I. Itenberg, An Invitation to Abstract Dalla geometria di ... · 7 A partire da immagini familiari...

News 2/2013 Mathematics

59

V. I. Arnold, Russian Academy of Sciences, Moscow, Russia; I. Itenberg, University Pierre et Marie Curie, Paris, France; V. Kharlamov, University of Strasbourg I, France; E. I. Shustin, University of Tel Aviv, Israel (Eds)

Real Algebraic GeometryTransl. Russian: G. G. Gould, Cardiff University, Cardiff, UK

This book is concerned with one of the most fun-damental questions of mathematics: the relation-ship between algebraic formulas and geometric images. At one of the first international mathemat-ical congresses (in Paris in 1900), Hilbert stated a special case of this question in the form of his 16th problem (from his list of 23 problems left over from the nineteenth century as a legacy for the twentieth century). In spite of the simplicity and importance of this problem (including its numer-ous applications), it remains unsolved to this day (although, as you will now see, many remarkable results have been discovered).

Features 7 Written by one of the most eminent mathema-ticians of the 20th and 21st centuries 7 Masterful exposition 7 Lecture courses do not get better than this

Contents Publisher‘s Foreword.- Editors‘ Foreword.- Intro-duction.- 2 Geometry of Conic Sections.- 3 The Physics of Conic Sections and Ellipsoids.- 4 Pro-jective Geometry.- 5 Complex Algebraic Curves.- 6 A Problem for School Pupils.- A Into How Many Parts do n Lines Divide the Plane?- Editors‘ Com-ments on Gudkov‘s Conjecture.- Notes

Fields of interestAlgebraic Geometry; Mathematical Methods in Physics; Geometry

Target groupsLower undergraduate

Product categoryUndergraduate textbook

Due April 2013

2013. Approx. 100 p. 105 illus. (UNITEXT / La Matematica per il 3+2, Volume 66) Softcover7 * € (D) 32,09 | € (A) 32,99 | sFr 40,007 € 29,99 | £26.99ISBN 978-3-642-36242-2

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F. Arzarello, Università di Torino, Italy; C. Dané, L. Lovera, M. Mosca, Torino, Italy; N. Nolli, Cremona, ITaly; A. Ronco, Torino, Italy

Dalla geometria di Euclide alla geometria dell‘UniversoGeometria su sfera, cilindro, cono, pseudosfera

Il testo confronta con la usuale geometria del pia-no (euclidea) vari tipi di geometrie che si hanno su superfici note e meno note: geometria sulla sfera, sul cilindro, sul cono e sulla pseudosfera. L‘idea di fondo è di giungere alla descrizione „intrinseca“ di queste geometrie analizzando che cosa significa l‘andare diritto su queste superficie (cioè l‘idea di geodetica). Si giunge così a vari tipi di geomet-rie che si discostano da quella euclidea usuale: geometrie localmente euclidee (su cilindro e cono deprivato del vertice), geometria ellittica (sulla sfera), geometria iperbolica (sulla pseudosfera). Si scopre che la chiave di volta concettuale che distingue queste diverse geometrie è la nozione di curvatura gaussiana, rispettivamente nulla su piani, cilindri, coni; (costante) positiva sulla sfera e (costante) negativa sulla pseudosfera.

Features 7 A partire da immagini familiari (un pallone, un cono gelato, un fiasco di Chianti) introduce a importanti concetti geometrici 7 Il conti-nuo riferimento ai movimenti corpo-sintonici che occorre fare per camminare sulle superfici considerate fonda in modo corporeo (embodied) i concetti matematici introdotti: si apprende non tramite formule ma tramite il movimento del pro-prio corpo 7 Collega la geometria alla geografia e alla vita tecnologica di tutti i giorni (GPS)

Fields of interestGeometry

Target groupsProfessional/practitioner

Product categoryMonografia

Available

2012. XI, 198 pagg. (Convergenze) Brossura7 * € (D) 25,67 | € (A) 26,39 | sFr 32,007 € 23,99 | £19.99ISBN 978-88-470-2573-8

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B. Bajnok, Gettysburg College, PA, USA

An Invitation to Abstract MathematicsFeatures 7 Gives a broad view of the field of mathematics without the artificial division of subjects 7 Pro-vides students with a broad exposure to math-ematics by including an unusually diverse array of topics 7 Discusses important milestones in the history of mathematics and features some of the most interesting recent accomplishments in the field 7 Goes beyond the typical elementary text by providing a more thorough and deeper treat-ment whenever feasible 7 The text can be stud-ied at various levels and depths, with, hopefully, plenty of fun for students and instructors alike

Contents Preface to Instructors.- Preface to Students.- Acknowledgments.- I What‘s Mathematics.- 1 Let‘s Play a Game!.- 2 What‘s the Name of the Game?.- 3 How to Make a Statement?- 4 What‘s True in Mathematics?.- 5 Famous Classical Theorems.- 6 Recent Progress in Mathematics.- II How to Solve It?.- 7 Let‘s be Logical!.- 8 Setting Examples.- 9 Quantifier Mechanics.- 10 Math-ematical Structures.- 11 Working in the Fields (and Other Structures).- 12 Universal Proofs.- 13 The Domino Effect.- 14 More Domino Games.- 15 Existential Proofs.- 16 A Cornucopia of Famous Problems.- III Advanced Math for Beginners.- 17 Good Relations.- 18 Order, Please!.- 19 Let‘s be Functional!.- 20 Now That‘s the Limit!.- 21 Sizing It Up.- 22 Infinite Delights.- 23 Number Systems Systematically.- 24 Games Are Valuable!.- IV. Appendices.- A. Famous Conjectures in Math-ematics.- B The Foundations of Set Theory.- C All Games Considered.- D Top 40 List of Math Theorems. - Index.

Fields of interestMathematics, general; History of Mathematical Sciences; Mathematical Logic and Foundations



Due May 2013

2013. XVI, 416 p. 55 illus. (Undergraduate Texts in Mathematics) Hardcover7 * € (D) 48,14 | € (A) 49,49 | sFr 60,007 € 44,99 | £40.99ISBN 978-1-4614-6635-2

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www.springer.com/978-3-642-36242-2



Mathematics springer.com/NEWSonline

60

K. A. Bencsath, Manhattan College, NY, USA; M. C. Bonanome, New York City College of Technology, NY, USA; M. H. Dean, M. Zyman, Borough of Manhattan Community College, NY, USA

Lectures on Finitely Generated Solvable GroupsLectures on Finitely Generated Solvable Groups are based on the “Topics in Group Theory“ course focused on finitely generated solvable groups that was given by Gilbert G. Baumslag at the Graduate School and University Center of the City Univer-sity of New York. While knowledge about finitely generated nilpotent groups is extensive, much less is known about the more general class of solvable groups containing them. The study of finitely generated solvable groups involves many different threads; therefore these notes contain discussions on HNN extensions; amalgamated and wreath products; and other concepts from combinatorial group theory as well as commutative algebra.

Features 7 Includes a foreword by Gilbert Baumslag, a world renowned expert in combinatorial group theory 7 Serves as a field guide to the class of finitely generated solvable groups from a combi-natorial group theory perspective 7 Provides examples to help illustrate key concepts

Contents Foreword.- Preface.- Preliminaries.- Tools: Pre-sentations and their Calculus.- Constructions.- Representations and a Theorem of Krasner and Kaloujnine.- The Bieri-Strebel Theorems.- Finitely Generated Metabelian Groups.- An Embed-ding Theorem for Finitely Generated Metabelian Groups .- Sketch of Proof of Lemma 1.1.- Theorem 2.1 Details.- Presenting an (Internal) HNN-Exten-sion.- References.

