins and process.- Fields of interest The Astronomers.- The Observatory and its Calculus of Variations and Optimal Control; Opti- Fields of interest instruments.- The Records.- Evaluation of the mization; Continuum Mechanics and Mechanics History of Mathematics; Number Theory; Algebra season-granting system, part 1.- Evaluation of of Materials; Global Analysis and Analysis on the season-granting system, part 2.- Canon of the Manifolds Target groups season-granting system, part 1.- Canon of the Mathematicians, anyone interested in 20th century season-granting system, part 2. Target groups mathematics Applied mathematicians and advanced graduate Fields of interest students wishing to enter the field of VIs; Type of publication History of Mathematics; Astronomy researchers interested in applications of numerical Biography analysis pertaining to VIs; assuming a reason- Target groups able knowledge of functional analysis, a must for Graduate students and researchers in the fields graduate students, practitioners, and engineers of history of science, mathematics, and Chinese engaged in contact mechanics astronomy Type of publication Type of publication Monograph Monograph
Mathematics Mathematics Mathematics Due December 2008 Due January 2009 Due December 2008 2009. VI, 664 p. 49 illus. (Sources and Studies in the 2009. Approx. 250 p. 5 illus. (Advances in Mechanics and 2009. VI, 212 p. 5 illus. Hardcover History of Mathematics and Physical Sciences) Hardcover Mathematics, Volume 18) Hardcover 7 € 24,95 | £19.00 7 € 46,95 | £37.99 7 € 54,95 | £43.99 9
A. Soifer, University of Colorado, Colorado Springs, A. Soifer, University of Colorado, Colorado Springs, W. Stein, University of Washington, Seattle, WA, USA CO, USA CO, USA Elementary Number Theory: How Does One Cut a Triangle? Mathematics as Primes, Congruences, and Problem-Solving Secrets A Computational Approach This second edition, “How Does One Cut a Triangle?”, shows how different areas of math- Various elementary techniques for solving prob- ematics can be intertwined to solve a given lems in algebra, geometry, and combinatorics are problem. Soifer brings together geometry, algebra, explored in this new second edition, “Mathematics This is a textbook about classical elementary trigonometry, linear algebra, and rings in a as Problem Solving”. Each new chapter builds off number theory and elliptic curves. The first part juxtaposition of different mathematical areas that the previous one, enhancing the reader to reach discusses elementary topics such as primes, factor- enables mathematics to come alive. In the process new levels of using logic to solve problems. ization, continued fractions, and quadratic forms, the reader is given a taste of what mathematics Every topic is presented in self-contained chapters, in the context of cryptography, computation, can do and how mathematicians go about their offering classical solutions as well as Soifer’s own and deep open research problems. The second research. discoveries that he found through his problem- part is about elliptic curves, their applications to “How Does One Cut a Triangle?” contains many solving experiences. With roughly 200 different algorithmic problems, and their connections with analytical proofs and counterexamples such as a problems and multiple proofs for each, the reader problems in number theory such as Fermat’s Last pool table problem, fifty-dollar problem, five-point is challenged to approach problems from different Theorem, the Congruent Number Problem, and problem, and joint problem. By proving these angles, and in this way can experience the beauty the Conjecture of Birch and Swinnerton-Dyer. additional examples, Soifer proves that research is of mathematics. The intended audience of this book is an under- a collection of mathematical ideas that have been graduate with some familiarity with basic abstract developed throughout the course of history. Features algebra, e.g. rings, fields, and finite abelian groups. 7 Aims to develop young mathematicians’ Features problem-solving abilities 7 Inspires readers to Contents 7 Aims to inspire talented students at various explore a range of methods of solving algebraic, Preface.- Prime Numbers.- The Ring of Integers levels and other mathematicians interested in geometric, and combinatorial problems 7 Offers Modulo n.- Public-Key Cryptography.- Quadratic similar problems 7 Offers insight on different examples and practice problems 7 Engages a Reciprocity.- Continued Fractions.- Elliptic problem solving methods used to attack the general audience 7 First edition was Endorsed by Curves.- Answers and Hints.- References. problem, “How Does One Cut a Triangle?” the NCTM 7 Presents example problems and solutions as Fields of interest well as open problems 7 Engages a general audi- Contents Number Theory; Algebraic Geometry ence Preface.- Language and a Few Celebrated Ideas.- Numbers.- Algebra.- Geometry.- Combinatorial Target groups Contents Problems.- Literature. Undergraduate mathematics students, graduate Introductions.