advances in mathematical further developments in fractals ... › sgw › documents › 1355702 ›...

Mathematics springer.com/NEWSonline

28

Advances in Mathematical EconomicsSeries editors: S. Kusuoka, R. Anderson, C. Castaing, F. H. Clarke, E. Dierker, D. Duffie, L. C. Evans, T. Fujimoto, N. Hirano, T. Ichiishi, A. Ioffe, S. Iwamoto, K. Kamiya, K. Kawamata, H. Matano, K. Nishimura, M. Richter, Y. Takahashi, J.‑M. Grandmont, T. Maruyama, M. Yano, A. Yamazaki

Volume 16

S. Kusuoka, The University of Tokyo, Japan; T. Maruyama, Keio University, Japan (Eds)

Advances in Mathematical Economics Volume 16A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispen-sable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

Features 7 International scientific association that aims to promote research activities in mathematical economics 7 This series is designed to bring together those mathematicians who are seriously interested in obtaining new challenging stimuli from economic theories and those economists who are seeking effective mathematical tools for their research 7 This series is published once a year under the auspices of the Research Center for Mathematical Economics

Field of interestGame Theory, Economics, Social and Behav. Sciences

Target groupsProfessional/practitioner

Product categoryContributed volume

Available

2012. V, 134 p. 2 illus. Hardcover7 * € (D) 106,95 | € (A) 109,95 | sFr 133,507 € 99,95 | £90.00ISBN 978-4-431-54113-4

9<HTPEOB=febbde>

H. Andréka, Rényi Institute of Mathematics, Budapest, Hungary; M. Ferenczi, Budapest University of Technology and Economics, Hungary; I. Németi, Rényi Institute of Mathematics, Budapest, Hungary (Eds)

Cylindric-like Algebras and Algebraic LogicContents Introduction.- H. Andréka and I. Németi: Re-ducing First-order Logic to Df3, Free Algebras.- N.Bezhanishvili: Varieties of Two-Dimensional Cylindric Algebras.- R. Hirsch and I. Hodkinson: Completions and Complete Representations.- J. Madarász and T. Sayed Ahmed: Amalgamation, Interpolation and Epimorphisms in Algebraic Logic.- T. Sayed Ahmed: Neat Reducts and Neat Embeddings in Cylindric Algebras.- M. Feren-czi: A New Representation Theory: Represen-ting Cylindric-like Algebras by Relativized Set Algebras.- A. Simon: Representing all Cylindric Algebras by Twisting, On a Problem of Henkin.- A. Kurucz: Representable Cylindric Algebras and Many-Dimensional Modal Logics.- T. Sayed Ah-med: Completions, Complete Representations and Omitting Types.- G. Serény: Elements of Cylindric Algebraic Model Theory.- Y. Venema: Cylindric Modal Logic.- J. van Benthem: Crs and Guarded Logics: A Fruitful Contact.- R. S. Dordevic and M. D. Raskovic: Cylindric Probability Algebras.-I. Duentsch: Cylindric Algebras and Relational Databases. – M. Ferenczi: Probability Measures and Measurable Functions on Cylindric Algebras. – A. Mann: Cylindric Set Algebras and IF Logic. – G. Sági: Polyadic Algebras. – I. Sain: Definability Issues in Universal Logic. – Bibliography. - Index

Fields of interestMathematical Logic and Foundations; Algebra; Combinatorics

Target groupsResearch

Product categoryMonograph

Due December 2012

2012. Approx. 480 p. (Bolyai Society Mathematical Studies, Volume 22) Hardcover7 approx. * € (D) 106,95 | € (A) 109,95 | sFr 133,507 approx. € 99,95 | £90.00ISBN 978-3-642-35024-5

9<HTOGPC=dfacef>

J. Barral, Université Paris 13, Villetaneuse, France; S. Seuret, Université Paris-Est Créteil, France (Eds)

Further Developments in Fractals and Related FieldsMathematical Foundations and Connections

Features 7 Provides an overview of recent developments in the mathematical fields related to frac-tals 7 Includes original research contributions as well as surveys written by experts in their respective fields 7 Readers will find interesting and motivating results as well as new avenues for further research