Fields of interestGroup Theory and Generalizations; Combinator-ics; Algebra

Target groupsResearch

Product categoryBrief

Available

2013. XIV, 52 p. (SpringerBriefs in Mathematics) Softcover7 * € (D) 53,45 | € (A) 54,95 | sFr 66,507 € 49,95 | £44.99ISBN 978-1-4614-5449-6

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L. Berger, Ecole Normale Supérieure, Lyon, France; G. Böckle, Universität Heidelberg, Germany; L. Dembélé, University of Warwick, Coventry, UK; M. Dimitrov, Université Lille, Villeneuve d‘Ascq, France; T. Dokchitser, University of Bristol, UK; J. Voight, University of Vermont, Burlington, VT, USA

Elliptic Curves, Hilbert Modular Forms and Galois DeformationsEditorial coordination: B. Edixhoven, Universiteit Leiden, Netherlands; V. Rotger, H. DARMON, McGill University, Montreal, QC, Canada; F. Diamond, King‘s College, London, UK; L. V. Dieulefait, Universitat de Barcelona, Spain

Features 7 The book contains the first published notes on the recent developments and major changes in Galois deformation theory during the last decade (deformations of pseudo-representations, framed deformations, groupoids, etc.) 7 A proof of the parity conjecture is presented 7 Computational aspects of Hilbert modular forms are presented by the people responsible for the most powerful and widely spread algorithms available

Contents Part I: Galois Deformations.- On p-adic Galois Representations.- Deformations of Galois Rep-resentations.- Part II: Hilbert Modular Forms.- Arithmetic Aspects of Hilbert Modular Forms and Varieties.- Explicit Methods for Hilbert Modular Forms.- Part III: Elliptic Curves.- Notes on the Parity Conjecture.

Fields of interestNumber Theory; Algebraic Geometry; Algebra

Target groupsGraduate

Product categoryGraduate/Advanced undergraduate textbook

Due April 2013

2013. Approx. 270 p. (Advanced Courses in Mathematics - CRM Barcelona) Softcover7 approx. * € (D) 32,05 | € (A) 32,94 | sFr 40,007 approx. € 29,95 | £26.99ISBN 978-3-0348-0617-6

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R. Betti, Politecnico di Milano, Italy; A. Guerraggio, Università dell‘Insubria, Varese, Italy; S. Termini, Università di Palermo, Italy (Rédacteurs)

Storie e protagonisti della matematica italiana20 anni di „Lettera Matematica“

Il volume conterrà alcuni articoli scelti, già pub-blicati su Lettera Matematica Pristem negli ultimi venti anni, ciascuno con una introduzione, a cura degli editors, che ne precisi il senso, alla luce anche degli avvenimenti culturali del periodo in cui sono stati pubblicati.

Features 7 Divulgazione utile per i docenti di matemati-ca 7 Favorisce la cultura scientifica nel passaggio dalla scuola superiore all'università 7 Collega la cultura matematica all'impegno civile 7 Discute la politica culturale del nostro tempo 7 Informa su storia e grandi personaggi della scienza

Contents L’inizio: il 1991.- Premesse e Promesse.- Signi-ficato e limiti di Scientia nella cultura europea del Novecento.- 1992.- La Storia del pensiero filosofico e scientifico di Ludovico Geymonat.- Ludovico Geymonat e la rinascita della logica italiana.- 1993.- Lucio Lombardo Radice: una commemorazione.- Lucio Lombardo-Radice: cul-tura e metodo.- 1994.- La democrazia impossibi-le.- 1995.- Sul valore sapienzale della matematica.- 1996.- Entartete Mathematik.- 1997.- Una scuola senza memoria.- 1998.- Metafore matematiche dell’Informatica.- 1999-2011.

Fields of interestApplications of Mathematics; History of Math-ematical Sciences; Mathematics Education

Target groupsPopular/general

Product categoryContributed volume

Pubblicazione prevista per il mese di May 2013

2013. Approx. 250 pagg. (I blu) Brossura7 approx. * € (D) 25,71 | € (A) 26,43 | sFr 32,007 approx. € 24,03 | £19.99ISBN 978-88-470-2777-0

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61

F. Biagini, A. Richter, University of Munich, Germany; H. Schlesinger, University of Alabama, Tuscaloosa, AL, USA (Eds)

Risk Measures and AttitudesRisk has been described in the past by a simple measure, such as the variance, and risk attitude is often considered simply a degree of risk aversion. However, this viewpoint is usually not suffi-cient. Risk Measures and Attitudes collects contri-butions which illustrate how modern approaches to both risk measures and risk attitudes are inevi-tably intertwined. The settings under which this is discussed include portfolio choice, mitigating credit risk and comparing risky alternatives. This book will be a useful study aid for students and researchers of actuarial science or risk manage-ment as well as practitioners.

Features 7 Illustrates the interplay between modern advances in both risk measures and risk atti-tudes 7 Multi-disciplinary coverage appeals to students, researchers and practitioners 7 Con-tains papers presented at the Ludwig-Maximilians University in Munich in December 2010

Contents Weak Closedness of Monotone Sets of Lotteries and Robust Representation of Risk Preferences.- Multivariate Concave and Convex Stochastic Dominance.- Reliable Quantification and Efficient Estimation of Credit Risk.- Diffusion-based models for financial markets without martingale measures.

Fields of interestApplications of Mathematics; Actuarial Sciences; Probability Theory and Stochastic Processes



Due February 2013

2013. IX, 91 p. 4 illus. in color. (EAA Series) Softcover7 * € (D) 42,79 | € (A) 43,99 | sFr 53,507 € 39,99 | £35.99ISBN 978-1-4471-4925-5

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F. Bogomolov, New York University, NY, USA; B. Hassett, Rice University, Houston, TX, USA; Y. Tschinkel, New York University, NY, USA (Eds)

Birational Geometry, Rational Curves, and Arithmetic This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics.

Features 7 Leading experts report on recent advances in higher-dimensional birational geometry, with special regard to arithmetic applications 7 High-lights the tight connections between arithmetic and geometry 7 Documents the central role of the theory of rational curves

Contents Foreword.- Introduction.- A. Bertram and I. Coskun, The birational geometry of the Hilbert scheme of points on surfaces.- F. Bogomolov and Ch. Böhning, Isoclinism and stable cohomology of wreath products.- F. Bogomolov, I. Karzhemanov, and K. Kuyumzhiyan, Unirationality and exis-tence of infinitely transitive models.- I. Cheltsov, L. Katzarkov, and V. Przyjalkowski, Birational geometry via moduli spaces.- O. Debarre, Curves of low degrees on projective varieties.- S. Kebekus, Uniruledness criteria and applications.- S. Kovács, The cone of curves of K3 surfaces revisited.- V. Lazić, Around and beyond the canonical class.- C. Liedtke, Algebraic surfaces in positive characteris-tic.- A. Varilly-Alvarado, Arithmetic of Del Pezzo surfaces.

Fields of interestAlgebraic Geometry; Number Theory; Geometry



Due May 2013

2013. X, 328 p. 37 illus. Hardcover7 * € (D) 101,64 | € (A) 104,49 | sFr 126,507 € 94,99 | £85.50ISBN 978-1-4614-6481-5

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O. Bordellès, Aiguilhe, France

Arithmetic TalesTranslated by: V. Bordellès, Aiguilhe, France

Number theory was once famously labeled the queen of mathematics by Gauss. The multiplicative structure of the integers in particular deals with many fascinating problems some of which are easy to understand but very difficult to solve. In the past, a variety of very different techniques has been applied to further its understanding. Clas-sical methods in analytic theory such as Mertens’ theorem and Chebyshev’s inequalities and the celebrated Prime Number Theorem give estimates for the distribution of prime numbers. Later on, multiplicative structure of integers leads to mul-tiplicative arithmetical functions for which there are many important examples in number theory. Their theory involves the Dirichlet convolution product which arises with the inclusion of several summation techniques and a survey of classical results such as Hall and Tenenbaum’s theorem and the Möbius Inversion Formula.

Features 7 An easily accessible overview of elementary, analytic and algebraic number theory in one book 7 A wide variety of exercises that not only directly illustrate the theory but target problems that are rarely covered in existing literature 7 In-cludes a number of topics that are not covered in existing undergraduate texts for example counting integer points close to smooth curves

Contents Basic Tools.- Bézout and Gauss.- Prime Numbers.- Arithmetic Functions.- Integer Points Close to Smooth Curves.- Exponential Sums.- Algebraic Number Fields.

Fields of interestNumber Theory; Mathematics, general



Available

Originally published by Edition Marketing S.A, 2006

Distribution Rights in France: Editions Ellipses

2012. XXI, 556 p. 5 illus. (Universitext) Softcover7 * € (D) 74,85 | € (A) 76,95 | sFr 93,507 € 69,95 | £49.99ISBN 978-1-4471-4095-5

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62

U. Bottazzini, Università degli Studi di Milano, Italy; J. Gray, The Open University, Milton Keynes, UK

Hidden Harmony—Geometric FantasiesThe Rise of Complex Function Theory

This book is a history of complex function theory from its origins to 1914, when the essential fea-tures of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject – Cauchy, Riemann, and Weierstrass – it looks at the contributions of authors from d’Alembert to Hilbert, and Laplace to Weyl. Particular chapters examine the rise and importance of elliptic function theory, differen-tial equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables.