- Contents.- Preface.- Pool Table, mathematics students, mathematicians, math- Irrational Numbers, and Integral Independence.- Fields of interest ematics teachers How does One Cut a Triangle? I.- Excursions Algebra; Combinatorics; Geometry in Algebra.- How Does One Cut a Triangle? Type of publication II.- Excursion in Trigonometry.- Is There Anything Target groups Undergraduate textbook Beyond the Solution?.- Pursuit of the Best Result.- Students at various levels, educators; the general Convex Figures and Functions S(F).- Faul Erdos: public interested in the methods of mathematical Our Joint.- Convex Figures and Erdos’ Function.- problem solving Appendices.- Bibliography.- Index.- Notations. Type of publication Fields of interest Undergraduate textbook Algebra; Combinatorics; Mathematics, general
Target groups Students at various levels; general readership
Type of publication Undergraduate textbook
Mathematics Mathematics Mathematics Due February 2009 Due February 2009 Due February 2009 Originally published by Soifer, Alexander, 1990 Originally published by Soifer, Alexander, 1987 2009. Approx. 175 p. 45 illus. (Undergraduate Texts in 2nd ed. 2009. Approx. 155 p. 80 illus. Softcover 2nd ed. 2009. Approx. 130 p. 67 illus. Softcover Mathematics) Hardcover 7 approx. € 16,95 | £15.00 7 approx. € 16,95 | £15.00 7 approx. € 34,95 | £27.99 9
H. Stichtenoth, Sabanci University, Istanbul, Turkey M. Tucsnak, Université Nancy, France; G. Weiss, A. Tveito, Simula Research Laboratory, Lysaker, Tel Aviv University, Israel Norway; R. Winther, University of Oslo, Norway Algebraic Function Fields and Codes Observation and Control for Introduction to Partial Operator Semigroups Differential Equations A Computational Approach The theory of algebraic function fields has its origins in number theory, complex analysis This book studies observation and control opera- (compact Riemann surfaces), and algebraic tors for linear systems where the free evolution This is the softcover reprint of a popular book geometry. Since about 1980, function fields have of the state can be described by an operator teaching the basic analytical and computa- found surprising applications in other branches of semigroup on a Hilbert space. The emphasis is on tional methods of partial differential equations. mathematics such as coding theory, cryptography, well-posedness, observability and controllability Standard topics such as separation of variables, sphere packings and others. The main objective properties. The abstract results are supported by Fourier analysis, maximum principles, and energy of this book is to provide a purely algebraic, self- a large number of examples coming mostly from estimates are included. Prerequisites for this text contained and in-depth exposition of the theory of partial differential equations. These examples are are the very basics of calculus, linear algebra function fields. worked out in detail. This book is meant to be an and ordinary differential equations. Numerical This new edition, published in the series Graduate elementary introduction in this theory. The first methods are included in the book to show the Texts in Mathematics, has been considerably meaning of “elementary’’ is that the text is aimed significance of computations in partial differential expanded. Moreover, the present edition contains to be accessible to any reader familiar with linear equations, and to illustrate the strong interac- numerous exercises. Some of them are fairly easy algebra, calculus, the basics of Hilbert spaces and tion between mathematical theory and numerical and help the reader to understand the basic mate- differential equations. We introduce everything methods. Great care has been taken throughout rial. Other exercises are more advanced and cover needed on operator semigroups and most of the the book to seek a sound balance between the additional material which could not be included background used is summarized in the Appen- analytical and numerical techniques. The authors in the text. dices, often with proofs. The second meaning present the material at an easy pace with exercises This volume is mainly addressed to graduate of “elementary’’ is that we only cover results for and projects ranging from the straightforward to students in mathematics and theoretical computer which we can provide complete proofs. the challenging. The text would be suitable for science, cryptography, coding theory and electrical advanced undergraduate and graduate courses engineering. Features in mathematics and engineering, and it develops 7 Book is to large extent self-contained basic tools of computational science. Features 7 Attempts to unify two approaches traditionally 7 Well-established popular textbook different, one using essentially abstract functional Contents analysis and the other based on techniques coming Setting the Scene.- Two-Point Boundary Value From the contents from partial differential equations 7 Main exact Problems.- The Heat Equation.