t. andreescu m. arkowitz y. arlinskii b. enescu introduction to … · 2012-04-27 · dynamic...

springer.com/NEWSonline74 News 8/2011Mathematics

T. Andreescu, University of Texas, Dallas, TX, USA; B. Enescu, B.P. Hasdeu National College, Buzau, Romania

Mathematical Olympiad Treasures

This second edition of Mathematical Olympiad Treasures contains a stimulating collection of problems in geometry and trigonometry, algebra, number theory, and combinatorics. It encourages readers to think creatively about techniques and strategies for solving real-world problems, with new sections, revisions, and many more Olym-piad-like problems at various levels of difficulty. The problems are clustered by topic into three self-contained chapters.

Features 7 Second edition includes new sections, revi-sions, and many more Olympiad-like problems at various levels of difficulty 7 Aims at building a bridge between ordinary high school exercises and more sophisticated, intricate and abstract concepts and problems in undergraduate math-ematics 7 Contains a stimulating collection of problems in the subjects of algebra, geometry and trigonometry, number theory and combina-torics 7 Should benefit undergraduate students, advanced high school students, instructors, and coaches 7 Encourages readers to think creatively about techniques and strategies for solving real-world problems

Contents I Problems.- 1 Algebra.- 2 Geometry and Trigo-nometry.- 3 Number Theory and Combinatorics.- II Solutions.- 4 Algebra.- 5 Geometry and Trigo-nometry.- 6 Number Theory and Combinatorics

Fields of interestCombinatorics; Number Theory; Algebraic Geometry

Target groupsLower undergraduate

Type of publicationUndergraduate textbook

M. Arkowitz, Dartmouth College, Hanover, NH, USA

Introduction to Homotopy Theory

This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows: Basic Homotopy; H-spaces and co-H-spaces; fibrations and cofibrations; exact sequences of homotopy sets, actions, and coactions; homo-topy pushouts and pullbacks; classical theorems, including those of Serre, Hurewicz, Blakers-Massey, and Whitehead; homotopy Sets; homotopy and homology decompositions of spaces and maps; and obstruction theory. The underlying theme of the entire book is the Eckmann-Hilton duality theory.

Features 7 Carefully written treatment of a basic subject by a research worker in the field 7 Provides motivation with many illustrations and exercises 7 Exposition moves at a moderate pace, even in the later chapters 7 Differs from other texts on homotopy theory, in that the unifying theme of the entire book is the Eckmann-Hilton duality theory 7 Several appendices provide background information

Contents 1 Basic Homotopy.- 2 H-Spaces and Co-H-Spaces.- 3 Cofibrations and Fibrations.- 4 Exact Sequences.- 5 Applications of Exactness.- 6 Homo-topy Pushouts and Pullbacks.- 7 Homotopy and Homology Decompositions.- 8 Homotopy Sets.- 9 Obstruction Theory.- A Point-Set Topology.- B The Fundamental Group.- C Homology and Cohomology.- D Homotopy Groups and the n-Sphere.- E Homotopy Pushouts and Pullbacks.- F Categories and Functors.- Hints to Some of the Exercises.- References.- Index.-

Fields of interestAlgebraic Topology

Target groupsGraduate

Type of publicationGraduate/Advanced undergraduate textbook

Y. Arlinskii, East Ukrainian National University, Lugansk, Ukraine; S. Belyi, Troy University, Troy, AL, USA; E. Tsekanovskii, Niagara University, NY, USA

Conservative Realizations of Herglotz-Nevanlinna Functions

This book is devoted to conservative realizations of various classes of Stieltjes, inverse Stieltjes, and general Herglotz-Nevanlinna functions as impedance functions of linear systems. The main feature of the monograph is a new approach to the realization theory profoundly involving devel-oped extension theory in triplets of rigged Hilbert spaces and unbounded operators as state-space operators of linear systems.

Features 7 Only book covering this spectrum of prob-lems and methods of the Herglotz-Nevanlinna functions realization 7 First comprehensive coverage of the realization theory for Herglotz-Nevanlinna matrix functions 7 Contains useful and important applications

Contents Preface.- 1 Extensions of Symmetric Operators.- 2 Rigged Hilbert Spaces.- 3 Bi-extensions of Closed Symmetric Operators.-.4 Quasi-self-adjoint Extensions.- 5 The Livsic Canonical Systems with Bounded Operators.- 6 Herglotz-Nevanlinna func-tions and Rigged Canonical Systems.- 7 Classes of realizable Herglotz-Nevanlinna functions.- 8 Normalized Canonical Systems.- 9 Canonical L-systems with Contractive and Accretive Opera-tors.- 10 Systems with Schrödinger operator.- 11 Non-self-adjoint Jacobi Matrices and System Interpolation.- 12 Non-canonical Systems.- Notes and Comments.- References.- Index.

Fields of interestOperator Theory; Mathematical Methods in Physics

Target groupsResearch

Type of publicationMonograph

Due October 2011

2nd Edition. 2012. X, 324 p. 93 illus. Hardcover

7 € 44,95 | £40.997 * € (D) 48,10 | € (A) 49,45 | sFr 64,50ISBN 978-0-8176-8252-1

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Due September 2011

2011. XIII, 344 p. 333 illus. (Universitext) Softcover

7 € 59,95 | £53.997 * € (D) 64,15 | € (A) 65,95 | sFr 86,00ISBN 978-1-4419-7328-3

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Available

2011. XVIII, 528 p. 21 illus., 1 in color. Hardcover

7 € 99,95 | £90.007 * € (D) 106,95 | € (A) 109,95 | sFr 143,50ISBN 978-3-7643-9995-5

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www.springer.com/978-0-8176-8252-1



springer.com/NEWSonline 75News 8/2011 Mathematics

L. Barreira, Instituto Superior Técnico, Lisbon, Portugal

Thermodynamic Formalism and Applications to Dimension Theory

This self-contained monograph presents a unified exposition of the thermodynamic formalism and some of its main extensions, with emphasis on the relation to dimension theory and multifractal analysis of dynamical systems.

Features 7 First comprehensive exposition of several main extensions of the thermodynamic formalism. 7 The emphasis of the text is on the relation to dimension theory and multifractal analysis. 7 Includes a discussion of very recent results in the area as well as some open problems. 7 The text is self-contained and all the results are included with detailed proofs.

Contents Preface.- 1 Introduction.- I Classical Ther-modynamic Formalism.- 2 Thermodynamic Formalism: Basic Notions.- 3 The Case of Symbolic Dynamics.- II Nonadditive Thermodynamic Formalism.- 4 Nonadditive Thermodynamic Formalism.- 5 Dimension Estimates for Repel-lers.- 6 Dimension Estimates for Hyperbolic Sets.- III Subadditive Thermodynamic Formalism.- 7 Asymptotically Subadditive Sequences.- 8 Limit Sets of Geometric Constructions.- 9 Entropy Spectra.- IV Almost Additive Thermodynamic Formalism.- 10 Almost Additive Sequences.- 11 Nonconformal Repellers.- 12 Multifractal Analysis.- Bibliography.

Field of interestDynamical Systems and Ergodic Theory



P. Boito, Université de Limoges, France

Structured Matrix Based Methods for Approximate Polynomial GCD

Defining and computing a greatest common divisor of two polynomials with inexact coeffi-cients is a classical problem in symbolic-numeric computation. The first part of this book reviews the main results that have been proposed so far in the literature. As usual with polynomial compu-tations, the polynomial GCD problem can be expressed in matrix form: the second part of the book focuses on this point of view and analyses the structure of the relevant matrices, such as Toeplitz, Toepliz-block and displacement structures. New algorithms for the computation of approximate polynomial GCD are presented, along with exten-sive numerical tests.

Features 7 Topics situated at the crossroads between two fields of increasing interest to the mathematical community: symbolic-numeric polynomial computation and structured numerical linear algebra 7 Survey of the main tools and tech-niques used in either domain 7 State-of-the-art methods that exploit matrix structure to improve the performance of polynomial computations

Contents i. Introduction.- ii. Notation.- 1. Approximate polynomial GCD.- 2. Structured and resultant matrices.- 3. The Euclidean algorithm.- 4. Matrix factorization and approximate GCDs.- 5. Opti-mization approach.- 6. New factorization-based methods.- 7. A fast GCD algorithm.- 8. Numerical tests.- 9. Generalizations and further work.- 10. Appendix A: Distances and norms.- 11. Appendix B: Special matrices.- 12. Bibliography.- 13. Index.