Contents The Rauzy Gasket.- On the Hausdorff Dimension of Graphs of Prevalent Continuous Functions on Compact Sets.- Hausdorff Dimension and Dio-phantine Approximation.- Singular Integrals on Self-Similar Subsets of Metric Groups.- Multivari-ate Davenport Series.- Dimensions of Self-Affine Sets.- The Multifractal Spectra of V-Statistics.- Projections of Measures Invariant Under the Ge-odesic Flow.- Multifractal Tubes.- The Multipli-cative Golden Mean Shift has Infinite Hausdorff Measure.- The Law of Iterated Logarithm and Equilibrium Measures Versus Hausdorff Measures For Dynamically Semi-Regular Meromorphic Functions.- Cookie-Cutter-Like Sets with Graph Directed Construction.- Recent Developments on Fractal Properties of Gaussian Random Fields.

Fields of interestGeometry; Abstract Harmonic Analysis; Functio-nal Analysis



Due February 2013

2013. XV, 275 p. 28 illus., 12 in color. (Trends in Mathematics) Hardcover7 * € (D) 74,85 | € (A) 76,95 | sFr 93,507 € 69,95 | £62.99ISBN 978-0-8176-8399-3

9<HTLIMH=gidjjd>

www.springer.com/978-4-431-54113-4



News 12/2012 Mathematics

29

L. Barreira, C. Valls, Instituto Superior Técnico, Portugal

Complex Analysis and Differential EquationsThis text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include ho-lomorphic functions, Fourier series, ordinary and partial differential equations. The text is divided into two parts: part one focuses on complex ana-lysis and part two on differential equations. Each part can be read independently, so in essence this text offers two books in one. In the second part of the book, some emphasis is given to the applica-tion of complex analysis to differential equations. Half of the book consists of approximately 200 worked out problems, carefully prepared for each part of theory, plus 200 exercises of variable levels of difficulty. Tailored to any course giving the first introduction to complex analysis or differential equations, this text assumes only a basic know-ledge of linear algebra and differential and integral calculus.

Features 7 Emphasis is given to the applications of com-plex analysis to differential equations 7 Provides a rigorous approach with the right balance bet-ween theory and practice 7 Includes appro-ximately 200 examples and 200 problems with detailed solutions

Contents Part 1 Complex Analysis.- Basic Notions.- Ho-lomorphic Functions.- Sequences and Series.- Analytic Functions.- Part 2 Differential Equa-tions.- Ordinary Differential Equations.- Solving Differential Equations.- Fourier Series.- Partial Differential Equations .

Fields of interestFourier Analysis; Functions of a Complex Variab-le; Ordinary Differential Equations

Target groupsUpper undergraduate

Product categoryUndergraduate textbook

Available

Original Portugese edition published by IST Press, Portugal, 2010

2012. VIII, 415 p. 37 illus. (Springer Undergraduate Mathematics Series) Softcover7 * € (D) 37,40 | € (A) 38,45 | sFr 47,007 € 34,95 | £24.95ISBN 978-1-4471-4007-8

9<HTMEPH=beaahi>

L. Barreira, C. Valls, Instituto Superior Técnico, Lisbon, Portugal

Dynamical SystemsAn Introduction

The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An In-troduction undertakes the difficult task to provide a self-contained and compact introduction. Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a brief introduction to ergodic theory. In particu-lar, the authors consider topological recurrence, topological entropy, homeomorphisms and diffeo-morphisms of the circle, Sharkovski‘s ordering, the Poincaré-Bendixson theory, and the construction of stable manifolds, as well as an introduction to geodesic flows and the study of hyperbolicity (the latter is often absent in a first introduction). Moreover, the authors introduce the basics of symbolic dynamics, the construction of symbolic codings, invariant measures, Poincaré‘s recurrence theorem and Birkhoff ‘s ergodic theorem.

Features 7 Short and self-contained introduction to dynamical systems 7 Direct and rigorous exposi-tion 7 Contains a large number of examples and exercises 7 Includes an accessible introduction to ergodic theory

Contents Introduction.- Basic Notions and Examples.- To-pological Dynamics.- Low-Dimensional Dyna-mics.- Hyperbolic Dynamics I.- Hyperbolic Dyna-mics II.- Symbolic Dynamics.- Ergodic Theory.