- Finite Difference 1. Foundations of the Theory of Algebraic Func- observability results are obtained by combining Schemes for the Heat Equation.- The Wave Equa- tion Fiels.- 2. Geometric Goppa Codes.- 3. Exten- functional analysis with various methods such as tion.- Maximum Principles.- Poisson’s Equation sions of Algebraic Function Fields.- 4. Differen- multipliers, Ingham-Beurling-type inequalities and in Two Space Dimensions.- Orthogonality and tials of Algebraic Function Fields.- 5. Algebraic Carleman estimates General Fourier Series.- Convergence of Fourier Function Fields over Finite Constant Fields.- 6. Series.- The Heat Equation Revisited.- Reaction- Examples of Algebraic Function Fields.- 7. More Fields of interest Diffusion Equations.- Applications of the Fourier about Geometric Goppy Codes. Systems Theory, Control; Partial Differential Transform.- References.- Index. Equations; Operator Theory Fields of interest Fields of interest Algebra; Algebraic Geometry; Data Structures, Target groups Analysis; Partial Differential Equations; Scientific Cryptology and Information Theory Graduate students, lecturers and researchers in Computing pure and applied mathematics, and in control Target groups engineering Target groups Graduate students and lecturers in mathematics Senior undergraduate and graduate students and computer science Type of publication Graduate/Advanced undergraduate textbook Type of publication Type of publication Graduate/Advanced undergraduate textbook Graduate/Advanced undergraduate textbook
Mathematics
Due December 2008 Mathematics Mathematics
Originally published in the series: Universitext Due March 2009 Due December 2008
2nd ed. 2009. Approx. 365 p. (Graduate Texts in Approx. 475 p. 2009. Approx. 475 p. (Birkhäuser 1st ed. 2004. Corr. 2nd printing 2009. XVI, 392 p. (Texts in Mathematics, Volume 254) Softcover Advanced Texts / Basler Lehrbücher) Hardcover Applied Mathematics, Volume 29) Softcover 7 € 39,95 | £31.99 7 € 59,90 | £47.99 7 approx. € 29,95 | £23.99 9
Z. Wang, University of Nebraska at Omaha, NE, USA; K. Williams, Torino, Italy (Ed.) G. J. Klir, Binghamton University, Binghamton, NY, USA Nexus Network Journal 11,1 Generalized Measure Theory Architecture and Mathematics
In celebration of the 2009 International Year This comprehensive text examines the relatively of Astronomy, this issue of the Nexus Network new mathematical area of generalized measure Journal is devoted to relationships between theory. This area expands classical measure theory astronomy, mathematics and architecture. Ancient by abandoning the requirement of additivity and cultures looked to the heavens in order to identify replacing it with various weaker requirements. timeless principles for their own creations. Know Each of these weaker requirements characterizes ledge gained in astronomy was transformed into a class of nonadditive measures. This results in culture through architecture and design. Papers new concepts and methods that allow us to deal in this issue look at how astronomy influenced with many problems in a more realistic way. For architecture and urban design. example, it allows us to work with imprecise prob- abilities. Features The exposition of generalized measure theory 7 A group of specialised research papers in the unfolds systematically. It begins with preliminaries relationships between astronomy, mathematics and new concepts, followed by a detailed treat- and architecture 7 Each research paper includes ment of important new results regarding various a bibliography for further reading 7 Authors are types of nonadditive measures and the associated from Italy, Portugal, Iran, Germany, and South integration theory. The latter involves several types Korea of integrals: Sugeno integrals, Choquet integrals, pan-integrals, and lower and upper integrals. All Fields of interest of the topics are motivated by numerous examples, Mathematics, general; Architectural History and culminating in a final chapter on applications of Theory generalized measure theory. Target groups Features Architects, mathematicians, and everyone inter- 7 Most up-to-date textbook in the field, covering ested in the subject recent applications 7 Numerous examples motivate the theory and exercises at the end of the Type of publication chapter provide practice to the student 7 Useful Contributed volume to an interdisciplinary cadre of mathematicians, engineers, computer scientists and specialists working in decision making
Fields of interest Measure and Integration; Mathematical Logic and Foundations; Systems Theory, Control
Target groups Graduate students, instructors, researchers in mathematics, engineering, and computer science
Type of publication Graduate/Advanced undergraduate textbook
Mathematics Mathematics Due December 2008 Due April 2009 2009. Approx. 415 p. 25 illus. (IFSR International Series on Systems Science and Engineering, Volume 25) 2009. Approx. 200 p. (Nexus Network Journal, Hardcover Volume 11,1) Softcover 7 € 62,95 | £49.99 7 € 79,90 | £63.99 9