Features 7 Presents the first complete account of the development of the work and ideas of Cauchy, Riemann, and Weierstrass in complex function theory 7 Analyzes the history of elliptic function theory and its implications for the development of complex function theory as the first full-length treatment of the interactions between these two fields 7 Examines the interaction of complex function theory with other fields, including num-ber theory, mechanics, and differential equations

Contents List of Figures.- Introduction.- 1. Elliptic Func-tions.- 2. From real to complex.- 3. Cauch.- 4. Elliptic integrals.- 5. Riemann.- 6. Weierstrass.- 7. Differential equations.- 8. Advanced topics.- 9. Several variables.- 10. Textbooks.

Fields of interestFunctional Analysis; Functions of a Complex Vari-able; Number Theory


Product categoryMonograph

Due May 2013

2013. XVI, 808 p. 36 illus., 1 in color. (Sources and Studies in the History of Mathematics and Physical Sciences) Hardcover7 * € (D) 149,79 | € (A) 153,99 | sFr 186,507 € 139,99 | £126.00ISBN 978-1-4614-5724-4

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D. Bump, Stanford University, CA, USA; S. Friedberg, Boston College, MA, USA; D. Goldfeld, Columbia University, New York, NY, USA (Eds)

Multiple Dirichlet Series, L-functions and Automorphic FormsFeatures 7 Provides a comprehensive overview of an emerging area at the boundary among many fields of mathematics 7 Includes high-quality papers from a conference on Multiple Dirichlet Series with contributions by international experts in their respective fields

Contents Preface.- Introduction: Multiple Dirichlet Series.- A Crystal Description for Symplectic Multiple Dirichlet Series.- Metaplectic Whittaker Func-tions and Crystals of Type B.- Metaplectic Ice.- Littelmann patterns and Weyl Group Multiple Dirichlet Series of Type D.- Toroidal Automorphic Forms, Waldspurger Periods and Double Dirichlet Series.- Natural Boundaries and Integral Moments of L-functions.- A Trace Formula of Special Values of Automorphic L-functions.- The Ad-joint L-function of SU(2,1).- Symplectic Ice.- On Witten Multiple Zeta-Functions Associated with Semisimple Lie Algebras III.- A Pseudo Twin-Prime Theorem.- Principal Series Representations of Metaplectic Groups over Local Fields.- Two-Dimensional Adelic Analysis and Cuspidal Auto-morphic Representations of GL(2).

Fields of interestNumber Theory; Group Theory and Generaliza-tions; Mathematical Physics



Available

2012. VIII, 361 p. 78 illus. (Progress in Mathematics, Volume 300) Hardcover7 * € (D) 101,60 | € (A) 104,45 | sFr 126,507 € 94,95 | £85.50ISBN 978-0-8176-8333-7

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M. Colangeli, Politecnico di Torino, Italy

From Kinetic Models to HydrodynamicsSome Novel Results

From Kinetic Models to Hydrodynamics serves as an introduction to the asymptotic methods necessary to obtain hydrodynamic equations from a fundamental description using kinetic theory models and the Boltzmann equation. The work is a survey of an active research area, which aims to bridge time and length scales from the particle-like description inherent in Boltzmann equation theory to a fully established “continuum” approach typical of macroscopic laws of physics.The author sheds light on a new method—us-ing invariant manifolds—which addresses a functional equation for the nonequilibrium single-particle distribution function.

Features 7 Bridges time and length scales from the particle-like description inherent in Boltzmann equation theory to a fully established “continuum” approach typical of macroscopic laws of phys-ics 7 Addresses a functional equation for the nonequilibrium single-particle distribution func-tion

Contents 1. Introduction.- 2. From the Phase Space to the Boltzmann Equation.- 3. Methods of Reduced De-scription.- 4. Hydrodynamic Spectrum of Simple Fluids.- 5. Hydrodynamic Fluctuations from the Boltzmann Equation.- 6. 13 Moment Grad Sys-tem.- 7. Conclusions.- References.

Fields of interestMathematical Physics; Mathematical Methods in Physics; Mathematical Applications in the Physical Sciences


Product categoryBrief

Due February 2013

2013. VIII, 102 p. 21 illus., 9 in color. (SpringerBriefs in Mathematics) Softcover7 * € (D) 53,49 | € (A) 54,99 | sFr 67,007 € 49,99 | £44.99ISBN 978-1-4614-6305-4

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63

P. Constantin, University of Princeton, NJ, USA; A. Debussche, ENS de Cachan Bretagne, France; G. P. Galdi, University of Pittsburgh, PA, USA; M. Růžička, University of Freiburg, Freiburg, Germany; G. Seregin, Oxford University, UK

Topics in Mathematical Fluid MechanicsCetraro, Italy 2010, Editors: Hugo Beirão da Veiga, Franco Flandoli

Scientific editors: F. Flandoli, H. Beirão da Veiga, University of Pisa, Italy

This volume brings together five contributions to mathematical fluid mechanics, a classical but still very active research field which overlaps with physics and engineering. The contributions cover not only the classical Navier-Stokes equations for an incompressible Newtonian fluid, but also gen-eralized Newtonian fluids, fluids interacting with particles and with solids, and stochastic models.

Features 7 The range of theoretical fluid-mechanics problems treated here is unique in its kind 7 The lectures are updated versions of contemporary knowledge in the field 7 It is an outstanding introduction to research on fluids for young scientists

Contents Fluids and Particles.- Stochastic Navier-Stokes Equations: well Posedness and Ergodic Proper-ties.- Topics in the Mathematical Theory of Fluid-Solid Interaction.- Analysis of Generalized Newtonian Fluids.- Local Regularity Theory for the Navier-Stokes Equations.

Fields of interestPartial Differential Equations; Fluid- and Aerody-namics; Engineering Fluid Dynamics



Due April 2013

2013. Approx. 370 p. (Lecture Notes in Mathematics / C.I.M.E. Foundation Subseries, Volume 2073) Softcover7 * € (D) 74,89 | € (A) 76,99 | sFr 93,507 € 69,99 | £62.99ISBN 978-3-642-36296-5

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F. Dai, University of Alberta, Edmonton, AB, Canada; Y. Xu, University of Oregon, Eugene, OR, USA

Approximation Theory and Harmonic Analysis on Spheres and BallsThis monograph records progress in approxima-tion theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area.

Features 7 Written by experts in the field 7 Contains up-to-date research in approximation theory and harmonic analysis on balls and spheres 7 Pro-vides useful research material for both experts and advanced graduate students

Contents 1 Spherical Harmonics.- 2 Convolution and Spherical Harmonic Expansion.- 3 Littlewood-Paley Theory and Multiplier Theorem.- 4 Approxi-mation on the Sphere.- 5 Weighted Polynomial Inequalities.- 6 Cubature Formulas on Spheres.- 7 Harmonic Analysis Associated to Reflection Groups .- 8 Boundedness of Projection Operator and Cesàro Means.- 9 Projection Operators and Cesàro Means in L^p Spaces.- 10 Weighted Best Approximation by Polynomials.- 11 Harmonic Analysis on the Unit Ball.- 12 Polynomial Approx-imation on the Unit Ball.- 13 Harmonic Analysis on the Simplex.- 14 Applications.- A Distance, Difference and Integral Formulas.- B Jacobi and Related Orthogonal Polynomials.- References.- In-dex.- Symbol Index.

Fields of interestAnalysis; Approximations and Expansions; Fou-rier Analysis



Due April 2013

2013. XVI, 414 p. (Springer Monographs in Mathematics) Hardcover7 * € (D) 101,64 | € (A) 104,49 | sFr 126,507 € 94,99 | £85.50ISBN 978-1-4614-6659-8

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M. Efendiev, Helmholtz Center Munich, Neuherberg, Germany

Evolution Equations Arising in the Modelling of Life SciencesThis book deals with the modeling, analysis and simulation of problems arising in the life sciences, and especially in biological processes. The models and findings presented result from intensive discussions with microbiologists, doctors and medical staff, physicists, chemists and industrial engineers and are based on experimental data.