Fields of interestDynamical Systems and Ergodic Theory; Global Analysis and Analysis on Manifolds; Ordinary Differential Equations

Target groupsGraduate

Product categoryGraduate/Advanced undergraduate textbook

Due February 2013

2013. X, 206 p. 44 illus. (Universitext) Softcover7 * € (D) 53,45 | € (A) 54,95 | sFr 66,507 € 49,95 | £29.99ISBN 978-1-4471-4834-0

9<HTMEPH=beidea>

I. Beyna, Frankfurt School of Finance & Management, Germany

Interest Rate DerivativesValuation, Calibration and Sensitivity Analysis

The class of interest rate models introduced by O. Cheyette in 1994 is a subclass of the general HJM framework with a time dependent volatility para-meterization. This book addresses the above men-tioned class of interest rate models and concen-trates on the calibration, valuation and sensitivity analysis in multifactor models. It derives analytical pricing formulas for bonds and caplets and applies several numerical valuation techniques in the class of Cheyette model, i.e. Monte Carlo simulation, characteristic functions and PDE valuation based on sparse grids. Finally it focuses on the sensitivity analysis of Cheyette models and derives Model- and Market Greeks.

Features 7 Presents sensitivity analysis of interest rate derivatives in the class of Cheyette models that is unique in the literature 7 Uses sparse grid technique, adjusts it slightly and can solve high-dimensional PDEs 7 Addressed to financial engineers and practitioners

Contents Preface.- 1.Literature Review.- 2.The Cheyette Mo-del Class.- 3.Analytical Pricing Formulas.- 4.Calib-ration.- 5.Monte Carlo Methods.- 6.Characteristic Function Method.- 7.PDE Valuation.- 8.Compa-rison of Valuation Techniques for Interest Rate Derivatives.- 9.Greeks.- 10.Conclusion.-Appendi-ces: A.Additional Calculus in the Class of Cheyette Models.- B.Mathematical Tools.- C.Market Data.- References.- Index.

Fields of interestQuantitative Finance; Applications of Mathema-tics; Numerical Analysis



Due December 2012

2013. XVIII, 208 p. 33 illus. (Lecture Notes in Economics and Mathematical Systems, Volume 666) Softcover7 * € (D) 74,85 | € (A) 76,95 | sFr 93,507 € 69,95 | £62.99ISBN 978-3-642-34924-9

9<HTOGPC=dejcej>





30

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

9<HTMEPH=beajff>

S. Bosch, Westfälische Wilhelms-Universität, Münster, Germany

Algebraic Geometry and Commutative AlgebraAlgebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry, like algebraic number theory. The new techniques paved the way to spectacular progress such as the proof of Fermat’s Last Theorem by Wi-les and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts.

Features 7 Explains schemes in algebraic geometry from a beginner's level up to advanced topics such as smoothness and ample invertible sheaves 7 Is self-contained and well adapted for self-stu-dy 7 Includes prerequisites from commutative algebra in a separate part 7 Gives motivating introductions to the different themes, illustrated by typical examples 7 Offers an abundance of exercises, specially adapted to the different sections

Contents Rings and Modules.- The Theory of Noetheri-an Rings.- Integral Extensions.- Extension of Coefficients and Descent.- Homological Methods: Ext and Tor.- Affine Schemes and Basic Const-ructions.- Techniques of Global Schemes.- Etale and Smooth Morphisms.- Projective Schemes and Proper Morphisms.

Fields of interestAlgebraic Geometry; Commutative Rings and Algebras



Due December 2012

2013. X, 504 p. (Universitext) Softcover7 * € (D) 74,85 | € (A) 76,95 | sFr 93,507 € 69,95 | £49.99ISBN 978-1-4471-4828-9

9<HTMEPH=beicij>

P. M. Gadea, Instituto de Fisica Fundamental, Madrid, Spain; J. Muñoz Masqué, Instituto de Seguridad de la Información, Madrid, Spain; I. V. Mykytyuk, Pedagogical University of Cracow, Poland

Analysis and Algebra on Differentiable ManifoldsA Workbook for Students and Teachers

This is the second edition of this best selling problem book for students, now containing over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Rieman-nian manifolds. The exercises go from elementary computations to rather sophisticated tools. Many of the definitions and theorems used throughout are explained in the first section of each chap-ter where they appear. A 56-page collection of formulae is included which can be useful as an aide-mémoire, even for teachers and researchers on those topics.

