Boccara, Nino

Modeling Complex Systems

Series: Graduate Texts in Contemporary Physics

2004, XII, 397 p. 158 illus., Hardcover
ISBN: 0-387-40462-7

About this textbook

This book explores the process of modeling complex systems in the widest sense of that term, drawing on examples from such diverse fields as ecology, epidemiology, sociology, seismology, as well as economics. It also provides the mathematical tools for studying the dynamics of these systems. Boccara takes a carefully inductive approach in defining what it means for a system to be "complex" (and at the same time addresses the equally elusive concept of emergent properties). This is the first text on the subject to draw comprehensive conclusions from such a wide range of analogous phenomena.

Written for:

Graduate students, researchers

Irving, Ronald S.

Integers, Polynomials, and Rings
A Course in Algebra

Series: Undergraduate Texts in Mathematics

2004, XV, 284 p., Softcover
ISBN: 0-387-20172-6

About this textbook

Mathematics is often regarded as the study of calculation, but in fact, mathematics is much more. It combines creativity and logic in order to arrive at abstract truths. This book is intended to illustrate how calculation, creativity, and logic can be combined to solve a range of problems in algebra. Originally conceived as a text for a course for future secondary-school mathematics teachers, this book has developed into one that could serve well in an undergraduate course in abstract algebra or a course designed as an introduction to higher mathematics. Not all topics in a traditional algebra course are covered. Rather, the author focuses on integers, polynomials, their ring structure, and fields, with the aim that students master a small number of serious mathematical ideas. The topics studied should be of interest to all mathematics students and are especially appropriate for future teachers. One nonstandard feature of the book is the small number of theorems for which full proofs are given. Many proofs are left as exercises, and for almost every such exercise a detailed hint or outline of the proof is provided. These exercises form the heart of the text. Unwinding the meaning of the hint or outline can be a significant challenge, and the unwinding process serves as the catalyst for learning. Ron Irving is the Divisional Dean of Natural Sciences at the University of Washington. Prior to assuming this position, he served as Chair of the Department of Mathematics. He has published research articles in several areas of algebra, including ring theory and the representation theory of Lie groups and Lie algebras. In 2001, he received the University of Washington's Distinguished Teaching Award for the course on which this book is based.

Written for:

Undergraduate students and teachers in mathematics

Atkinson, Anthony C., Riani, Marco, Cerioli, Andrea

Exploring Multivariate Data with the Forward Search

Series: Springer Series in Statistics
2004, Approx. 650 p., Hardcover
ISBN: 0-387-40852-5

About this book

This book is concerned with data in which the observations are independent and in which the response is multivariate. Anthony Atkinson has been Professor of Statistics at the London School of Economics since 1989. Before that he was a Professor at Imperial College, London. He is the author of Plots, Transformations, and Regression, co-author of Optimum Experimental Designs, and joint editor of The Fascination of Statistics, a volume celebrating the centenary of the International Statistical Institute. Professor Atkinson has served as editor of The Journal of the Royal Statistical Society, Series B and as associate editor of Biometrika and Technometrics. He has published well over 100 articles in these and other journals including The Annals of Statistics, Biometrics, The Journal of the American Statistical Association, and Statistics and Computing. Marco Riani, after receiving his Ph.D. in Statistics in 1995 from the University of Florence, joined the Faculty of Economics at Parma University as postdoctoral fellow. In 1997 he won the prize for the best Italian Ph.D. thesis in Statistics. He is currently Associate Professor of Statistics in the University of Parma. He has published in Technometrics, The Journal of Computational and Graphical Statistics, The Journal of Business and Economic Statistics, The Journal of Forecasting, Environmetrics, Computational Statistics and Data Analysis, Metron, and other journals.

Written for:

Researchers, graduate students

Carmona, Rene A.

Statistical Analysis of Financial Data in S-PLUS

Series: Springer Texts in Statistics
2004, Approx. 490 p., Hardcover
ISBN: 0-387-20286-2

About this textbook

This book develops the use of statistical data analysis in finance, and it uses the statistical software environment of S-PLUS as a vehicle for presenting practical implementations from financial engineering. It is divided into three parts. Part I, Exploratory Data Analysis, reviews the most commonly used methods of statistical data exploration. Its originality lies in the introduction of tools for the estimation and simulation of heavy tail distributions and copulas, the computation of measures of risk, and the principal component analysis of yield curves. Part II, Regression, introduces modern regression concepts with an emphasis on robustness and non-parametric techniques. The applications include the term structure of interest rates, the construction of commodity forward curves, and nonparametric alternatives to the Black Scholes option pricing paradigm. Part III, Time Series and State Space Models, is concerned with theories of time series and of state space models. Linear ARIMA models are applied to the analysis of weather derivatives, Kalman filtering is applied to public company earnings prediction, and nonlinear GARCH models and nonlinear filtering are applied to stochastic volatility models. The book is aimed at undergraduate students in financial engineering, master students in finance and MBA's, and to practitioners with financial data analysis concerns.