Features 7 Deals with a new class of nonlinear reaction-diffusion convective equations simultaneously comprising two kinds of degeneracy 7 Derives and analyses realistic life science models based on experimental data 7 Represents a good example of the usefulness of interdisciplinary re-search 7 Adresses researchers in biomathemat-ics as well as (post-)graduate students interested in applications of new mathematical methods in the life sciences

Contents Preface.- 1 Auxiliary Materials.- 2 Global at-tractors for autonomous evolution equations.- 3 Verifying life science models containing diffusion, transport and interaction of species.- 4 Positivity criterion for systems of stochastic PDEs.- Exis-tence and longtime behaviour of a biofilm model.- 6 The blood coagulation cascade in a perfusion experiment: example from pharmaceutical industry.- Index.

Fields of interestMathematical and Computational Biology; Physiological, Cellular and Medical Topics; Partial Differential Equations



Due April 2013

2013. XII, 250 p. 27 illus., 12 in color. (International Series of Numerical Mathematics, Volume 163) Hardcover7 * € (D) 90,94 | € (A) 93,49 | sFr 113,507 € 84,99 | £76.50ISBN 978-3-0348-0614-5

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64

M. Emmer, Sapienza Università di Roma, Italy (Ed)

Imagine Math 2Between Culture and Mathematics

Contents Exotic Spheres and John Milnor by M. Abate.- The Solitude of Last Words by C. Ambrosini.- From Pollock’s Summertime to Jacksontime by D. Amodio.- Spatial Rhythms in Cinema between the Avant-Garde and Entertainment by G.P. Brunetta.- Myrmedrome: Simulating the life of an Ant Colony by S. Cacace, E. Cristiani, D. D’Eustacchio.- From Canvas to Music: Math-ematics as a Tool for the Composition of Jackson Time by C. de Fabritiis.- Gödel’s Childhood and Other Algorithms by V. Della Mea.- Lessons in Mathematics, at the Cinema by M. Emmer.- The Fascination of Numbers, between Music and Poetry by M. Emmer.- Numeri Malefici (Evil Numbers): Homage to Fabio Mauri by M. Em-mer.- Extracting Information from Chaos: a Case in Climatological Analysis by F. Bonghi, R. Fer-retti.- Morphogenesis and dynamical systems by S. Franceschelli.- Mathematics, Love, and Tattoos by E. Frenkel.- Alan Turing and the Poisoned Apple by M. Vincenzi.- Mathematics according to Italo Calvino by G. Lolli.- Alan M. Turing (1912-1954) by G. Lolli.- Empirical Evidence that the World Is Not a Computer by J.W. McAllister.- On the Tangible Boundary between Real and Virtual by A. Mondot.- Arithmétique by G. Munari.- The Mathematical Mind - Iconography of a Tension by P. Pagli.- The Wild Number Problem: Math or Fiction? by P. Schogt.- Fort Marghera and the French and Austrian Plans of Defence by M. Scroccaro.- L’art du Trait est l’Attrait de l’Art by S. Skaf.- Cellular Automata: the Game of Life by G.M. Todesco.- A Play at Dusk Mathematics in Literature by C. Toffalori.

Fields of interestMathematics in the Humanities and Social Sci-ences; Popular Science in Mathematics/Computer Science/Natural Science/Technology; Humanities, general

Target groupsPopular/general


Due March 2013

2013. Approx. 300 p. 60 illus., 10 in color. Hardcover7 approx. * € (D) 64,15 | € (A) 65,95 | sFr 80,007 approx. € 59,95 | £53.99ISBN 978-88-470-2888-3

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O. Furdui, Technical University of Cluj-Napoca, Romania

Limits, Series, and Fractional Part IntegralsProblems in Mathematical Analysis

This book features challenging problems of classi-cal analysis that invite the reader to explore a host of strategies and tools used for solving problems of modern topics in real analysis. This volume offers an unusual collection of problems — many of them original — specializing in three topics of mathematical analysis: limits, series, and fractional part integrals. The work is divided into three parts, each containing a chapter dealing with a particular problem type as well as a very short section of hints to select problems.

Features 7 Provides original problems on special topics in classical analysis such as the computation of limits, series, and exotic integrals 7 The first book to concern the calculation of fractional part integrals and series of various types 7 Illustrates funda-mental results of real analysis and reveals new, simple methods of proofs for classical facts 7 In-cludes full solutions and new techniques for solving problems in integration theory and the computation of limits of special sequences

Contents Preface.- Notations.- 1. Limits.- 2. Fractional Part Integrals.- 3. A Bouquet of Series.- A. Elements of Classical Analysis.- B. Stolz–Cesàro Lemma.- Ref-erences.- Index.

Fields of interestAnalysis; Sequences, Series, Summability; Special Functions



Due May 2013

2013. Approx. 280 p. (Problem Books in Mathematics) Hardcover7 * € (D) 53,49 | € (A) 54,99 | sFr 67,007 € 49,99 | £44.99ISBN 978-1-4614-6761-8

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L. J. Gerstein, University of California, Santa Barbara, CA, USA

Introduction to Mathematical Structures and ProofsReviews of the first edition: „...Gerstein wants-very gently-to teach his students to think. He wants to show them how to wrestle with a problem (one that is more sophisticated than „plug and chug“), how to build a solution, and ultimately he wants to teach the students to take a statement and develop a way to prove it...Gerstein writes with a certain flair that I think students will find appealing.

Features 7 Discusses the multifaceted process of math-ematical proof by thoughtful oscillation between what is known and what is to be demonstrat-ed 7 Presents more than one proof for many results, for instance for the fact that there are infinitely many prime numbers 7 Shows how the processes of counting and comparing the sizes of finite sets are based in function theory, and how the ideas can be extended to infinite sets via Cantor's theorems 7 Contains a wide assort-ment of exercises, ranging from routine checks of a student's grasp of definitions through problems requiring more sophisticated mastery of funda-mental ideas 7 Demonstrates the dual impor-tance of intuition and rigor in the development of mathematical ideas

Contents Preface to the Second Edition.- Preface to the First Edition.- 1. Logic.- 2. Sets.- 3. Functions.- 4. Finite and Infinite Sets.- 5. Combinatorics.- 6. Number Theory.- 7. Complex Numbers.- Hints and Partial Solutions to Selected Odd-Numbered Exercises.- Index.

Fields of interestMathematical Logic and Foundations; Number Theory; Combinatorics



Available

2nd ed. 2012. XIII, 401 p. 133 illus. (Undergraduate Texts in Mathematics) Hardcover7 * € (D) 48,10 | € (A) 49,45 | sFr 60,007 € 44,95 | £40.99ISBN 978-1-4614-4264-6

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65

G. Gui, Northwest University,Xi’an,China

Stability to the Incompressible Navier-Stokes EquationsThis thesis contains results of Dr. Guilong Gui during his PhD period with the aim to under-stand incompressible Navier-Stokes equations. It is devoted to the study of the stability to the incompressible Navier-Stokes equations. There is great potential for further theoretical and numeri-cal research in this field. The techniques developed in carrying out this work are expected to be useful for other physical model equations. It is also hopeful that the thesis could serve as a valuable reference on current developments in research topics related to the incompressible Navier-Stokes equations. It was nominated by the Graduate University of Chinese Academy of Sciences as an outstanding PhD thesis.

Features 7 Devoted to the study of the stability to the incompressible Navier-Stokes equations 7 A valuable reference on current developments in re-search topics related to the incompressible Navier-Stokes equations; 7 Nominated by the Graduate University of Chinese Academy of Sciences as an outstanding Ph.D. thesis

Contents Introduction.- Stability to the global large solu-tions of the Navier-Stokes equations.- Global Smooth Solutions to the 2-D inhomogeneous Navier-Stokes Equations with Variable Viscosity.- On the decay and stability to global solutions of the 3-D inhomogeneous Navier-Stokes equations.

Field of interestPartial Differential Equations


Product categoryPh.D. Thesis

Due March 2013

2013. Approx. 150 p. (Springer Theses) Hardcover7 * € (D) 106,99 | € (A) 109,99 | sFr 133,507 € 99,99 | £90.00ISBN 978-3-642-36027-5

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T. Hawkins, Boston University, MA, USA

The Mathematics of Frobenius in ContextA Journey Through 18th to 20th Century Mathematics

Frobenius made many important contributions to mathematics in the latter part of the 19th century. Hawkins here focuses on his work in linear alge-bra and its relationship with the work of Burnside, Cartan, and Molien, and its extension by Schur and Brauer.