Features 7 Exercises range from rudimentary to chal-lenging, so will benefit the beginner as well as advanced students 7 Over 400 completely solved exercises 7 56-page index of formulae

Contents Differentiable manifolds.- Tensor Fields and Differential Forms.- Integration on Manifolds.- Lie Groups.- Fibre Bundles.- Riemannian Geometry.- Some Formulas and Tables.

Field of interestDifferential Geometry



Due December 2012

2nd ed. 2013. Approx. 630 p. 68 illus., 38 in color. (Problem Books in Mathematics) Hardcover7 * € (D) 74,85 | € (A) 76,95 | sFr 93,507 € 69,95 | £62.99ISBN 978-94-007-5951-0

9<HTUELA=hfjfba>





31

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

Introduction to Mathematical Structures and ProofsReviews of the first edition: „...Gerstein wants-ve-ry 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 mathe-matical proof by thoughtful oscillation between what is known and what is to be demonstra-ted 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 assortment 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

Target groupsLower undergraduate


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

9<HTMERB=eecgeg>

M. Joswig, TU Darmstadt, Germany; T. Theobald, Goethe-Universität Frankfurt am Main, Germany

Polyhedral and Algebraic Methods in Computational GeometryPolyhedral and Algebraic Methods in Computati-onal Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geo-metry. The first part of the book studies classical problems and techniques that refer to polyhedral structures.

Features 7 Provides a mathematical introduction to linear and non-linear (i.e. algebraic) computational geometry 7 Applies the theory to computer gra-phics, curve reconstruction and robotics 7 Esta-blishes interconnections with other disciplines such as algebraic geometry, optimization and numerical mathematics

Contents Introduction and Overview.- Geometric Fun-damentals.- Polytopes and Polyhedra.- Linear Programming.- Computation of Convex Hulls.- Voronoi Diagrams.- Delone Triangulations.- Alge-braic and Geometric Foundations.- Gröbner Bases and Buchberger’s Algorithm.- Solving Systems of Polynomial Equations Using Gröbner Bases.- Reconstruction of Curves.- Plücker Coordinates and Lines in Space.- Applications of Non-Linear Computational Geometry.- Algebraic Structures.- Separation Theorems.- Algorithms and Complexi-ty.- Software.- Notation.

Fields of interestGeometry; Convex and Discrete Geometry; Ma-thematical Applications in Computer Science



Due February 2013

2013. XII, 260 p. 67 illus., 15 in color. (Universitext) Softcover7 * € (D) 53,45 | € (A) 54,95 | sFr 66,507 € 49,95 | £29.99ISBN 978-1-4471-4816-6

9<HTMEPH=beibgg>

A. Kawauchi, Osaka City University,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 coope-ration 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 Mathema-tics?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 Elementa-ry 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

9<HTPEOB=febdha>





32

S. G. Krantz, Washington University St. Louis, MO, USA; H. R. Parks, Oregon State University Corvallis, OR, USA

The Implicit Function TheoremHistory, Theory, and Applications

The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blosso-med into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for Ck functions, (ii) formu-lations in other function spaces, (iii) formulations for non-smooth function, and (iv) formulations for functions with degenerate Jacobian. Particu-larly powerful implicit function theorems, such as the Nash–Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present uncorrected reprint of this classic monograph.

Features 7 Affordable reprint of a classic mono-graph 7 Accessible and thorough treatment of the implicit and inverse function theorems and their applications 7 Unifies disparate ideas that have played an important role in modern mathematics

Contents Preface.- Introduction to the Implicit Function Theorem.- History.- Basic Ideas.- Applications.- Variations and Generalizations.- Advanced Implicit Function Theorems.- Glossary.- Bibliogra-phy.- Index.

Fields of interestAnalysis; Partial Differential Equations; Differen-tial Geometry



Due November 2012

Originally published as a softcover

2013. XIII, 163 p. (Modern Birkhäuser Classics) Softcover7 * € (D) 53,45 | € (A) 54,95 | sFr 66,507 € 49,95 | £44.99ISBN 978-1-4614-5980-4

9<HTMERB=efjiae>

S. Lang, Yale University, New Haven, CT, USA

Collected Papers II1971–1977

Serge Lang (1927-2005) was one of the top mathematicians of our time. He was born in Paris in 1927, and moved with his family to Califor-nia, where he graduated from Beverly Hills High School in 1943. He subsequently graduated from California Institute of Technology in 1946, and received a doctorate from Princeton University in 1951 before holding faculty positions at the University of Chicago and Columbia University (1955-1971). At the time of his death he was pro-fessor emeritus of Mathematics at Yale University. An excellent writer, Lang has made innumerable and invaluable contributions in diverse fields of mathematics. He was perhaps best known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He was also a member of the Bourbaki group. He was honored with the Cole Prize by the American Ma-thematical Society as well as with the Prix Carrière by the French Academy of Sciences. These five vo-lumes collect the majority of his research papers, which range over a variety of topics.