Field of interestAlgebra



V. G. Boltyanski, CIMAT, Guanajuato, México; A. S. Poznyak, CINVESTAV, Instituto Politécnico Nacional, México D.F., México

The Robust Maximum PrincipleTheory and Applications

Contents Preface.- Introduction.- I Topics of Classical Optimal Control.- 1 Maximum Principle.- 2 Dynamic Programming.- 3 Linear Quadratic Optimal Control.- 4 Time-Optimization Problem.- II Tent Method.- 5 Tent Method in Finite Dimen-sional Spaces.- 6 Extrenal Problems in Banach Space.- III Robust Maximum Principle for Deter-ministic Systems.- 7 Finite Collection of Dynamic Systems.- 8 Multi-Model Bolza and LQ-Problem.- 9 Linear Multi-Model Time-Optimization.- 10 A Measured Space as Uncertainty Set.- 11 Dynamic Programming for Robust Optimization.- 12 Min-Max Sliding Mode Control.- 13 Multi-model Differential Games.- IV Robust Maximum Principle for Stochastic Systems.- 14 Multi-Plant Robust Control.- 15 LQ-Stochastic Multi-Model Control.- 16 A Compact as Uncertainty Set.- References.- Index.

Fields of interestSystems Theory, Control; Control; Calculus of Variations and Optimal Control; Optimization



Due September 2011

2011. XII, 292 p. (Progress in Mathematics, Volume 294) Hardcover

7 approx. € 89,95 | £81.007 approx. * € (D) 96,25 | € (A) 98,95 | sFr 129,50ISBN 978-3-0348-0205-5

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Available

Only available in print

2011. Approx. 250 p. (Publications of the Scuola Normale Superiore / Theses (Scuola Normale Superiore), Volume 15) Softcover

7 € 18,00 | £15.997 * € (D) 19,26 | € (A) 19,80 | sFr 30,00ISBN 978-88-7642-380-2

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Due November 2011

2012. XXX, 494 p. 36 illus. (Systems & Control: Founda-tions & Applications) Hardcover

7 € 99,95 | £90.007 * € (D) 106,95 | € (A) 109,95 | sFr 143,50ISBN 978-0-8176-8151-7

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A. Bonfiglioli, R. Fulci, University of Bologna, Italy

Topics in Noncommutative AlgebraThe Theorem of Campbell, Baker, Hausdorff and Dynkin

Features 7 A full historical treatise on the early proofs of the Theorem of Campbell, Baker, Hausdorff and Dynkin is presented here for the first time 7 The book is completely self-contained and accessible to all audiences 7 The book contains the proofs of all the algebraic prerequisites and can also provide a textbook for topics in non-commutative algebra

Contents 1 Historical Overview.- Part I Algebraic Proofs of the CBHD Theorem.- 2 Background Algebra.- 3 The Main Proof of the CBHD Theorem.- 4 Some ‘Short’ Proofs of the CBHD Theorem.- 5 Conver-gence and Associativity for the CBHD Theorem.- 6 CBHD, PBW and the Free Lie Algebras.- Part II Proofs of the Algebraic Prerequisites.- 7 Proofs of the Algebraic Prerequisites.- 8 Construction of Free Lie Algebras.- 9 Formal Power Series in One Indeterminate.- 10 Symmetric Algebra.

Fields of interestTopological Groups, Lie Groups; History of Mathematical Sciences; Non-associative Rings and Algebras



M. Bounkhel, King Saud University, Riyadh, Saudi Arabia

Regularity Concepts in Nonsmooth AnalysisTheory and Applications

The results presented in this book are a product of research conducted by the author independently and in collaboration with other researchers in the field. In this light, this work encompasses the most recent collection of various concepts of regularity and nonsmooth analysis into one monograph. The first part of the book attempts to present an accessible and thorough introduction to nons-mooth analysis theory. Main concepts and some useful results are stated and illustrated through examples and exercises. The second part gathers the most prominent and recent results of various regularity concepts of sets, functions, and set-valued mappings in nonsmooth analysis.

Features 7 Didactic approach treats various concepts of regularity in smooth variational analysis and prepares the reader for future research 7 Unique presentation in book form discusses different concepts of regularity and their relationships 7 Thorough introduction to nonsmooth analysis is complemented by a variety of results and appli-cations

Contents 1. Nonsmooth Concepts.- 2. Regularity.- 3. Regu-larity of Functions.- 4. Regularity of Set-Valued Mappings.- 5. First Order Differential Inclu-sions.- 6. Second Order Differential Inclusions.- 7. Quasi-Variational Inequalities.- 8. Time Depen-dent Quasi-Variational Inequalities.- 9. Economic Problems and Equilibrium Theory.- Index.

Fields of interestOptimization; Calculus of Variations and Optimal Control; Optimization



A. Brudnyi, University of Calgary, AB, Canada; Y. Brudnyi, Technion - Israel Institute of Technology, Haifa, Israel

Methods of Geometric Analysis in Extension and Trace ProblemsVolume 1

The book presents a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori differential structure (Whitney problems). The account covers development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific these problems have been from the very beginning a powerful source of ideas, concepts and methods that essentially influ-enced and in some cases even transformed consid-erable areas of analysis. Aside from the material linked by the aforementioned problems the book also is unified by geometric analysis approach used in the proofs of basic results.

Features 7 Covers the development of the area from the first half of the 20th century to the last decade 7 Well suited for self-study 7 Necessary facts presented mostly with detailed proofs

Contents Preface.- Basic Terms and Notation.- Part 1. Classical Extension-Trace Theorems and Related Results.- Chapter 1. Continuous and Lipschitz Functions.- Chapter 2. Smooth Functions on Subsets of Rn.- Part 2. Topics in Geometry of and Analysis on Metric Spaces.- Chapter 3. Topics in Metric Space Theory.- Chapter 4. Selected Topics in Analysis on Metric Spaces.- Chapter 5. Lipschitz Embedding and Selections.- Bibliography.- Index.

Fields of interestFunctional Analysis



Due October 2011

2011. XXII, 498 p. 3 illus. (Lecture Notes in Mathematics, Volume 2034) Softcover

7 € 89,95 | £81.007 * € (D) 96,25 | € (A) 98,95 | sFr 129,00ISBN 978-3-642-22596-3

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Due December 2011

2011. XVI, 262 p. 15 illus., 14 in color. (Springer Optimiza-tion and Its Applications, Volume 59) Hardcover

7 € 79,95 | £72.007 * € (D) 85,55 | € (A) 87,95 | sFr 106,50ISBN 978-1-4614-1018-8

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Due October 2011

2012. XX, 580 p. (Monographs in Mathematics, Volume 102) Hardcover


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A. Brudnyi, University of Calgary, AB, Canada; Y. Brudnyi, Technion - Israel Institute of Technology, Haifa, Israel

Methods of Geometric Analysis in Extension and Trace ProblemsVolume 2

The book presents a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori differential structure (Whitney problems). The account covers development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific these problems have been from the very beginning a powerful source of ideas, concepts and methods that essentially influ-enced and in some cases even transformed consid-erable areas of analysis. Aside from the material linked by the aforementioned problems the book also is unified by geometric analysis approach used in the proofs of basic results.

Features 7 Covers the development of the area from the first half of the 20th century to the last decade 7 Well suited for self-study 7 Necessary facts presented mostly with detailed proofs

Contents Part 3. Lipschitz Extensions from Subsets of Metric Spaces.- Chapter 6. Extensions of Lipschitz Maps.- Chapter 7. Simultaneous Lipschitz Exten-sions.- Chapter 8. Linearity and Nonlinearity.- Part 4. Smooth Extension and Trace Problems for Functions on Subsets of Rn.- Chapter 9. Traces to Closed Subsets: Criteria, Applications.- Chapter 10. Whitney Problems.- Bibliography.- Index.

Fields of interestFunctional Analysis



J. Bustamante, Benemerita Univesidad Autonoma de Puebla, Mexico

Algebraic Approximation: A Guide to Past and Current Solutions

This book contains an exposition of several results related with direct and converse theorems in the theory of approximation by algebraic polyno-mials in a finite interval. In addition, some facts concerning trigonometric approximation that are necessary for motivation and comparisons are included. The selection of papers that are referenced and discussed document some trends in polynomial approximation from the 1950s to the present day.

Features 7 Puts together different known solutions to problems in algebraic approximation not collected in any other text book 7 Helps finding the correct references for a specific result 7 Compre-hensive bibliographic references give a unique understanding of the evolution of approximation theory

Contents Preface.- Some notes on trigonometric approxi-mation.- The end points effect.- Looking for new moduli.- Exact estimates and asymptotic.- Construction of special operators.- Bibliography.