Features 7 Written by an expert in the field with forty years of research on the subject 7 Presented in three parts for optimal accessibility 7 Contains a detailed table of contents to guide readers to the works of greatest interest to them

Contents 1. A Berlin Education.- 2. Professor at the Zurich Polytechnic.- 3. Berlin Professor.- 4. The Para-digm.- 5. Further Development of the Paradigm.- 6. The Problem of Pfaff.- 7. The Cayley-Hermite Problem and Matrix Algebra.- 8. Arithmetical Investigations: Linear Algebra.- 9. Arithmeti-cal Investigations: Groups.- 10. Abelian Func-tions.- 11. Frobenius‘ Generalized Theory of Theta Functions.- 12. The Group Determinant Problem.- 13. Group Characters and Representations.- 14. Alternate Routes to Representation Theory.- 15. Characters and Representations after 1897.- 16. Loose Ends.- 17. Nonnegative Matrices.- 18. The Mathematics of Frobenius in Retrospect.- Refer-ences.- Index.

Fields of interestHistory of Mathematical Sciences; Linear and Multilinear Algebras, Matrix Theory



Due March 2013

2013. X, 684 p. 9 illus. (Sources and Studies in the History of Mathematics and Physical Sciences) Hardcover7 * € (D) 117,69 | € (A) 120,99 | sFr 146,507 € 109,99 | £99.00ISBN 978-1-4614-6332-0

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N. Hilber, ZHAW Zurich University of Applied Sciences, Switzerland; O. Reichmann, C. Schwab, ETH Zurich, Switzerland; C. Winter, Allianz Deutschland AG, Munich, Germany

Computational Methods for Quantitative FinanceFinite Element Methods for Derivative Pricing

Many mathematical assumptions on which clas-sical derivative pricing methods are based have come under scrutiny in recent years.

Features 7 Offers an accessible introduction to mod-ern deterministic numerical methods of option pricing 7 Presents methods for all standard European plain vanilla option as well as for widely used exotic derivative contracts, such as Barrier, American and multiperiod contracts 7 Includes a large section on methods for pricing derivatives on baskets, such as Lévy Copula models

Contents 1.Introduction.- Part I.Basic techniques and models: 2.Notions of mathematical finance.- 3.Ele-ments of numerical methods for PDEs.- 4.Finite element methods for parabolic problems.- 5.Euro-pean options in BS markets.- 6.American options.- 7.Exotic options.- 8.Interest rate models.- 9.Multi-asset options.- 10.Stochastic volatility models-. 11.Lévy models.- 12.Sensitivities and Greeks.- Part II.Advanced techniques and models: 13.Wavelet methods.- 14.Multidimensional diffusion models.- 15.Multidimensional Lévy models.- 16.Stochastic volatility models with jumps.- 17.Multidimen-sional Feller processes.- Apendices: A.Elliptic variational inequalities.- B.Parabolic variational inequalities.- References. - Index.

Fields of interestProbability Theory and Stochastic Processes; Quantitative Finance; Numerical Analysis

Target groupsProfessional/practitioner


Due March 2013

2013. XIII, 299 p. 57 illus., 48 in color. (Springer Finance) Hardcover7 * € (D) 64,15 | € (A) 65,95 | sFr 80,007 € 59,95 | £53.99ISBN 978-3-642-35400-7

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66

A. Kawauchi, Osaka City University, Osaka City, Japan; T. Yanagimoto, Osaka Kyoiku University ,Japan (Eds)

Teaching and Learning of Knot Theory in School Mathematics This book is the result of a joint venture between Professor Akio Kawauchi, Osaka City University, well-known for his research in knot theory, and the Osaka study group of mathematics education, founded by Professor Hirokazu Okamori and now chaired by his successor Professor Tomoko Yanagimoto, Osaka Kyoiku University. The seven chapters address the teaching and learning of knot theory from several perspectives.

Features 7 It serves as a comprehensive text for teaching and learning knot theory from elementary school to high school 7 It provides a model for coop-eration between mathematicians and mathematics educators based on substantial mathematics 7 It is a thorough introduction to the Japanese art of lesson studies again in the context of substantial mathematics

Contents 1. What is Knot Theory?---Why Is It in Mathemat-ics?2. The Evolution of Mathematics Education---forwarding the research and practice of teaching knot theory in mathematics education---3. The Background of Developing Teaching Contents of Knot Theory 4. Education Practice in Elementary School 5. Education Practices in Junior High School 6. Education Practices in Senior High School 7. Education Practice at the University as Liberal Arts and Teacher Education-Index

Fields of interestGeometry; Topology; Mathematics Education



Available

2012. XIV, 188 p. 327 illus., 93 in color. Hardcover7 * € (D) 90,90 | € (A) 93,45 | sFr 113,507 € 84,95 | £76.50ISBN 978-4-431-54137-0

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M. Kisielewicz, University of Zielona Góra, Poland

Stochastic Differential Inclusions and Applications This book aims to further develop the theory of stochastic functional inclusions and their applica-tions for describing the solutions of the initial and boundary value problems for partial differential inclusions. The self-contained volume is designed to introduce the reader in a systematic fashion, to new methods of the stochastic optimal control theory from the very beginning. The exposi-tion contains detailed proofs and uses new and original methods to characterize the properties of stochastic functional inclusions that, up to the present time, have only been published recently by the author.

Features 7 Written by an award-winning expert in the field of Control Theory and Stochastic Pro-cesses 7 Presents new and original methods of solving select problems of optimal control theory and contains both solved problems and new open ones 7 Develops the theory of certain stochastic functional inclusions and its applications 7 May be treated as an introduction to a new approach to stochastic optimal control theory

Contents Preface.- List of Symbols.- 1. Stochastic Processes.- 2. Set-Valued Stochastic Processes.- 3. Set-Valued Stochastic Intergrals.- 4. Stochastic Differential Inclusions.- 5.Viability Theory.- 6. Partial Dif-ferential Inclusions.- 7. Some Optimal Control Problems.- Bibliography.- Subject Index.

Fields of interestCalculus of Variations and Optimal Control; Optimization; Ordinary Differential Equations; Numerical Analysis



Due May 2013

2013. XXII, 325 p. 6 illus. (Springer Optimization and Its Applications, Volume 80) Hardcover7 * € (D) 101,64 | € (A) 104,49 | sFr 126,507 € 94,99 | £85.50ISBN 978-1-4614-6755-7

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E. Kunz, Universität Regensburg, Germany

Introduction to Commutative Algebra and Algebraic GeometryOriginally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geom-etrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduc-tion to Commutative Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic variet-ies as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings.

Features 7 Affordable reprint of a classic text-book 7 Presents areas of commutative algebra that are best understood together 7 Includes numerous examples and exercises

Contents Foreword.- Preface.- Preface to the English Edi-tion.- Terminology.- Algebraic varieties.- Dimen-sion.- Regular and rational functions on algebraic varieties.- The local-global principle in commuta-tive algebra.- On the number of equations needed to describe an algebraic variety.- Regular and singular points of algebraic varieties.- Projective Resolutions.- Bibliography.- List of Symbols.- In-dex.

Fields of interestAlgebraic Geometry; Algebra; Commutative Rings and Algebras

Target groupsUpper undergraduate


Available

2013. XIII, 238 p. (Modern Birkhäuser Classics) Softcover7 * € (D) 42,75 | € (A) 43,95 | sFr 53,507 € 39,95 | £35.99ISBN 978-1-4614-5986-6

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67

R. Laza, Stony Brook University, NY, USA; M. Schütt, The University of Hannover, Germany; N. Yui, Queen‘s University, Kingston, ON, Canada (Eds)

Arithmetic and Geometry of K3 Surfaces and Calabi–Yau ThreefoldsContents .-Preface.-Introduction.- List of Participants.- K3 and Enriques Surfaces (S. Kondo).- Transcenden-tal Methods in the Study of Algebraic Cycles with a Special Emphasis on Calabi–Yau Varieties (J.D. Lewis).- Two Lectures on the Arithmetic of K3 Surfaces (M. Schütt).- Modularity of Calabi–Yau Varieties (N. Yui).- Explicit Algebraic Coverings of a Pointed Torus (A. Anema, J. Top).- Elliptic Fibrations on the Modular Surface Associated to Γ1(8).- Universal Kummer Families over Shimura Curves (A. Besser, R. Livné).- Numerical Trivial Automorphisms of Enriques Surfaces in Arbitrary Characteristic (I.V. Dolgachev).- Picard-Fuchs Equations of Special One-Parameter Families of Invertible Polynomials (S. Gährs).- A Structure Theorem for Fibrations on Delsarte Surfaces (B. Heijne, R. Kloosterman).- Fourier–Mukai Partners and Polarised K3 Surfaces (K. Hulek, D. Ploog).- On a Family of K3 Surfaces with S4 Symmetry (D. Karp, J. Lewish, D. Moore, D. Skjorshammer, U. Whitcher).- K1ind of Elliptically Fibered K3 Surfaces (M. Kerr).- A Note About Special Cycles on Moduli Spaces of K3 Surfaces (S. Kudla).- En-riques Surfaces of Hutchinson–Göpel Type and Mathieu Automorphisms (S. Mukai, H. Ohashi).- Quartic K3 Surfaces and Cremona Transforma-tions (K. Oguiso).- Invariants of Regular Models of the Product of Two Elliptical Curves at a Place of Multiplicative Reduction (C. Schoen).- Dynam-ics of Special Points on Intermediate Jacobians (X. Chen, J.D. Lewis). [...]