Features 7 Integrates classic material 7 Authored by the winner of the Cole prize 7 Historical signifi-cance

Contents Bibliography through 1999.- Papers from1971-1977.

Fields of interestNumber Theory; Algebraic Geometry; Mathema-tical Methods in Physics


Product categoryCollected works

Due December 2012

2000. XVI, 590 p. (Springer Collected Works in Mathematics) Softcover7 approx. * € (D) 64,15 | € (A) 65,95 | sFr 80,007 approx. € 59,95 | £53.99ISBN 978-1-4614-6137-1

9<HTMERB=egbdhb>


Collected Papers III1978–1990

Serge Lang (1927-2005) was one of the top mathematicians of our time. He was born in Paris in 1927, and moved with his family to Califor-nia, where he graduated from Beverly Hills High School in 1943. He subsequently graduated from California Institute of Technology in 1946, and received a doctorate from Princeton University in 1951 before holding faculty positions at the University of Chicago and Columbia University (1955-1971). At the time of his death he was pro-fessor emeritus of Mathematics at Yale University. An excellent writer, Lang has made innumerable and invaluable contributions in diverse fields of mathematics. He was perhaps best known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He was also a member of the Bourbaki group. He was honored with the Cole Prize by the American Mathematical Society as well as with the Prix Car-rière by the French Academy of Sciences. These five volumes collect the majority of his research papers, which range over a variety of topics


Contents Bibliography (through 1999). - The Zurich Lectu-res. - Articles on Scientific Responsibility. - Books on Scientific Responsibility.

Fields of interestNumber Theory; Algebraic Geometry



Due December 2012


9<HTMERB=egbdjf>





33


Collected Papers V1993–1999

With contrib. by: J. Jorgensen, City College of New York, NY, USA

Serge Lang (1927-2005) was one of the top mathematicians of our time. He was born in Paris in 1927, and moved with his family to Califor-nia, where he graduated from Beverly Hills High School in 1943. He subsequently graduated from California Institute of Technology in 1946, and received a doctorate from Princeton University in 1951 before holding faculty positions at the University of Chicago and Columbia University (1955-1971). At the time of his death he was pro-fessor emeritus of Mathematics at Yale University. An excellent writer, Lang has made innumerable and invaluable contributions in diverse fields of mathematics. He was perhaps best known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He was also a member of the Bourbaki group.


Contents On Cramer‘s theorem of general Euler products with functional equations.- Basic Analysis of Re-gularized Series and Products.- Artin Formalism and Heat Kernels.- Explicit Formulas for Regula-rized Products and Series.- Extension of Analytic Number Theory and the Theory of Regularized Harmonic Series from Dirichlet Series to Bessel Series.- Hilbert-Asai Eisenstein Series, Regularized Products and Heat Kernels

Fields of interestNumber Theory; Algebraic Geometry



Due December 2012


9<HTMERB=egbegd>

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

Target groupsUpper undergraduate


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

9<HTMEPH=bchcjb>

P. Petersen, University of California, Los Angeles, CA, USA

Linear AlgebraThis textbook on linear algebra includes the key topics of the subject that most advanced under-graduates need to learn before entering graduate school. All the usual topics, such as complex vec-tor spaces, complex inner products, the Spectral theorem for normal operators, dual spaces, the minimal polynomial, the Jordan canonical form, and the rational canonical form, are covered, along with a chapter on determinants at the end of the book. In addition, there is material throughout the text on linear differential equations and how it integrates with all of the important concepts in linear algebra. This book has several distingu-ishing features that set it apart from other linear algebra texts. For example: Gaussian elimination is used as the key tool in getting at eigenvalues; it takes an essentially determinant-free approach to linear algebra; and systems of linear differential equations are used as frequent motivation for the reader. Another motivating aspect of the book is the excellent and engaging exercises that abound in this text. This textbook is written for an upper-division undergraduate course on Linear Algebra.