Fields of interestApproximations and Expansions



L. A. Caffarelli, University of Texas, Austin, TX, USA; F. Golse, Ecole Polytechnique, Palaiseau, France; Y. Guo, Brown University, Providence, RI, USA; C. E. Kenig, University of Chicago, Chicago, IL, USA; A. Vasseur, University of Texas, Austin, TX, USA

Nonlinear Partial Differential Equations

Editorial coordination: X. Cabré, Universitat Politèc-nica de Catalunya; J. Soler, Universidad de Granada, Spain

The book covers several topics of current interest in the field of nonlinear partial differential equa-tions and their applications to the physics of continuous media and particle interactions.

Features 7 Describes in a careful and expository manner some powerful methods from recent top research articles in partial differential equa-tions. 7 Contains recent new applications of several classical tools to macroscopic problems (continuous media) and microscopic problems (particle interactions). 7 Describes in an elegant way the basis and most recent advances about the quasigeostrophic equation, integral diffusions, periodic Lorentz gas, Boltzmann equation, and critical dispersive nonlinear Schrödinger and wave equations

Contents Foreword. 1 The De Giorgi Method for Nonlocal Fluid Dynamics.- 2 Recent Results on the Peri-odic Lorentz Gas.- 3 The Boltzmann Equation in Bounded Domains.- 4 The Concentration-Compactness/Rigidity Method for Critical Disper-sive and Wave Equations.

Fields of interestPartial Differential Equations; Mathematical Physics



Due October 2011

2011. XV, 415 p. (Monographs in Mathematics, Volume 103) Hardcover


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Due September 2011

2011. 210 p. (Frontiers in Mathematics) Softcover


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Due October 2011

2011. VIII, 150 p. 16 illus. in color. (Advanced Courses in Mathematics - CRM Barcelona) Softcover


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L. Debnath, University of Texas, Edinburg, TX, USA

Nonlinear Partial Differential Equations for Scientists and Engineers

The revised and enlarged third edition of this successful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied and updated applications.

Features 7 Extraordinary breadth of coverage 7 Highly systematic presentation 7 Hundreds of examples and exercises, with hints, selected solutions, and a complete solutions manual for instructors 7 Useful for students and researchers alike in not only mathematics, but also engineering, physics, and other natural sciences

Contents Preface to the Third Edition.- Preface.- Linear Partial Differential Equations.- Nonlinear Model Equations and Variational Principles.- First-Order, Quasi-Linear Equations and Method of Characteristics.- First-Order Nonlinear Equations and Their Applications.- Conservation Laws and Shock Waves.- Kinematic Waves and Real-World Nonlinear Problems.- Nonlinear Dispersive Waves and Whitham’s Equations.- Nonlinear Diffusion-Reaction Phenomena.- Solitons and the Inverse Scattering Transform.- The Nonlinear Schroed-inger Equation and Solitary Waves.- Nonlinear Klein--Gordon and Sine-Gordon Equations.- Asymptotic Methods and Nonlinear Evolution Equations.- Tables of Integral Transforms.- Answers and Hints to Selected Exercises.- Bibliog-raphy.- Index.

Fields of interestPartial Differential Equations; Applications of Mathematics; Theoretical, Mathematical and Computational Physics



M. Emmer, University “La Sapienza”, Rome, Italy (Ed.)

Mathematics and Culture IIIThis work contains the proceedings of the “Math-ematics and Culture” conference held in Venice in March 2002. The conference aims to act as a bridge across the various aspects of human knowledge. While keeping mathematics as its core, it is aimed at anyone endowed with cultural curiosity and interests, whether within or (even more so) outside mathematics. This volume therefore covers music, cinema, art, theatre and literature, with topics ranging from Tibet to comics.

Features 7 Research and cultural mathematics highlights from a well-known conference 7 Covers interac-tion of mathematics and art 7 Best conference on links between general culture and mathematics

Contents I. Mathematicians.- II. Mathematics and Music.- III. Mathematics and Art.- IV. Mathematics and Cinema.- V. Mathematics in the Movies.- VI. Peking 2002.- VII. Mathematics and Theatre.- VIII. Mathematics and Comic Strips

Fields of interestMathematics, general; Visualization; Applications of Mathematics



F. Forstnerič, University of Ljubljana, Slovenia

Stein Manifolds and Holomorphic MappingsThe Homotopy Principle in Complex Analysis

The main theme of this book is the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds. The book contains the first complete account of Oka-Grauert theory and its modern extensions, initiated by Mikhail Gromov and developed in the last decade by the author and his collaborators. Included is the first systematic presentation of the theory of holomorphic auto-morphisms of complex Euclidean spaces, a survey on Stein neighborhoods, connections between the geometry of Stein surfaces and Seiberg-Witten theory, and a wide variety of applications ranging from classical to contemporary.

Features 7 First systematic presentation of the theory of holomorphic automorphisms of complex Euclidean spaces 7 First complete account of Oka-Grauert theory and its modern extensions 7 Contains a wide variety of applications ranging from classical to contemporary

Contents Preliminaries. - Stein Manifolds. - Stein Neighbor-hoods and Holomorphic Approximation. - Auto-morphisms of Complex Euclidean Spaces. - Oka Manifolds. - Elliptic Complex Geometry and Oka Principle. - Applications. - Embeddings, Immer-sions and Submersions.- Topological Methods in Stein Geometry. - References. - Index.

Fields of interestReal Functions; Functions of a Complex Variable



Due November 2011

3rd Edition. 2012. XXVI, 894 p. 103 illus. Hardcover

7 € 69,95 | £62.997 * € (D) 74,85 | € (A) 76,95 | sFr 100,50ISBN 978-0-8176-8264-4

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Due October 2011


Original Italian edition published by Springer-Verlag Italia, 2003

2011. 280 p. 128 illus., 13 in color. With CD-ROM. Hardcover

7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 72,00ISBN 978-3-540-34259-5

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Due August 2011

2011. XII, 492 p. 27 illus. (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics, Volume 56) Hardcover

7 € 139,95 | £126.007 * € (D) 149,75 | € (A) 153,94 | sFr 201,00ISBN 978-3-642-22249-8

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M. Ghergu, University College Dublin, Ireland; V. D. Rӑdulescu, Romanian Academy, Bucharest, Romania

Nonlinear PDEsMathematical Models in Biology, Chemistry and Population Genetics

The emphasis throughout the present volume is on the practical application of theoretical math-ematical models helping to unravel the underlying mechanisms involved in processes from math-ematical physics and biosciences.

Features 7 Foreword by Viorel Barbu 7 Methods developed can be applied to large classes of models arising in applications 7 Interdisciplinary dialogue between mathematics, biology, chemistry and population genetics

Contents Viorel Barbu: Foreword.- 1.Overview of merhods in PDEs.- 2.Liouville Type Theorems for Elliptic Operators in Divergence Form.- 3.Blow-up Boundary Solutions.- 4.Singular Lane-Emden-Fowler Equations and Systems.- 5.Singular Elliptic Inequalities in Exterior Domains.- 6.Two Quasilinear Elliptic Problems.- 7.Some Classes of Polyharmonic Problems.- 8.Large Time Behavior of Solutions for Degenerate Parabolic Equa-tions.- 9.Rection-Diffusion Systems in Chem-istry.- 10.Pattern Formation and Gierer-Meinhardt Model.- Appendices.- References.- Index.

Fields of interestPartial Differential Equations; Calculus of Varia-tions and Optimal Control; Optimization; Applica-tions in the Physical Sciences



S. J. Gustafson, University of British Columbia, Vancouver, BC, Canada; I. M. Sigal, University of Toronto, ON, Canada

Mathematical Concepts of Quantum Mechanics

Features 7 A very readable introduction to modern math-ematical topics in quantum mechanics 7 Solves the problem of how to teach quantum mechanics to mathematically oriented students in an optimal way 7 Shows how the mathematical treatment of quantum mechanics brings insights to physics 7 Useful guide to the literature

Contents 1 Physical Background.- 2 Dynamics.- 3 Observ-ables.- 4 Quantization.- 5 Uncertainty Principle and Stability of Atoms and Molecules.- 6 Spectrum and Dynamics.- 7 Special Cases.- 8 Bound States and Variational Principle.- 9 Scattering States.- Existence of Atoms and Molecules.- 11 Pertur-bation Theory: Feshbach-Schur Method.- 12 General Theory of Many-particle Systems.- 13 Self-consistent Approximations.- 14 The Feynman Path Integral.- 15 Quasi-classical Analysis.- 16 Resonances.- 17 Quantum Statistics.- 18 The Second Quantization.- 19 Quantum Electro-Magnetic Field – Photons.- 20 Standard Model of Non-relativistic Matter and Radiation.- 21 Theory of Radiation.- 22 Renormalization Group.- 23 Mathematical Supplement: Spectral Analysis.- 24 Mathematical Supplement: The Calculus of Varia-tions.- 25 Comments on Literature, and Further Reading.- References.- Index

Fields of interestFunctional Analysis; Theoretical, Mathematical and Computational Physics; Quantum Physics



K. Hentschel, Universität Stuttgart, Germany

Physics and National SocialismAn Anthology of Primary Sources Translated by Ann M. Hentschel

Translated by: A. M. Hentschel, Stuttgart, Germany

This anthology of primary sources is a collection of 121 documents in English translation portraying the role of physics, both perceived and actual, in the Nazi state. These texts were written predomi-nantly by influential German scientists, particu-larly physicists, both inside and outside Germany in the period from 1933 to 1945. The semipopular articles, private correspondence, and official memoranda selected for the volume reflect the contemporary developments in science as well as the change in political climate and working condi-tions after the National Socialists’ rise to power.

