Takayasu, H., Sony Computer Science Laboratories, Tokyo, Japan (Ed.)

Empirical Science of Financial Fluctuations
The Advent of Econophysics

2002. X, 352 pp. 195 figs. Hardcover
4-431-70316-0

Financial fluctuations were generally neglected in classical ecnomics and their basic statistical properties have only recently been elucidated in the emerging field of econophysics, a new science that analyzes data using methods developed by statistical physics, such as chaos, fractals, and phase transitions. This volume is the proceedings of a workshop at which leading international researchers in this discipline discussed their most recent results and examined the validity of the empirical laws of econophysics. Topics include stock market prices and foreign exchange rates, income distribution, market anomalies, and risk management. The papers herein relate econophysics to other models, present new models, and illustrate the mechanisms by which financial fluctuations occur using actual financial data. Containing the most recent econophysics results, this volume will serve as an indispensable reference for economic theorists and practitioners alike.

Contents: Preface
Part 1. Empirical Facts of Financial Market Fluctuations:
1-1. Basic Market Statistics
1-2. Cross-Correlations
1-3. Market Anomalies
Part 2. Various Approaches to Financial Markets:
2-1. Agent-Based Modeling
2-2. Stochastic Modeling
2-3. Prediction and Investment Strategy
Part 3. Other Topics:
3-2. Corporate and Individual Statistics

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

Algebra

3rd rev. ed. 2002. Approx. 910 pp. Hardcover
0-387-95385-X

This book is intended as a basic text for a one-year course in Algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra. It successfully addresses the basic concepts of algebra. For the revised third edition, the author has added exercises and made numerous corrections to the text.

Comments on Serge Lang's Algebra:
Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books.
April 1999 Notices of the AMS, announcing that the author was awarded the Leroy P. Steele Prize for Mathematical Exposition for his many mathematics books.

The author has an impressive knack for presenting the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism which pervades some parts of algebra.
MathSciNet's review of the first edition

Contents: Foreword.- Groups.- Rings.- Modules.- Polynomials.- Algebraic Equations.- Galois Theory.- Extensions of Rings.- Transcendental Extensions.- Algebraic Spaces.- Noetherian Rings and Modules.- Real Fields.- Absolute Values.- Matrices and Linear Maps.- Representation of One Endomorphism.- Structure of Bilinear Forms.- The Tensor Product Semisimplicity.- Representations of Finite Groups.- The Alternating Product.- General Homology Theory.- Finite Free Resolutions.- Appendices.- Bibliography.

Series: Graduate Texts in Mathematics. VOL. 211

Bhatia, N.P., University of Maryland, Baltimore, USA;
Szego, G.P., Universita di Roma "LA Sapienza", Rome, Italy

Stability Theory of Dynamical Systems

Reprint of the 1st ed. Berlin Heidelberg New York 1970. 2002. XI, 225 pp. Softcover
3-540-42748-1

From the reviews:
"This is an introductory book intended for beginning graduate students or, perhaps advanced undergraduates. ... The book has many good points: clear organization, historical notes and references at the end of every chapter, and an excellent bibliography. The text is well written, at a level appropriate for the intended audience, and it represents a very good introduction to the basic theory of dynamical systems."
Mathematical Reviews, 1972
"The exposition is remarkably clear, definitions are separated explicitly, theorems are often provided together with the motivation for changing one or other hypothesis, as well as the relevance of certain generalisations... This study is an excellent review of the current situation for problems of stability of the solution of differential equations. It is addressed to all interested in non-linear differential problems, as much from the theoretical as from the applications angle."
Bulletin de la Societe Mathematique de Belgique, 1975

Keywords: dynamical systems, metric spaces, stability theory, autonomous differential equations

Series: Classics in Mathematics.

Hasse, H.

Number Theory

Reprint of the 1st ed. Berlin Heidelberg New York 1980. 2002. XVII, 638 pp. 49 figs. Softcover
3-540-42749-X

From the reviews:
"...a fine book ... treats algebraic number theory from the valuation-theoretic viewpoint. When it appeared in 1949 it was a pioneer. Now there are plenty of competing accounts. But Hasse has something extra to offer. This is not surprising, for it was he who inaugurated the local-global principle (universally called the Hasse principle). This doctrine asserts that one should first study a problem in algebraic number theoy locally, that is, at the completion of a vaulation. Then ask for a miracle: that global validity is equivalent to local validity. Hasse proved that miracles do happen in his five beautiful papers on quadratic forms of 1923-1924. ... The exposition is discursive. ... It is trite but true: Every number-theorist should have this book on his or her shelf."
(Irving Kaplansky in Bulletin of the American Mathematical Society, 1981)

Keywords: number theory, arithmetic, quadratic forms, valuation theory

Series: Classics in Mathematics.