Features 7 Contains considerably more material on differential equations, as examples and as motivation, than is typical in a linear algebra textbook 7 Includes an excellent selection of good exercises 7 Classroom tested for an upper undergraduate course in linear algebra

Contents Preface.- 1 Basic Theory.- 2 Linear Operators.- 3 Inner Product Spaces.- 4 Linear Operators on Inner Product Spaces.- 5 Determinants.- Biblio-graphy.- Index

Field of interestLinear and Multilinear Algebras, Matrix Theory

Target groupsLower undergraduate


Available

2012. X, 387 p. 10 illus. (Undergraduate Texts in Mathematics) Hardcover7 * € (D) 48,10 | € (A) 49,45 | sFr 60,007 € 44,95 | £40.99ISBN 978-1-4614-3611-9

9<HTMERB=edgbbj>





34

P. Schneider, University of Münster, Germany

Modular Representation Theory of Finite GroupsRepresentation theory studies maps from groups into the general linear group of a finite-dimen-sional vector space. For finite groups the theory comes in two distinct flavours. In the ‚semisimple case‘ (for example over the field of complex num-bers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divi-des the order of the group. Modular Representati-on Theory of finite Groups comprises this second situation. Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as well as Green‘s direct analysis of indecompo-sable representations. There is also the strategy of writing the category of all representations as the direct product of certain subcategories, the so-called ‚blocks‘ of the group. Brauer‘s work then establishes correspondences between the blocks of the original group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation.

Features 7 Provides a concise introduction to modular representation theory 7 Is aimed at students at masters level 7 Compares group theoretic and module theoretic concepts

Contents Prerequisites in module theory.- The Cartan{Brauer triangle.- The Brauer character.- Green‘s theory of indecomposable modules.- Blocks.

Fields of interestAssociative Rings and Algebras; Group Theory and Generalizations



Due February 2013

2013. VIII, 184 p. Softcover7 * € (D) 53,45 | € (A) 54,95 | sFr 66,507 € 49,95 | £44.99ISBN 978-1-4471-4831-9

9<HTMEPH=beidbj>

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 computatio-nal 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.- Genera-ting 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

9<HTMEPH=bcjjcj>

K. Williams, Kim Williams Books, Torino, Italy (Ed)

Nexus Network Journal 14,3Architecture and Mathematics

Contents Letter from the Guest Editor.- Kim Williams: Digital Fabrication.- Alexandra Paio, Sara Eloy, Vasco Moreira Rato, Ricardo Resende Maria João de Oliveira: Prototyping Vitruvius, New Challen-ges: Digital Education, Research and Practice.- Kevin R. Klinger: Design-Through-Production Formulations.- Bob Sheil: Manufacturing Bespoke Architecture.- Tomas Diez: Personal Fabrication: Fab Labs as Platforms for Citizen-Based Innova-tion, from Microcontrollers to Cities.- Gabriela Celani: Digital Fabrication Laboratories: Pedagogy and Impacts on Architectural Education.- Tobias Bonwetsch: Robotic Assembly Processes as a Dri-ver in Architectural Design.- Aineias Oikonomou: Design and Tracing of Post-Byzantine Churches in Northwestern Greece.- Farah Habib, Iraj Etesam, S. Hadi Ghoddusifar, Nahid Mohajeri: Corres-pondence Analysis: A New Method for Analyzing Qualitative Data in Architecture.- Francisco Roldán: Method of Modulation and Sizing of His-toric Architecture.- Riccardo Migliari: Descriptive Geometry: From its Past to its Future.- José Pedro Sousa: Material Customization: Digital Fabrication Workshop at ISCTE/IUL.- Kim Williams: Review of Galileo’s Muse: Renaissance Mathematics and the Arts by Mark A. Peterson.

Fields of interestMathematics, general; Architecture, general



Due November 2012

2013. Approx. 200 p. (Nexus Network Journal, Volume 14, 3) Softcover7 * € (D) 85,55 | € (A) 87,95 | sFr 139,007 € 79,95 | £72.00ISBN 978-3-0348-0581-0

9<HTOAOE=iafiba>




advances in mathematical further developments in fractals ... › sgw › documents › 1355702 ›...

Documents