Features 7 Summary of the historiography of physics in the Third Reich 7 Survey of the variety of opinions and events 7 Essential reference to historians of science, especially physics and math-ematics 7 Includes an extensive bibliography of 969 items

Contents Introduction.- 1 Aim and General Description of the Anthology.- 2 Notes on the Historiography of National Socialism.- 3 The Impact of Nazi Science Policy on Physics Instruction and Research.- 4 Emigration Research.- 5 Physics in Nazi Germany.- 6 Style and Rhetoric.- 7 The Text.- I Controversies Prior to 1933.- II After the Nazi Seizure of Power.- III The Ideological Schism: 1936-1939.- IV Physics at War: 1939-1945.- V The Legacy of National Socialism.- Appendix.- Bibliography.- Name Index.

Fields of interestMathematics, general; Physics, general; Chemistry/Food Science, general



Due October 2011

2011. XVIII, 397 p. 10 illus., 4 in color. (Springer Mono-graphs in Mathematics) Hardcover

7 € 89,95 | £81.007 * € (D) 96,25 | € (A) 98,95 | sFr 129,00ISBN 978-3-642-22663-2

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Due September 2011

2nd Edition. 2011. XIV, 376 p. 37 illus., 1 in color. (Universitext) Softcover

7 € 59,95 | £53.997 * € (D) 64,15 | € (A) 65,95 | sFr 86,00ISBN 978-3-642-21865-1

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Due August 2011

Reprint of the 1996 Edition. 1996. CCVI, 406 p. 30 illus. (Modern Birkhäuser Classics) Softcover

7 € 64,95 | £58.997 * € (D) 69,50 | € (A) 71,45 | sFr 93,50ISBN 978-3-0348-0202-4

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M. Hindry, Université Paris 7 Denis Diderot, Paris, France

ArithmeticsNumber theory is a branch of mathematics which draws its vitality from a rich historical back-ground. It is also traditionally nourished through interactions with other areas of research, such as algebra, algebraic geometry, topology, complex analysis and harmonic analysis. More recently, it has made a spectacular appearance in the field of theoretical computer science and in questions of communication, cryptography and error-correcting codes. Providing an elementary intro-duction to the central topics in number theory, this book spans multiple areas of research. The first part corresponds to an advanced undergraduate course. All of the statements given in this part are of course accompanied by their proofs, with perhaps the exception of some results appearing at the end of the chapters. A copious list of exercises, of varying difficulty, are also included here. The second part is of a higher level and is relevant for the first year of graduate school.

Features 7 Explores the multi-faceted nature of number theory, spanning several areas of research in one text 7 Begins at undergraduate level and takes the reader through to graduate level 7 Includes recent proofs, such as the polynomial primality algorithm

Contents Finite Structures.- Applications: Algorithms, Primality and Factorization, Codes.- Algebra and Diophantine Equations.- Analytic Number Theory.- Elliptic Curves.- Developments and Open Problems.- Factorization.- Elementary Projective Geometry.- Galois Theory

Fields of interestNumber Theory; Algebra; Algebraic Geometry



A. Holme, University of Bergen, Norway

A Royal Road to Algebraic Geometry

This book is about modern algebraic geometry.

Features 7 Compact exposition: Self contained introduc-tion to algebraic curves in 5 chapters, complete exposition of foundations from category theory in 3 chapters and modern algebraic geometry in 14 chapters 7 Detailed exposition: Proofs, or the essential parts of proofs, are included for all major theorems given 7 Numerous illustrations

Contents Part I Curves: 1 Affine and Projective Space.- 2 Curves in A2 k and in P2.- 3 Higher Geometry in the Projective Plane.- 4 Plane Curves and Algebra.- 5 Projective Varieties in PNk.- Part II Introduction to Grothendieck’s Theory of Schemes: 6 Categories and Functors.- 7 Constructions and Representable Functors.- 8 Abelian Categories.- 9 The Concept of Spec(A).- 10 The Category of Schemes.- 11 Properties of Morphisms of Schemes.- 12 Modules, Algebras and Bundles on a Scheme.- 13 More Properties of Morphisms, Scheme Theoretic Image and the “Sorite”.- 14 Projective Schemes and Bundles.- 15 Further Properties of Morphisms.- 16 Conormal Sheaf and Projective Bundles.- 17 Cohomology Theory on Schemes.- 18 Intersection Theory.- 19 Characteristic Classes in Algebraic Geometry.- 20 The Riemann-Roch Theorem.- 21 Some Basic constructions in the category of projective kvarieties.- 22 More on Duality.- Refer-ences.- Index

Fields of interestAlgebraic Geometry; Category Theory, Homo-logical Algebra; Geometry



N. Jeevanjee, University of California, Berkeley, CA, USA

An Introduction to Tensors and Group Theory for Physicists

This title provides a thorough but clear study of tensors and groups and their role in theoretical physics and applied mathematics. In particular, it aims to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Linking the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, An Introduction to Tensors and Group Theory for Physicists is a valuable addition to the literature on tensors and group theory.

Features 7 Ideal for self-study or for use in the class-room 7 Includes many physical applications, particularly in quantum physics and relativity 7 Provides ample exercises for practice of the definitions and techniques

Contents Some Mathematical Shorthand.- Dirac Dictionary.- 1 A Quick Introduction to Tensors.- 2 Vector Spaces.- 3 Tensors.- 4 Groups, Lie Groups, and Lie Algebras.- 5 Basic Representation Theory.- 6 The Winger-Echart Theorem and Other Applica-tions.- Complexifications of Real Lie Algebras and the Tensor Product Decomposition of sl(2,C)R.- References.- Index.

Fields of interestMathematical Physics; Mathematical Methods in Physics; Linear and Multilinear Algebras, Matrix Theory



Due September 2011

Translation from the French language edition: ‘Arith-métique’ by Marc Hindry Copyright © 2008 Calvage et Mounet, France

2012. XVIII, 322 p. 3 illus. (Universitext) Softcover

7 € 59,95 | £39.997 * € (D) 64,15 | € (A) 65,95 | sFr 86,00ISBN 978-1-4471-2130-5

9<HTMEPH=bcbdaf>

Due November 2011

2011. XIV, 350 p. 26 illus. Hardcover

7 € 59,95 | £53.997 * € (D) 64,15 | € (A) 65,95 | sFr 86,00ISBN 978-3-642-19224-1

9<HTOGPC=bjcceb>

Due October 2011


7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 72,00ISBN 978-0-8176-4714-8

9<HTLIMH=gehbei>





A. Joseph, Weizmann Institute, Rehovot, Israel; A. Melnikov, University of Haifa, Israel; I. Penkov, Jacobs University, Bremen, Germany (Eds.)

Highlights in Lie Algebraic Methods

This volume consists of expository and research articles that highlight the various Lie algebraic methods used in mathematical research today. Key topics discussed include spherical varieties, Littelmann Paths and Kac–Moody Lie algebras, modular representations, primitive ideals, repre-sentation theory of Artin algebras and quivers, Kac–Moody superalgebras, categories of Harish–Chandra modules, cohomological methods, and cluster algebras.

Features 7 Consists of invited contributions highlighting recent developments in Lie algebraic methods 7 Self-contained volume 7 Written by leading experts in their respective fields

Contents Preface.- Part I: The Courses.- 1 Spherical Vari-eties.- 2 Consequences of the Littelmann Path Model for the Structure of the Kashiwara B(∞) Crystal.- 3 Structure and Representation Theory of Kac–Moody Superalgebras.- 4 Categories of Harish–Chandra Modules.- 5 Generalized Harish–Chandra Modules.- Part II: The Papers.- 6 B-Orbits of 2-Nilpotent Matrices.- 7 The Weyl Denominator Identity for Finite-Dimensional Lie Superalge-bras.- 8 Hopf Algebras and Frobenius Algebras in Finite Tensor Categories.- 9 Mutation Classes of 3 x 3 Generalized Cartan Matrices.- 10 Contractions and Polynomial Lie Algebras.