Fields of interestAlgebraic Geometry; Number Theory; Differential Geometry



Due April 2013

2013. X, 602 p. 20 illus., 12 in color. (Fields Institute Communications, Volume 67) Hardcover7 * € (D) 117,69 | € (A) 120,99 | sFr 146,507 € 109,99 | £99.00ISBN 978-1-4614-6402-0

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M. Ludwig, TU Wien, Austria; V. D. Milman, University of Tel Aviv, Israel; V. Pestov, University of Ottawa, ON, Canada; N. Tomczak-Jaegermann, University of Alberta, Edmonton, AB, Canada (Eds)

Asymptotic Geometric AnalysisProceedings of the Fall 2010 Fields Institute Thematic Program

Contents Preface.- The Variance Conjecture on Some Polytopes (D. Alonso Gutirrez, J. Bastero).- More Universal Minimal Flows of Groups of Automor-phisms of Uncountable Structures (D. Bartosova).- On the Lyapounov Exponents of Schrodinger Operators Associated with the Standard Map (J. Bourgain).- Overgroups of the Automor-phism Group of the Rado Graph (P. Cameron, C. Laflamme, M. Pouzet, S. Tarzi, R. Wood-row).- On a Stability Property of the Generalized Spherical Radon Transform (D. Faifman).- Banach Representations and Affine Compactification of Dynamical Systems (E. Glasner, M. Megrelish-vili).- Flag Measures for Convex Bodies (D. Hug, I. Turk, W. Weil).- Operator Functional Equations in Analysis (H. Konig, V. Milmann).- A Remark on the External Non-Central Sections of the Unit Cube (J. Moody, C. Stone, D. Zach, A. Zvavitch).- Universal Flows of Closed Subgroups of S∞ and Relative Extreme Amenability (L. Nguyen Van The).- Oscillation of Urysohn Type Spaces (N.W. Sauer).- Euclidean Sections of Convex Bodies (G. Schechtman).- Duality on Convex Sets in Generalized Regions (A. Segal, B.A. Slomka).- On Polygons and Injective Mappings of the Plane (B.A. Slomka).- Abstract Approach to Ramsey Theory and Ramsey Theorems for Finite Trees (S. Solecki).- Some Affine Invariants Revisited (A. Stancu). [...]

Fields of interestFunctional Analysis; Probability Theory and Sto-chastic Processes; Real Functions



Due January 2013

2013. X, 395 p. 14 illus., 8 in color. (Fields Institute Communications, Volume 68) Hardcover7 * € (D) 101,64 | € (A) 104,49 | sFr 126,507 € 94,99 | £85.50ISBN 978-1-4614-6405-1

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N. Madras, York University, Toronto, ON, Canada; G. Slade, The University of British Columbia, Vancouver, Canada

The Self-Avoiding WalkThe self-avoiding walk is a mathematical model that has important applications in statistical mechanics and polymer science. In spite of its simple definition—a path on a lattice that does not visit the same site more than once—it is difficult to analyze mathematically. The Self-Avoiding Walk provides the first unified account of the known rigorous results for the self-avoiding walk, with particular emphasis on its critical behavior. Its goals are to give an account of the current mathematical understanding of the model, to indicate some of the applications of the concept in physics and in chemistry, and to give an introduc-tion to some of the nonrigorous methods used in those fields.

Features 7 Affordable reprint of a classic mono-graph 7 Provides a focused look at an impor-tant mathematical model 7 Includes an intro-duction to methods used in physics and chemistry

Contents Preface.- Introduction.- Scaling, polymers and spins.- Some combinatorial bounds.- Decay of the two-point function.- The lace expansion.- Above four dimensions.- Pattern theorems.- Polygons, slabs, bridges and knots.- Analysis of Monte Carlo methods.- Related Topics.- Random walk.- Proof of the renewal theorem.- Tables of exact enumera-tions.- Bibliography.- Notation.- Index.

Fields of interestProbability Theory and Stochastic Processes; Combinatorics; Mathematical Applications in the Physical Sciences



Available

2013. XVI, 427 p. (Modern Birkhäuser Classics) Softcover7 * € (D) 64,15 | € (A) 65,95 | sFr 80,007 € 59,95 | £53.99ISBN 978-1-4614-6024-4

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68

E. Meinrenken, University of Toronto, ON, Canada

Clifford Algebras and Lie TheoryThis monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bi-linear forms and Clifford algebras. It develops the spin groups and the spin representation, culminat-ing in Cartan’s famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci’s proof of the Poincaré–Birkhoff–Witt theorem. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator.

Features 7 Convenient and up-to-date reference for back-ground material from Clifford theory, relevant for students and researchers in mathematics and physics 7 Included are many developments from the last 15 years, drawn in part from the author's research 7 Largely self-contained exposition

Contents Preface.- Conventions.- List of Symbols.- 1 Sym-metric bilinear forms.- 2 Clifford algebras.- 3 The spin representation.- 4 Covariant and contravari-ant spinors.- 5 Enveloping algebras.- 6 Weil alge-bras.- 7 Quantum Weil algebras.- 8 Applications to reductive Lie algebras.- 9 D(g; k) as a geometric Dirac operator.- 10 The Hopf–Koszul–Samelson Theorem.- 11 The Clifford algebra of a reductive Lie algebra.- A Graded and filtered super spaces.- B Reductive Lie algebras.- C Background on Lie groups.- References.- Index.

Fields of interestTopological Groups, Lie Groups; Associative Rings and Algebras; Mathematical Applications in the Physical Sciences



Due May 2013

2013. Approx. 325 p. (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, Volume 58) Hardcover7 * € (D) 101,64 | € (A) 104,49 | sFr 126,507 € 94,99 | £85.50ISBN 978-3-642-36215-6

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J. P. Morais, University of Aveiro, Portugal; S. Georgiev, Sorbonne University, Paris, France, and Sofia University, Bulgaria; W. Sprößig, TU Bergakademie, Freiberg, Germany

Real Quaternionic Calculus HandbookReal quaternion analysis is a multi-faceted subject. Created to describe phenomena in special relativ-ity, electrodynamics, spin etc., it has developed into a body of material that interacts with many branches of mathematics, such as complex analy-sis, harmonic analysis, differential geometry, and differential equations. It is also a ubiquitous factor in the description and elucidation of problems in mathematical physics. In the meantime real quaternion analysis has become a well established branch in mathematics and has been greatly suc-cessful in many different directions.

Features 7 Gives a brief introduction in the algebra, geometry and elementary analysis of quaternions and quaternion functions 7 Presents solutions or hints for the solution of 150 problems, and sup-plementary exercises for a course on quaterni-ons 7 Provides basic knowledge for computing with matrices with quaternion entries 7 Includes important historical remarks

Contents 1 An introduction to quaternions.- 2 Quaternions and spatial rotation.- 3 Applications to plane ge-ometry.- 4 Quaternion sequences.- 5 Quaternion series and infinite products.- 6 Exponents and logarithms.- 7 Trigonometry.- 8 Hyperbolic.- 9 In-verse hyperbolic and trigonometric functions.- 10 Quaternion matrices.- 11 Monomials, polynomials and binomials.