Written for:

Undergraduate and graduate students and practitioners in mathematical finance

Chudnovsky, David, Chudnovsky, Gregory, Nathanson, Melvyn

Number Theory
New York Seminar 2003

2004, Approx. 270 p. 6 illus., Hardcover
ISBN: 0-387-40655-7

About this book

This volume marks the 20th anniversary of the New York Number Theory Seminar (NYNTS). Beginning in 1982, the NYNTS has tried to present a broad spectrum of research in number theory and related fields of mathematics, from physics to geometry to combinatorics and computer science. The list of seminar speakers includes not only Fields Medallists and other established researchers, but also many other younger and less well known mathematicians whose theorems are significant and whose work may become the next big thing in number theory.

Table of contents

* The spanning number and the independence number of a subset of an abelian group * A formula related to the Frobenius problem in two dimensions * One bit world * Use of Pade approximation in spline construction * Interactions between number theory and operator algebras in the study of Riemann zeta function (d'apres Bost-Connes and Connes) * A hyperelliptic curve with real multiplication of degree two * Humbert's conic model and the Kummer surface * Arithmeticity and theta correspondence of an orthogonal group * Morphis heights and periodic points * The elementary proof of the prime number theorem: An historical perspective * Additive bases representations and the Erdos-Turan conjecture * The boundary structure of the sumset in Z^2 * On NTU's in function fields * Continued fractions and quadratic irrationals * The inverse problem for representation functions of additive bases * On the ubiquity of Sidon sets

Oliver, David

The Shaggy Steed of Physics
Mathematical Beauty in the Physical World

2nd ed., 2004, XVII, 300 p. 74 illus., Hardcover
ISBN: 0-387-40307-8

About this book

The Shaggy Steed is an unassuming figure from Irish folklore who reveals himself as an inspiring teacher of the forces hidden in the universe. This book celebrates an unassuming bit of physics that also turns out to be an inspiring teacher. The two-body problem - the motion of two bodies bound by the inverse-square force of gravity and electricity - is the Shaggy Steed of physics, guiding the reader to an understanding of both the forces and the mathematical beauty hidden in the physical world. The book begins with an exposition of the action principle and its revelation of invariants created by the symmetries of nature. It then turns to the two-body problem and the grand unifying themes of symmetry and topology in physics, both classical and quantum. On the scale of the solar system this motion generates the Kepler ellipse - the fundamental orbit of celestial mechanics. On the microscopic scale of the quantum, the same motion generates the hydrogen atom - the primal element. This remarkable unity of the heavens and the elements rests upon hidden symmetry - the symmetry of rotations in four dimensions. This richly endowed symmetry also contains the symmetry of the relativistic space-time of Einstein. In addition it is the paradigm for the unitary symmetries of the elementary particles and pointed the way to them. This is a book for those seeking to know what breathes life into the equations of physics. It is also a fine tutorial book from which one can learn classical and quantum mechanics with pleasure. The Shaggy Steed of Physics is a spirited companion to the textbooks, a book that all students of physics, chemistry, and mathematics will want to read.

Written for:

Graduate students, advanced undergraduates, physicists

Table of contents

The Shaggy Steed of Physics.- The Heavens and the Elements.- The Law of Motion.- Classical Mechanics: The Heavens.- Quantum Mechanics: The Elements.- The Hidden Unity of Space and Time.- The Manifold Universe.

Teuscher, Christof (Ed.)

Alan Turing: Life and Legacy of a Great Thinker

2004, XXVIII, 542 p. 77 illus., 4 tabs., Hardcover
ISBN: 3-540-20020-7

About this book

Alan Turing's fundamental contributions to computing led to the development of modern computing technology, and his work continues to inspire researchers in computing science and beyond. This book is the definitive collection of commemorative essays, and the distinguished contributors have expertise in such diverse fields as artificial intelligence, natural computing, mathematics, physics, cryptology, cognitive studies, philosophy and anthropology. The volume spans the entire rich spectrum of Turing's life, research work and legacy. New light is shed on the future of computing science by visionary Ray Kurzweil. Notable contributions come from the philosopher Daniel Dennett, the Turing biographer Andrew Hodges, and the distinguished logician Martin Davis, who provides a first critical essay on an emerging and controversial field termed hypercomputation. A special feature of the book is the play by Valeria Patera which tackles the scandal surrounding the last apple, and presents as an enigma the life, death and destiny of the man who did so much to decipher the Enigma code during the Second World War. Other chapters are modern reappraisals of Turing's work on computability, and deal with the major philosophical questions raised by the Turing Test, while the book also contains essays addressing his less well-known ideas on Fibonacci phyllotaxis and connectionism.

Written for:

Researchers, students, and professionals