Fields of interestTopological Groups, Lie Groups; Category Theory, Homological Algebra; General Algebraic Systems


Type of publicationContributed volume

D. Joyner, US Naval Academy, Annapolis, MD, USA; J. Kim, University of Louisville, KY, USA

Selected Unsolved Problems in Coding Theory

This original monograph investigates several unsolved problems that currently exist in coding theory. A highly relevant branch of mathematical computer science, the theory of error-correcting codes is concerned with reliably transmitting data over a ‘noisy’ channel. Despite its fairly long history and consistent prominence, the field still contains interesting problems that have resisted solution by some of the most prominent mathematicians of recent decades. Employing SAGE—a free open-source mathematics software system—to illustrate ideas, this book is intended for graduate students and researchers in algebraic coding theory, especially those who are interested in finding some current unsolved problems. Famil-iarity with concepts in algebra, number theory, and modular forms is assumed.

Features 7 SAGE, a free open-source mathematics software system, is used with concrete examples in order to emphasize the computational aspects of coding theory 7 Introduces and explores unsolved open problems in an effort to illuminate the fundamentals of coding theory and stimulate further research 7 Appeals to academia and industry with real-world applications in electrical engineering and digital communication

Contents Preface.- Background.- Codes and Lattices.- Kittens and Blackjack.- RH and Coding Theory.- Hyperelliptic Curves and QR Codes.- Codes from Modular Curves.- Appendix.- Bibliography.- Index.

Fields of interestCoding and Information Theory; Signal, Image and Speech Processing



J. Kąkol, A. Mickiewicz University, Poznan, Poland; W. Kubiś, Jan Kochanowski University, Kielce, Poland; M. López-Pellicer, University of València, Valencia, Spain

Descriptive Topology in Selected Topics of Functional Analysis

Features 7 Presents numerous results that have previously only appeared in journal publications 7 Includes several newly developed and unpublished results 7 Can serve a supplementary text in course focusing on selected topics in functional analysis, set topology, or the theory or functional spaces 7 This is the first monograph to approach the topic of linear functional equations from the perspective of descriptive topology

Contents Preface.- 1. Overview.- 2. Elementary Facts about Baire and Baire-Type Spaces.- 3. K-analytic and quasi-Suslin Spaces.- 4. Web-Compact Spaces and Angelic Theorems.- 5. Strongly Web-Compact Spaces and a Closed Graph Theorem.- 6. Weakly Analytic Spaces.- 7. K-analytic Baire Spaces.- 8. A Three-Space Property for Analytic Spaces.- 9. K-analytic and Analytic Spaces Cp(X).- 10. Precompact sets in (LM)-Spaces and Dual Metric Spaces.- 11. Metrizability of Compact Sets in the Class G.- 12. Weakly Realcompact Locally Convex Spaces.- 13. Corson’s Propery (C) and tight-ness.- 14. Fréchet-Urysohn Spaces and Groups.- 15. Sequential Properties in the Class G.- 16. Tightness and Distinguished Fréchet Spaces.- 17. Banach Spaces with Many Projections.- 18. Spaces of Continuous Functions Over Compact Lines.- 19. Compact Spaces Generated by Retractions.- 20. Complementably Universival Banach Space.- Index.

Fields of interestFunctional Analysis; Topology; Special Functions



Due December 2011

2012. XIV, 246 p. 2 illus. (Progress in Mathematics, Volume 295) Hardcover

7 € 79,95 | £72.007 * € (D) 85,55 | € (A) 87,95 | sFr 115,00ISBN 978-0-8176-8273-6

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Due October 2011

2011. XII, 248 p. 17 illus. (Applied and Numerical Harmonic Analysis) Hardcover

7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 72,00ISBN 978-0-8176-8255-2

9<HTLIMH=gicffc>

Due October 2011

2011. XIV, 482 p. (Developments in Mathematics, Volume 24) Hardcover

7 € 119,95 | £108.007 * € (D) 128,35 | € (A) 131,95 | sFr 172,00ISBN 978-1-4614-0528-3

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D. Klyushin, S. Lyashko, D. Nomirovskii, Y. Petunin, V. Semenov, Kyiv National Taras Shevchenko Univer-sity, Ukraine

Generalized Solutions of Operator Equations and Extreme Elements

Abstract models for many problems in science and engineering take the form of an operator equation. The resolution of these problems often requires determining the existence and uniqueness of solu-tions to these equations. “Generalized Solutions of Operator Equations and Extreme Elements” presents recently obtained results in the study of the generalized solutions of operator equations and extreme elements in linear topological spaces. The presented results offer new methods of identifying these solutions and studying their properties.

Features 7 Contains recently obtained results in linear operator theory with applications to optimal control theory 7 Provides new methods of iden-tifying solutions of linear and nonlinear operator equations 7 Can serve as a text in graduate courses and seminars in functional analysis and optimal control theory

Contents Preface.- 1. Fundamental notions, general and auxiliary facts.- 2. Simplest schemes of generalized solution of linear operator equations.- 3. A priori estimations for linear continuous operator.- 4. Applications of the theory of generalized solv-ability of linear equations.- 5. Scheme of general-ized solutions of linear operator equations.- 6. Scheme of generalized solutions of nonlinear operator equations.- 7. Generalized extreme elements.- Reference.-

Fields of interestCalculus of Variations and Optimal Control; Optimization; Operator Theory; Difference and Functional Equations



U. Langer, P. Paule, Johannes Kepler University, Linz, Austria (Eds.)

Numerical and Symbolic Scientific ComputingProgress and Prospects

Features 7 Survey articles introduce to new methods connecting numerics and symbolic computation 7 New results in computational mathematics points out challenging future developments in scientific computing 7 Present state-of-the-art in this topic

Contents Fast solvers and a posteriori error estimates in elastoplasticity. - Symbolic analysis for boundary problems: from rewriting to parametrized Groebner Bases. - approximate implicitization of space curves. - A symbolic-numeric algorithm for genus computation. - Linear partial differential equations and linear partial differential operators in computer algebra. - Computer algebra meets finite elements: an efficient implementation for Maxwell’s Equations. - Sound and compelte verific-cation condition generator for functional recursive programs. - Analytical evaluations of double integral expressions related to total variation. - A symbolic approach to generation and analysis of finite difference schemes of partial differential equations. - The “Seven Dwarfs” of symbolic computation. - An introduction to automated discovery in geometry through symbolic computa-tion. - White noise analysis for stochastic partial differential equations. - Computing smoothing rates of collective point smoothers for optimal control problems using symbolic computation. - Sparsity optimized high-order finite element functions on simplices.

Fields of interestComputational Mathematics and Numerical Analysis; Algebra; Appl.Mathematics/Computa-tional Methods of Engineering



A. C. Luo, Southern Illinois University Edwardsville, Illinois, IL, USA

Discontinuous Dynamical Systems

“Discontinuous Dynamical Systems” presents a theory of dynamics and flow switchability in discontinuous dynamical systems, which can be as the mathematical foundation for a new dynamics of dynamical system networks. The book includes a theory for flow barriers and passability to boundaries in discontinuous dynamical systems that will completely change traditional concepts and ideas in the field of dynamical systems. Edge dynamics and switching complexity of flows in discontinuous dynamical systems are explored in the book and provide the mathematical basis for developing the attractive network channels in dynamical systems.

Features 7 Presents a theory and mathematical methods for discontinuous dynamical systems 7 Provides useful mathematical tools to describe the natural complexity in practical dynamical systems 7 Presents a theory for dynamical systems with flow barriers for the first time 7 Challenges current existing theories of dynamical systems under Lipschitz conditions

Contents Introduction.- Introduction to Flow Pass-ability.- Singularity and Flow Passability.- Flow Barriers and Switchability.- Transport Laws and Multi-valued Vector Fields.- Switchability and Attractivity of Domain Flows.- Dynamics and Singularity of Boundary Flows.- Edge Dynamics and Switching Complexity.- Dynamical System Interactions.