Fields of interestNon-associative Rings and Algebras; Functions of a Complex Variable; Combinatorics



Due May 2013

2013. Approx. 250 p. Softcover7 approx. * € (D) 42,75 | € (A) 43,95 | sFr 53,507 approx. € 39,95 | £35.99ISBN 978-3-0348-0621-3

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Y. Nievergelt, Eastern Washington University, Cheney, WA, USA

Wavelets Made EasyOriginally published in 1999, Wavelets Made Easy offers a lucid and concise explanation of mathematical wavelets. Written at the level of a first course in calculus and linear algebra, its accessible presentation is designed for under-graduates in a variety of disciplines—computer science, engineering, mathematics, mathematical sciences—as well as for practicing professionals in these areas. The present softcover reprint re-tains the corrections from the second printing (2001) and makes this unique text available to a wider audience. The first chapter starts with a description of the key features and applications of wavelets, focusing on Haar‘s wavelets but using only high-school mathematics. The next two chap-ters introduce one-, two-, and three-dimensional wavelets, with only the occasional use of matrix algebra.

Features 7 Affordable reprint of a classic undergradu-ate textbook 7 Accessible guide to wavelets with applications to many fields 7 Includes numer-ous exercises at the end of each section

Contents Preface.- Outline.- A. Algorithms for Wavelet Transforms.- Haar‘s Simple Wavelets.- Multidi-mensional Wavelets and Applications.- Algorithms for Daubechies Wavelets.- B. Basic Fourier Analy-sis.- Inner Products and Orthogonal Projections.- Discrete and Fast Fourier Transforms.- Fourier Series for Periodic Functions.- C. Computation and Design of Wavelets.- Fourier Transforms on the Line and in Space.- Daubechies Wavelets Design.- Signal Representations with Wavelets. D. Directories.- Acknowledgements.- Collection of Symbols.- Bibliography.- Index.

Fields of interestAbstract Harmonic Analysis; Fourier Analysis; Electrical Engineering



Available

2013. XIII, 297 p. (Modern Birkhäuser Classics) Softcover7 * € (D) 48,14 | € (A) 49,49 | sFr 60,007 € 44,99 | £40.99ISBN 978-1-4614-6005-3

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69

C. Norman, Royal Holloway, University of London, UK

Finitely Generated Abelian Groups and Similarity of Matrices over a FieldAt first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common. However, reduction to Smith normal form, named after its originator H.J.S.Smith in 1861, is a matrix version of the Euclidean algorithm and is exactly what the theory requires in both cases. Starting with matrices over the integers, Part 1 of this book provides a measured introduction to such groups: two finitely generated abelian groups are isomorphic if and only if their invariant factor sequences are identical.

Features 7 The theory of finitely generated abelian groups is introduced in an understandable and concrete way 7 The analogous theory of similarity of square matrices over a field, including the Jordan form, is explained step by step 7 Manipulative techniques are stressed to get students ‘on board’

Contents Part 1 :Finitely Generated Abelian Groups: Matrices with Integer Entries: The Smith Normal Form.- Basic Theory of Additive Abelian Groups.- Decomposition of Finitely Generated Z-Modules. Part 2: Similarity of Square Matrices over a Field: The Polynomial Ring F[x] and Matrices over F[x]- F[x] Modules: Similarity of t xt Matrices over a Field F.- Canonical Forms and Similarity Classes of Square Matrices over a Field.

Fields of interestField Theory and Polynomials; Group Theory and Generalizations; Linear and Multilinear Algebras, Matrix Theory



Available

2012. XII, 381 p. (Springer Undergraduate Mathematics Series) Softcover7 * € (D) 37,40 | € (A) 38,45 | sFr 47,007 € 34,95 | £24.95ISBN 978-1-4471-2729-1

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P. M. Pardalos, University of Florida, Gainesville, FL, USA; D.-Z. Du, University of Texas, Richardson, TX, USA; R. L. Graham, University of California, La Jolla, CA, USA (Eds)

Handbook of Combinatorial OptimizationContents Introduction.- Part 1. General Methodology.- Analysis of Greedy Approximations.- Guillotine Partition in Geometric Optimization.- Mixed-Integer Nonlinear Optimization in Process Synthesis.- Connection between Nonlinear Pro-gramming and Discrete Optimization.- Interior Point Methods for Combinatorial Optimization.- Fractional Combinatorial Optimization.- Refor-mulation-Linearization Techniques for Discrete Optimization Problems.- Grobner Bases in Integer Programming.- Dynamical System Approaches to Combinatorial Optimization.- Semidefinite Relaxation, Multivariate Norma Distribution and Order Statistics. [...]

Fields of interestOptimization; Combinatorics


Product categoryReference work

Due July 2013

Print

2nd ed. 2013. 4930 p. 500 illus. in color. 7 * € (D) 2675,00 | € (A) 2750,00 | sFr 3328,007 € 2500,00 | £2250.00ISBN 978-1-4419-7996-4

9<HTMEPB=jhjjge> eReference

2nd ed. 2013. 7 ** € (D) 2975,00 | € (A) 3000,00 | sFr 3497,007 € 2500,00 | £2250.00ISBN 978-1-4419-7997-1

9<HTMEPB=jhjjhb> Print + eReference

2nd ed. 2013. 4930 p. 500 illus. in color. 7 * € (D) 3343,75 | € (A) 3437,50 | sFr 4160,007 € 3125,00 | £2812.50ISBN 978-1-4614-3975-2

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A. Quarteroni, Politecnico di Milano, Italia

Modellistica Numerica per Problemi DifferenzialiATTENZIONE: COMUNICATO IMPOR-TANTE!! Springer desidera informare i propri let-tori che la presente edizione del volume con ISBN 978-88-470-2747-3 risulta fallata a causa di un errore generato da Springer in fase di compilazi-one dei file LateX forniti dall‘Autore.

Features 7 Non presuppone una approfondita cono-scenza matematica delle equazioni alle derivate parziali 7 Numerosi esercizi corredano i diversi capitoli 7 Rispetto alle edizioni precedenti, tutti i capitoli sono stati rivisti ed integrati, anche con nuovi risultati numerici

Contents Richiami sulle equazioni alle derivate parzia-li.- Richiami di analisi funzionale.- Equazioni di tipo ellittico.- Il metodo di Galerkin-elementi finiti per problemi ellittici.- Equazioni paraboli-che.- Generazione di griglie in 1D e 2D.- Algo-ritmi di risoluzione di sistemi lineari.- Cenni di programmazione degli elementi finiti.- Il metodo dei volumi finiti.- I metodi spettrali.- Metodi con elementi discontinui.- Equazioni di diffusione-tra-sporto-reazione.- Differenze finite per equazioni iperboliche.- Elementi finiti e metodi spettrali per equazioni iperboliche.- Cenni a problemi iperbo-lici non lineari.- Le equazioni di Navier-Stokes.- Introduzione al controllo ottimale per equazioni a derivate parziali.- Il metodo di decomposizione dei domini.

Fields of interestMathematics, general; Analysis; Numerical Analysis


Product categoryLibro di testo introduttivo

Available

5a ed. 2013. XVIII, 628 pagg. (UNITEXT / La Matematica per il 3+2) Brossura7 * € (D) 31,88 | € (A) 32,78 | sFr 40,007 € 29,80 | £26.99ISBN 978-88-470-5255-0

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70

I. Reider, Université d‘Angers, France

Nonabelian Jacobian of Projective SurfacesGeometry and Representation Theory

The Jacobian of a smooth projective curve is undoubtedly one of the most remarkable and beautiful objects in algebraic geometry. This work is an attempt to develop an analogous theory for smooth projective surfaces - a theory of the nonabelian Jacobian of smooth projective surfaces. Just like its classical counterpart, our nonabelian Jacobian relates to vector bundles (of rank 2) on a surface as well as its Hilbert scheme of points. But it also comes equipped with the variation of Hodge-like structures, which produces a sheaf of reductive Lie algebras naturally attached to our Ja-cobian. This constitutes a nonabelian analogue of the (abelian) Lie algebra structure of the classical Jacobian. This feature naturally relates geometry of surfaces with the representation theory of reduc-tive Lie algebras/groups. This work’s main focus is on providing an in-depth study of various aspects of this relation. It presents a substantial body of evidence that the sheaf of Lie algebras on the nonabelian Jacobian is an efficient tool for using the representation theory to systematically address various algebro-geometric problems.