E_Galois@msn.com wrote this review 2002 01 01

Hasse, Number Theory does show without doubt the bounty of German Mathematics over the English speaking mathematicians and the world. Despite the thousands of books on Algebraic Number Theory none of them can put on par with Hasse's Monumental Reference. The Price of the book is really very reasonable, however we could have hoped for copies of this book in hard cover too, no matter what the price might have been. Thanks very much to the Staff of Mathematics Editorial at Springer Verlag for bringing this book back to life.

Helleseth, T., University of Bergen, Norway;
Kumar, P.V., University of Southern California, Los Angeles, CA, USA;
Yang, K., Pohang University of Science and Technology, Pohang, Korea (Eds.)

Sequences and their Applications
Proceedings of SETA'01

2002. VIII, 324 pp. Softcover
1-85233-529-7

Pseudorandom sequences have widespread applications, for instance, in spread spectrum, code division multiple access, optical and ultrawide band communication systems, as well as in ranging systems global positioning systems, circuit testing and stream ciphers. Such sequences also have strong ties to error-correcting codes.
This volume contains survey and research papers on sequences and their applications. It brings together leading experts from discrete mathematics, computer science and communications engineering, and helps to bridge advances in these different areas. Papers in this volume discuss the theory of sequences and their applications in cryptography, coding theory, communications systems, numerical computation and computer simulation.

Contents: Invited Papers: Uniformly Representable Permutation Polynomials.- New p-ary perfect Sequences and Difference Sets with Singer Parameters.- On the crosscorrelation of m-sequences and related sequences with ideal autocorrelation.- Sequences for OFDM and Multi-Code CDMA: Two Problems in Algebraic Coding Theory.- Signal Design for Ultra-wideband Radio.- Constructions of Sequences from Algebraic Curves over Finite Fields.- Regular Papers: Description of Binary Sequences Based on the Interval Linear Complexity Profile .- On the Number of Kernel Elements of Automatic Sequences.- On the Coset Weight Divisibility and Nonlinearity of Resilient and Correlation-Immune Functions .- On the Linear Complexity of Generalised Legendre Sequence.- Hyper-Cyclotomic Algebra.- Cyclic Projective Planes, Perfect Circular Rulers, and Good Spanning Rulers.- Linear Recursive Sequences over Elliptic Curves.- On the Distinctness of Decimations of l-Sequences.- On Binary Sequences of Period n=pm-1 with Optimal Autocorrelation.- On the Profile of the k-Error Linear Complexity and the Zero Sum Property for Sequences over GF(pm) with Period pn.- Constant Sum Implies Statistical Independence of Chaotic Sequences.- First-Order Optimal Approximation of Binary Sequences.- On the Uniformity of Distribution of Congruential Generators over Elliptic Curves.- Further Constructions of Resilient Boolean Functions with Very High Nonlinearity.- On Certain 3-Weight Cyclic Codes Having Symmetric Weights and a Conjecture of Helleseth.- The Quantum Entanglement of Binary and Bipolar Sequences.- Characteristic Polynomials of Binary Kronekcker Sequences.- The Generation of PseudoRandom Numbers for the Simulation of White Gausssian Noise.

Series: Discrete Mathematics and Theoretical Computer Science.

Smirnov, V.A., Lomonosov Moscow State University, Moscow, Russia

Applied Asymptotic Expansions in Momenta and Masses

2002. IX, 263 pp. 52 figs. (Also available as online version). Hardcover
3-540-42334-6

The book presents asymptotic expansions of Feynman integrals in various limits of momenta and masses, and their applications to problems of physical interest. The problem of expansion is systematically solved by formulating universal prescriptions that express terms of the expansion using the original Feynman integral with its integrand expanded into a Taylor series in appropriate momenta and masses. Knowledge of the structure of the asymptotic expansion at the diagrammatic level is key in understanding how to perform expansions at the operator level. Most typical examples of these expansions are presented: the operator product expansion, the large-mass expansion, Heavy Quark Effective Theory, and Non-Relativistic QCD.

Keywords: Feynman diagrams, asymptotic expansions, threshold expansion

Series: Springer Tracts in Modern Physics. VOL. 177