Fields of interestSystems Theory, Control; Nonlinear Dynamics ; Vibration, Dynamical Systems, Control



Due November 2011

2011. XVIII, 198 p. (Springer Optimization and Its Appli-cations, Volume 55) Hardcover

7 € 79,95 | £72.007 * € (D) 85,55 | € (A) 87,95 | sFr 115,00ISBN 978-1-4614-0618-1

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Due September 2011

2011. XII, 250 p. 50 illus., 12 in color. (Texts & Mono-graphs in Symbolic Computation) Softcover

7 € 79,95 | £72.007 * € (D) 85,55 | € (A) 87,95 | sFr 115,00ISBN 978-3-7091-0793-5

9<HTOHLJ=bahjdf>

Due October 2011

Jointly published with Higher Education Press

Distribution rights in mainland China: Higher Education Press

2011. XI, 697 p. 228 illus., 5 in color. Hardcover

7 € 89,95 | £81.007 * € (D) 96,25 | € (A) 98,95 | sFr 129,00ISBN 978-3-642-22460-7

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Y. Matsumoto, Gakushuin University, Tokyo, Japan; J. M. Montesinos-Amilibia, Universidad Complutense de Madrid, Spain

Pseudo-periodic Maps and Degeneration of Riemann Surfaces

The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen’s incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces.

Features 7 The publication of the manuscript which has been circulated among specialists for 20 years 7 The first complete study of pseudo-periodic maps after J. Nielsen's original work 7 The first application of the pseudo-periodic maps to the topology of degeneration of Riemann surfaces 7 This book is self-contained and is readable by advanced students (master level)

Contents Part I: Conjugacy Classification of Pseudo-periodic Mapping Classes.- 1 Pseudo-periodic Maps.- 2 Standard Form.- 3 Generalized Quotient.- 4 Uniqueness of Minimal Quotient.- 5 A Theorem in Elementary Number Theory.- 6 Conjugacy Invariants.- Part II: The Topology of Degeneration of Riemann Surfaces.- 7 Topological Monodromy.- 8 Blowing Down Is a Topological Operation.- 9 Singular Open-Book.

Fields of interestAlgebraic Geometry; Manifolds and Cell Complexes (incl. Diff.Topology)



Y. A. Melnikov, Middle Tennessee University, Murfreesboro, TN, USA

Green’s Functions and Infinite ProductsBridging the Divide

Contents INTRODUCTION.- CHAPTER 1: Infinite Prod-ucts Elementary Functions.- 1.1 Classical Euler representations.- 1.2 Alternative derivations.- 1.3 Other elementary functions.- 1.4 Chapter exercises.- CHAPTER 2: Green’s Functions for the Laplace Equation.- 2.1 Construction by the method of images.- 2.2 Conformal mapping method.- 2.3 Chapter exercises.- CHAPTER 3: Green’s Functions for ODE.- 3.1 Construction by defining properties.- 3.2 Method of variation of parameters.- 3.3 Chapter exercises.- CHAPTER 4: Method of Eigenfunction Expansion.- 4.1 Hilbert’s theorem.- 4.2 Cartesian coordinates.- 4.3 Polar coordinates.- 4.4 Chapter exercises.- CHAPTER 5: New Infinite Product Representations.- 5.1 Method of images extends frontiers.- 5.2 Trigono-metric functions.- 5.3 Hyperbolic functions.- 5.4 Chapter exercises.- HINTS AND ANSWERS TO CHAPTER EXERCISES.- REFERENCES.- INDEX.

Fields of interestAnalysis; Ordinary Differential Equations; Partial Differential Equations



B. Michielsen, ONERA, Toulouse, France; J. Poirier, LAPLACE, Toulouse, France (Eds.)

Scientific Computing in Electrical Engineering SCEE 2010

Selected from papers presented at the 8th Scientific Computation in Electrical Engineering confer-ence in Toulouse in 2010, the contributions to this volume cover every angle of numerically model-ling electronic and electrical systems, including computational electromagnetics, circuit theory and simulation and device modelling. On compu-tational electromagnetics, the chapters examine cutting-edge material ranging from low-frequency electrical machine modelling problems to issues in high-frequency scattering.

Features 7 A unique combination of research papers on mathematics applied to electromagnetic, circuit theory and device modelling, covering all aspects of electronic and electrical engineering 7 A state of the art selection of mathematical methods and computational techniques for the modelling of electronic and electrical systems 7 Advanced methods for industry size problems complemented by research updates illustrated with more academic examples

Contents Introduction.- Part I Mathematical Methods.- Part II Computational Electromagnetics.- Part III Coupled Problems.- Part IV Circuit and Device Modelling Simulation.- Part V Model Order Reduction.- Index.

Fields of interestApplications of Mathematics; Numerical and Computational Physics ; Appl.Mathematics/Computational Methods of Engineering



Due August 2011

2011. XVI, 238 p. 56 illus. (Lecture Notes in Mathematics, Volume 2030) Softcover

7 € 44,95 | £40.997 * € (D) 48,10 | € (A) 49,45 | sFr 64,50ISBN 978-3-642-22533-8

9<HTOGPC=ccfddi>

Due November 2011

2012. X, 202 p. 32 illus. Hardcover

7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 72,00ISBN 978-0-8176-8279-8

9<HTLIMH=gichji>

Due November 2011

2011. XVII, 399 p. 176 illus., 115 in color. (Mathematics in Industry / The European Consortium for Mathematics in Industry, Volume 16) Hardcover

7 € 109,95 | £99.007 * € (D) 117,65 | € (A) 120,95 | sFr 158,00ISBN 978-3-642-22452-2

9<HTOGPC=ccefcc>





L. Nicolaescu, University of Notre Dame, IN, USA

An Invitation to Morse TheoryThis self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology. The book is divided into three concep-tually distinct parts. The first part contains the foundations of Morse theory. The second part consists of applications of Morse theory over the reals, while the last part describes the basics and some applications of complex Morse theory, a.k.a. Picard-Lefschetz theory. This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The exposition is enhanced with examples, problems, and illustrations, and will be of interest to graduate students as well as researchers.

Features 7 New edition extensively revised and updated with three new applications and a new chapter on Morse-Smale flows and Whitney stratifications 7 Provides a useful introduction to Morse Theory 7 Covers many of the most important topics in Morse theory along with a broad range of applica-tions 7 Contains many excellent exercises 7 Far more up-to-date and less specialized than any other book on Morse Theory

Contents Preface.- Notations and Conventions.- 1 Morse Functions.- 2 The Topology of Morse Functions.- 3 Applications.- 4 Morse-Smale Flows and Whitney Stratifications.- 5 Basics of Complex Morse Theory.- 6 Exercises and Solutions.- References.- Index

Fields of interestGlobal Analysis and Analysis on Manifolds; Differ-ential Geometry; Manifolds and Cell Complexes (incl. Diff.Topology)



S. Ovchinnikov, San Francisco State University, CA, USA

Graphs and CubesThis introductory text in graph theory focuses on partial cubes, which are graphs that are isometri-cally embeddable into hypercubes of an arbitrary dimension, as well as bipartite graphs, and cubical graphs. This branch of graph theory has developed rapidly during the past three decades, producing exciting results and establishing links to other branches of mathematics. Currently, Graphs and Cubes is the only book available on the market that presents a comprehensive coverage of cubical graph and partial cube theories. Many exercises, along with historical notes, are included at the end of every chapter, and readers are encouraged to explore the exercises fully, and use them as a basis for research projects.

Features 7 This is the only book available on the market that presents a comprehensive coverage of cubical graph and partial cube theories 7 Aimed towards lower-division graduate students in mathematics, but could be of interest to researchers using cubical graph and partial cube theories in mathematics and applications 7 Has applications in theoretical computer science, coding theory, data transmis-sion, genetics, and even the political and social sciences 7 With its numerous illustrations and exercises, this presentation of partial cubes theory is student-friendly

Contents Preface.- 1 Graphs.- 2 Bipartite Graphs.- 3 Cubes.- 4 Cubical Graphs.- 5 Partial Cubes.- 6 Lattice Embeddings.- 7 Hyperplane Arrangements.- 8 Token Systems.- Notation.- References.- Index.

Fields of interestGraph Theory



F. Poloni, Technische Universität Berlin, Germany

Algorithms for Quadratic Matrix and Vector Equations

This book is devoted to studying algorithms for the solution of a class of quadratic matrix and vector equations. These equations appear, in different forms, in several practical applications, especially in applied probability and control theory. The equations are first presented using a novel unifying approach; then, specific numerical methods are presented for the cases most relevant for applica-tions, and new algorithms and theoretical results developed by the author are presented. The book focuses on “matrix multiplication-rich” itera-tions such as cyclic reduction and the structured doubling algorithm (SDA) and contains a variety of new research results which, as of today, are only available in articles or preprints.