Contents 1 Introduction.- 2 Nonabelian Jacobian J(X; L; d): main properties.- 3 Some properties of the filtra-tion H.- 4 The sheaf of Lie algebras G.- 5 Period maps and Torelli problems.- 6 sl2-structures on F.- 7 sl2-structures on G.- 8 Involution on G.- 9 Stratification of T.- 10 Configurations and theirs equations.- 11 Representation theoretic construc-tions.- 12 J(X; L; d) and the Langlands Duality.

Fields of interestAlgebraic Geometry; Linear and Multilinear Alge-bras, Matrix Theory



Due March 2013

2013. VIII, 227 p. (Lecture Notes in Mathematics, Volume 2072) Softcover7 * € (D) 48,14 | € (A) 49,49 | sFr 60,007 € 44,99 | £40.99ISBN 978-3-642-35661-2

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R. E. Rodríguez, Pontificia Universidad Católica de Chile, Santiago, Chile; I. Kra, Stony Brook University, NY, USA; J. P. Gilman, Rutgers University, Newark, NJ, USA

Complex AnalysisIn the Spirit of Lipman Bers

Features 7 New edition extensively revised and updat-ed 7 New topics include Bers's theorem on iso-morphisms between rings of holomorphic func-tions on plane domains, necessary and sufficient conditions for the existence of a bounded analytic function on the disc, subharmonic functions, Per-ron's principle, the ring of holomorphic functions on a plane domain, solutions to the Dirichlet problem, Green's function and its relation to the Riemann Mapping Theorem 7 Covers vast majority of the material needed for a beginning graduate level course on complex analysis 7 Ma-terial may be of interest to mathematicians, com-puter scientists, physicists, and engineers

Contents Preface to Second Edition.- Preface to First Edition.- Standard Notation and Commonly Used Symbols.- 1 The Fundamental Theorem in Complex Function Theory.- 2 Foundations.- 3 Power Series.- 4 The Cauchy Theory - A Funda-mental Theorem.- 5 The Cauchy Theory - Key Consequences.- 6 Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions.- 7 Sequences and Series of Holomorphic Func-tions.- 8 Conformal Equivalence and Hyperbolic Geometry.- 9 Harmonic Functions.- 10 Zeros of Holomorphic Functions.- Bibliographical Notes.- Bibliography.- Index.

Field of interestFunctions of a Complex Variable



Available

2nd ed. 2013. XVIII, 306 p. 27 illus. (Graduate Texts in Mathematics, Volume 245) Hardcover7 * € (D) 64,15 | € (A) 65,95 | sFr 80,007 € 59,95 | £53.99ISBN 978-1-4419-7322-1

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K. A. Ross, University of Oregon, Eugene, OR, USA

Elementary AnalysisThe Theory of Calculus

For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of well-chosen examples and exercises range from routine to chal-lenging. The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, well-motivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton‘s method and the secant method, and continuous nowhere-differen-tiable functions.

Features 7 Revised and updated second edition with new material 7 Text for a transition course between calculus and more advanced analysis courses 7 Contains new material on topics such as irrationality of pi, the Baire category theo-rem, Newton's method and the secant method, and continuous nowhere-differentiable func-tions 7 Includes new examples and improved proofs

Contents Preface.- 1 Introduction.- 2 Sequences.- 3 Con-tinuity.- 4 Sequences and Series of Functions.- 5 Differentiation.- 6 Integration.- 7 Capstone.- Ap-pendix on Set Notation.- Selected Hints and Answers.- References.- Index.

Fields of interestAnalysis; Real Functions



Due May 2013

2nd ed. 2013. XIV, 404 p. 35 illus. (Undergraduate Texts in Mathematics) Hardcover7 * € (D) 48,14 | € (A) 49,49 | sFr 60,007 € 44,99 | £40.99ISBN 978-1-4614-6270-5

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71

R. U. Seydel, Universität Köln, Germany

Tools for Computational FinanceThe disciplines of financial engineering and numerical computation differ greatly, however computational methods are used in a number of ways across the field of finance. It is the aim of this book to explain how such methods work in finan-cial engineering; specifically the use of numerical methods as tools for computational finance. By concentrating on the field of option pricing, a core task of financial engineering and risk analysis, this book explores a wide range of computational tools in a coherent and focused manner and will be of use to the entire field of computational finance. Starting with an introductory chapter that presents the financial and stochastic background, the remainder of the book goes on to detail computational methods using both stochastic and deterministic approaches.

Features 7 Provides exercises at the end of each chapter that range from simple tasks to more challenging projects 7 Covers on an introductory level the very important issue of computational aspects of derivative pricing 7 People with a background of stochastics, numerics, and derivative pricing will gain an immediate profit

Contents Modeling Tools for Financial Options.- Generat-ing Random Numbers with Specified Distribu-tions.- Monte Carlo Simulation with Stochastic Differential Equations.- Standard Methods for Standard Options.- Finite-Element Methods.- Pricing of Exotic Options.- Beyond Black and Scholes.

Fields of interestQuantitative Finance; Numerical Analysis



Available

5th ed. 2012. XVII, 429 p. 98 illus. (Universitext) Softcover7 * € (D) 64,15 | € (A) 65,95 | sFr 80,007 € 59,95 | £39.99ISBN 978-1-4471-2992-9

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G. Sobczyk, Universidad de Las Américas, Puebla, Mexico

New Foundations in MathematicsThe Geometric Concept of Number

The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathemat-ics.

Features 7 Geometric algebra, the central topic of the book, provides a unique way to unify, streamline, and simplify teaching and applying many different areas of mathematics 7 Presents and casts new light on an impressively broad range of math from elementary level 7 Features many exercises and problems to enhance the reader's skills and under-standing 7 Topics and applications selected to encourage further, more specific research by both graduates and undergraduates

Contents 1 Modular Number Systems.- 2 Complex and Hyperbolic Numbers.- 3 Geometric Algebra.- 4 Vector Spaces and Matrices.- 5 Outer Product and Determinants.- 6 Systems of Linear Equations.- 7 Linear Transformations on R^n.- 8 Structure of a Linear Operator.- 9 Linear and Bilinear Forms.- 10 Hermitian Inner Product Spaces.- 11 Geometry of Moving Planes.- 12 Representations of the Sym-metric Group.- 13 Calculus on m-Surfaces.- 14 Differential Geometry of Curves.- 15 Differential Geometry of k-Surfaces.- 16 Mappings Between Surfaces.- 17 Non-Euclidean and Projective Ge-ometries.- 18 Lie Groups and Lie Algebras.- Refer-ences.- Symbols.

Fields of interestLinear and Multilinear Algebras, Matrix Theory; Topological Groups, Lie Groups; Group Theory and Generalizations



Available

2013. XIV, 370 p. 55 illus., 32 in color. Hardcover7 * € (D) 64,15 | € (A) 65,95 | sFr 80,007 € 59,95 | £53.99ISBN 978-0-8176-8384-9

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J. Vrbik, Brock University, St. Catharines, ON, Canada; P. Vrbik, The University of Western Ontario, London, ON, Canada

Informal Introduction to Stochastic Processes with MapleThe book presents an introduction to Stochastic Processes including Markov Chains, Birth and Death processes, Brownian motion and Autore-gressive models. The emphasis is on simplifying both the underlying mathematics and the con-ceptual understanding of random processes. In particular, non-trivial computations are delegated to a computer-algebra system, specifically Maple (although other systems can be easily substituted).

Features 7 Complex ideas are presented in an infor-mal way, while maintaining mathematical rigor 7 Emphasis is on historically neglected generating functions 7 Key ideas are demon-strated by Monte Carlo simulation done with modern computer algebra systems, followed by visual presentation of results

Contents Contents.- Preface.- Finite Markov Chains.- Fi-nite Markov Chains II.- Branching Processes.- Renewal Theory.- Poisson Process.- Birth and Death Processes I.- Birth and Death Processes II.- Continuous-Time Markov Chains.- Brownian Motion.- Autoregressive Models.- Basic Probabil-ity Review.- Maple Programming.- References.

Fields of interestProbability Theory and Stochastic Processes; Statistics and Computing/Statistics Programs; Operations Research, Management Science



Available

2013. X, 287 p. 54 illus. With online files/update. (Universitext) Softcover7 * € (D) 48,10 | € (A) 49,45 | sFr 60,007 € 44,95 | £39.99ISBN 978-1-4614-4056-7

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