Features 7 Contains a new unifying approach to quadratic vector and matrix equations in applied prob-ability 7 Gives new insight on the structured doubling algorithm which can be exploited to develop suitable modifications and generaliza-tions 7 Contains a variety of new research results which, as of today, are only available in articles or preprints

Contents Linear algebra preliminaries.– Quadratic vector equations.– A Perron vector iteration for QVEs.– Unilateral quadratic matrix equations.– Nonsym-metric algebraic Riccati equations.– Transforming NAREs into UQMEs.– Storage optimal algorithms for Cauchy-like matrices.– Newton method for rank-structured algebraic Riccati equations.– Lur’e equations.– Generalized SDA.– An effective matrix geometric mean.– Constructing other matrix geometric means.

Fields of interestAlgebra



Due November 2011

2nd Edition. 2011. XIV, 337 p. 47 illus., 13 in color. (Universitext) Softcover

7 € 56,95 | £51.997 * € (D) 60,94 | € (A) 62,65 | sFr 82,00ISBN 978-1-4614-1104-8

9<HTMERB=ebbaei>

Due October 2011

2011. IX, 287 p. 172 illus., 2 in color. (Universitext) Softcover

7 € 59,95 | £53.997 * € (D) 64,15 | € (A) 65,95 | sFr 86,00ISBN 978-1-4614-0796-6

9<HTMERB=eahjgg>

Due August 2011


2011. 250 p. (Publications of the Scuola Normale Superiore / Theses (Scuola Normale Superiore), Volume 16) Softcover


9<HTTISG=ecdidd>





R. B. Schinazi, University of Colorado, Colorado Springs, CO, USA

Probability with Statistical Applications

This second edition of Probability With Statistical Applications offers a practical introduction to probability for undergraduates at all levels with different backgrounds and views towards applica-tions. Calculus is a prerequisite for understanding the basic concepts, however the book is written with a sensitivity to students’ common difficulties with calculus that does not obscure the thorough treatment of the probability content. The first six chapters of this text neatly and concisely cover the material traditionally required by most undergrad-uate programs for a first course in probability.

Features 7 Practical introduction to probability 7 Numerous examples and exercises 7 Clear and concise presentation 7 Additional chapter and new material included throughout second edition 7

Contents Preface to the Second Edition.- Preface.- Prob-ability Space.- Random Variables.- Binomial and Poisson Random Variables.- Limit Theorems.- Estimation and Hypothesis Testing.- Linear Regression.- Moment Generating Functions and Sums of Independent Random Variables.- Trans-formations of Random Variables and Random Vectors.- Finding and Comparing Estimators.- Multiple Linear Regression.- Further Reading.- Common Distributions.- Normal Table.- Student Table.- Chi-Square Table.- Index.

Fields of interestProbability Theory and Stochastic Processes; Applications of Mathematics; Statistical Theory and Methods



J. Snygg, Upsala College, East Orange, NJ, USA

A New Approach to Differential Geometry using Clifford’s Geometric Algebra

Differential geometry is the study of the curva-ture and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford’s Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space.

Features 7 Includes chapter-by-chapter exercises 7 Provides a rare undergraduate-level approach to the subject matter 7 Promotes the applica-tion of Clifford algebra to differential geometry 7 Presents a significant portion of general rela-tivity without reference to such Newtonian terms as "force", "momentum", or "energy" 7 Only up-to-date title of its kind

Contents Preface.- Introduction.- Clifford Algebra in Euclidean 3-Space.- Clifford Algebra in Minkowski 4-Space.- Clifford Algebra in Flat n-Space.- Curved Spaces.- The Gauss-Bonnet Formula.- Non-Euclidean (Hyperbolic) Geometry.- Some Extrinsic Geometry in E^n.- Ruled Surfaces Continued.- Lines of Curvature.- Minimal Surfaces.- Some General Relativity.- Matrix Representation of a Clifford Algebra.- Construction of Coordinate Dirac Matrices.- A Few Terms of the Taylor’s Series for the Urdī-Copernican Model for the Outer Planets.- A Few Terms of the Taylor’s Series for Kepler’s Orbits.- References.- Index.

Fields of interestDifferential Geometry; Mathematical Methods in Physics; Mathematical Physics

Target groupsUpper undergraduate


B. Steinberg, Carleton University, Ottawa, Ontario, Canada

Representation Theory of Finite GroupsAn Introductory Approach

This book is intended to present group repre-sentation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.

Features 7 Concise focus enables the author to avoid prerequisites in analysis and topology 7 Provides a simple context for students to understand group representation theory 7 Author provides a gentle approach for students as well as the necessary motivation and exercises

Contents -Preface.-Introduction.-Review of Linear Algebra.-Group Representations.-Character Theory.-Fourier Analysis on Finite Groups.-Burnside’s Theorem.-Permutation Representations.-Induced Representations.-Another Theorem of Burnside.-The Symmetric Group.-Bibliography.-Index.

Fields of interestGroup Theory and Generalizations; Algebra



Due November 2011

2nd Edition. 2011. XII, 331 p. 27 illus. With AMS Codes: 60Axx, 62Exx, 60Fxx, 62Cxx, 62Jxx. Hardcover

7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 72,00ISBN 978-0-8176-8249-1

9<HTLIMH=gicejb>

Due November 2011

2012. XVIII, 465 p. 90 illus. Hardcover

7 € 59,95 | £53.997 * € (D) 64,15 | € (A) 65,95 | sFr 86,00ISBN 978-0-8176-8282-8

9<HTLIMH=gicici>

Due November 2011

2012. XII, 163 p. 4 illus. (Universitext) Softcover

7 € 39,95 | £29.997 * € (D) 42,75 | € (A) 43,95 | sFr 57,50ISBN 978-1-4614-0775-1

9<HTMERB=eahhfb>





D. W. Stroock, Massachusetts Institute of Technology, Cambridge, MA, USA

Essentials of Integration Theory for Analysis

‘A Concise Introduction to the Theory of Integra-tion’ was once a best-selling Birkhäuser title which published 3 editions. This manuscript is a substantial revision of the material. Chapter one now includes a section about the rate of conver-gence of Riemann sums. The second chapter now covers both Lebesgue and Bernoulli measures, whose relation to one another is discussed. The third chapter now includes a proof of Lebesgue’s differential theorem for all monotone func-tions. This is a beautiful topic which is not often covered. The treatment of surface measure and the divergence theorem in the fifth chapter has been improved. Loose ends from the discussion of the Euler-MacLauren in Chapter I are tied together in Chapter seven.

Features 7 Refocus and substantial revision of previous successful publication "A Concise Introduction to the Theory of Integration" by D.W. Stroock (Birkhauser) 7 Separate solutions manual avail-able to those who adopt the textbook 7 New material is complemented by the addition of several new problems

Contents -Preface.-1. The Classical Theory.-2. Measures. -3. Lebesgue Integration.-4. Products of Measures.-5. Changes of Variable.-6. Basic Inequalities and Lebesgue Spaces.-7. Hilbert Space and Elements of Fourier Analysis.-8. The Radon-Nikodym Theorem, Daniell Integration, and Carathéodory’s Extension Theorem.-Index.

Fields of interestAnalysis; Real Functions



M. Talagrand, Université Paris 6, Paris, France

Mean Field Models for Spin GlassesVolume II: Advanced Replica-Symmetry and Low Temperature

This is a new, completely revised, updated and enlarged edition of the author’s Ergebnisse vol. 46: “Spin Glasses: A Challenge for Mathemati-cians” in two volumes (this is the 2nd volume). In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called “spin glasses”.

Features 7 Completely rewritten, updated and enlarged edition of Talagrand's Ergebnisse Vol. 46: "Spin Glasses: A Challenge for Mathematicians" (2003) in two volumes 7 Will bring the reader with no previous knowledge of Spin Glasses to the frontier of current research 7 The only fully rigorous treatise of this scale on the subject 7 The present second volume contains a large amount of new results obtained after the publication of the first edition.

Contents Part I. Advanced Replica-Symmetry. - The Gardener Formula for the sphere. - The Gardener Formula for the Discrete Cube. - The Hopfield Model. - The SK Model Without External Field. - Part II. Low Temperature. - The Ghirlanda-Guerra Identities. - The High-Temperature Region of the SK Model. - The Parisi Formula. - The Parisi Solu-tion. - The p-spin Interaction Model. - Appendix: Elements of Probability Theory. - References. - Index.

Fields of interestProbability Theory and Stochastic Processes; Mathematical Methods in Physics; Condensed Matter Physics



M. T. Thai, P. M. Pardalos, University of Florida, Gainesville, FL, USA (Eds.)

Handbook of Optimization in Complex NetworksCommunication and Social Networks

Contents Preface.- 1. Structural Vulnerability and Robust-ness in Complex Networks: Different Approaches and Relationships between Them (R. Criado, M. Romance).- 2. Optimizing Network Topology for Cascade Resilience (A. Gutfraind).- 3. Opti-mizing Synchronization, Flow, and Robustness in Weighted Complex Networks (G. Korniss, R. Huang, S. Sreenivasan, B.K. Szymanski).- 4. Joint Optimization of Resources and Routes for Minimum Resistance: From Communication Networks to Power Grids (A. Tizghadam, A. Bigdeli, A. Leon-Garcia, H. Naser).- 5. Clique Relaxation Models in Social Network Analysis (J. Pattillo, N. Yourssef, S. Butenko).- 6. Applica-tion Traffic Activity Graph Analysis (Y. Jin, E. Sharafuddin, Z.-L. Zhang).- 7. Localized Bridging Centrality (S. Nanda, D. Kotz).- 8. On Throughput Maximization Problem for UWB-Based Sensor Networks via Reformulation-Linearization Tech-nique (Y. Shi, Y.T. Hou, H.D. Sherali).- 9. A Parallel Routing Algorithm for Traffic Optimization (M.L. Wang, K.H. Yeung, and F. Yan).- 10: Internet based Service Networks (L.-Y. Cui, S. Kumara, R. Albert).- 11. On Detection of Community Struc-ture in Dynamic Social Networks (N. P. Nguyen, Y. Xuan, M. T. Thai).- 12: Path Formation in Human Contact Networks (N. Sastry, P. Hui).- 13. Social Forwarding in Mobile Opportunistic Networks: A case of PeopleRank (A. Mtibaa, M. May, M. Ammar).- 14. Discount Targeting in Online Social Networks Using Backpressure-Based Learning (S....

Fields of interestOptimization; Computer Communication Networks; Communications Engineering, Networks



Due September 2011

2011. XII, 244 p. (Graduate Texts in Mathematics, Volume 262) Hardcover

7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 72,00ISBN 978-1-4614-1134-5

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Due September 2011

Originally published as Volume 46 in series “Ergebnisse der Marhematik”

2nd rev. and enlarged ed. 2011. XII, 632 p. (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics, Volume 55) Hardcover

7 € 139,95 | £126.007 * € (D) 149,75 | € (A) 153,94 | sFr 201,00ISBN 978-3-642-22252-8

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Due December 2011

2011. XII, 528 p. 200 illus., 131 in color. (Springer Optimi-zation and Its Applications, Volume 58) Hardcover

7 € 129,95 | £117.007 * € (D) 139,05 | € (A) 142,94 | sFr 186,50ISBN 978-1-4614-0856-7

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R. G. Underwood, Department of Mathematics, Auburn University, Montgomery, AL 36124 USA

An Introduction to Hopf Algebras

With wide-ranging connections to fields from theoretical physics to computer science, Hopf algebras offer students a glimpse at the appli-cations of abstract mathematics. This book is unique in making this engaging subject acces-sible to advanced undergraduate and beginning graduate students. After providing a self-contained introduction to group and ring theory, the book thoroughly treats the concept of the spectrum of a ring and the Zariski topology. In this way the student transitions smoothly from basic abstract algebra to Hopf algebras.

Features 7 Offers the only self-contained treatment of Hopf algebras, beginning with basic definitions of groups and rings 7 Makes Hopf algebras acces-sible to advanced undergraduates and beginning graduate students 7 Underscores importance of Hopf orders with applications to algebraic number theory, Galois module theory and the theory of formal groups

Contents Preface.- Some Notation.- 1. The Spectrum of a Ring.-2. The Zariski Topology on the Spectrum.-3. Representable Group Functors.-4. Hopf Alge-bras. -5. Larson Orders.-6. Formal Group Hopf Orders.-7. Hopf Orders in KC_p.-8. Hopf Orders in KC_{p^2}.-9. Hopf Orders in KC_{p^3}.-10. Hopf Orders and Galois Module Theory.-11. The Class Group of a Hopf Order.-12. Open Questions and Research Problems.-Bibliography.-Index.

Fields of interestAlgebra; Commutative Rings and Algebras; Group Theory and Generalizations



W. Wallis, Southern Illinois University, Carbondale, IL, USA

A Beginner’s Guide to Discrete Mathematics

Wallis’s book on discrete mathematics is a resource for an introductory course in a subject funda-mental to both mathematics and computer science, a course that is expected not only to cover certain specific topics but also to introduce students to important modes of thought specific to each disci-pline . . . Lower-division undergraduates through graduate students. —Choice reviews (Review of the First Edition) Very appropriately entitled as a ‘beginner’s guide’, this textbook presents itself as the first exposure to discrete mathematics and rigorous proof for the mathematics or computer science student.

Features 7 Includes a new chapter on the theory of voting as well as numerous new examples and exercises throughout the book 7 Introduces functions, vectors, matrices, number systems, scientific notations, and the representation of numbers in computers 7 Provides examples which then lead into easy practice problems throughout the text and full exercise at the end of each chapter 7 Full solutions for practice problems are provided at the end of the book

Contents Properties of Numbers.- Sets and Data Struc-tures.- Boolean Algebras and Circuits.- Relations and Functions.- The Theory of Counting.- Prob-ability.- Graph Theory.- Matrices.- Number Theory and Cryptography.- The Theory of Voting.- Solu-tions to Practic Exercises.- Answers to Selected Exercises.- Index.

Fields of interestMathematical Logic and Foundations; Discrete Mathematics in Computer Science; Combinatorics

Target groupsLower undergraduate


E. Zeidler, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

Quantum Field Theory III: Gauge TheoryA Bridge between Mathematicians and Physicists

In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appro-priate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure.

Features 7 A bridge between mathematicians and physicists 7 A bridge from classic mathematics and physics to modern mathematics and physics 7 Broad overview

Contents Prologue.- Part I. The Euclidean Manifold as a Paradigm.- Part II. Ariadne’s Thread in Gauge Theory.- Part III. Einstein’s Theory of Special Rela-tivity.- Part IV. Ariadne’s Thread in Cohomology.- Appendix.- Epilogue.- References.- List of Symbols.- Index.

Fields of interestPartial Differential Equations; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics



Due October 2011


7 € 59,95 | £53.997 * € (D) 64,15 | € (A) 65,95 | sFr 86,00ISBN 978-0-387-72765-3

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Due December 2011

2nd Edition. 2012. XIV, 414 p. 37 illus. Hardcover

7 € 59,95 | £53.997 * € (D) 64,15 | € (A) 65,95 | sFr 86,00ISBN 978-0-8176-8285-9

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Due September 2011

2011. XXXII, 1126 p. 152 illus. Hardcover

7 € 99,95 | £90.007 * € (D) 106,95 | € (A) 109,95 | sFr 143,50ISBN 978-3-642-22420-1

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M. Zili, Preparatory Institute to the Military Acad-emies (E.P.A.M.), Sousse, Tunisia; D. V. Filatova, Jan Kochanowski University in Kielce, Poland (Eds.)

Stochastic Differential Equations and ProcessesSAAP, Tunisia, October 7-9, 2010

Selected papers submitted by participants of the international Conference “Stochastic Analysis and Applied Probability 2010” ( www.saap2010.org ) make up the basis of this volume.

Features 7 Peer reviewed 7 Reference for researches in applied probability, stochastic numerical and theoretical analysis and statistics 7 Useful for graduate students

Contents Preface.- 1.H. Schurz: Basic Concepts of Numer-ical Analysis of Stochastic Differential Equations Explained by Balanced Implicit Theta Methods .- 2.C.A. Tudor: Kernel Density Estimation, Local Time and Chaos Expansion.- 3.W. Jedidi, J. Almhana, V. Choulakian, R. McGorman: General Shot Noise Processes and Functional Convergence to Stable Processes.- 4.C. El-Nouty: The Lower Classes of the Sub-Fractional Brownian Motion.- 5.M. Erraoui and Y. Ouknine: On the Bounded Variation of the Flow of Stochastic Differential Equation.- 6.A. Ayache, Q. Peng: Stochastic Vola-tility and Multifractional Brownian Motion.- 7.A. Gulisashvili, J. Vives: Two-sided Estimates for Distribution Densities in Models with Jumps.- 8.M. Lefebvre: Maximizing a Function of the Survival Time of a Wiener Process in an Interval.

Fields of interestProbability Theory and Stochastic Processes; Game Theory, Economics, Social and Behav. Sciences; Systems Theory, Control



Due November 2011

2011. X, 252 p. 2 illus., 1 in color. (Springer Proceedings in Mathematics, Volume 7) Hardcover

7 € 89,95 | £81.007 * € (D) 96,25 | € (A) 98,95 | sFr 129,00ISBN 978-3-642-22367-9

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t. andreescu m. arkowitz y. arlinskii b. enescu introduction to … · 2012-04-27 · dynamic...

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