Lakoff,G./Nunez,R.

Where Mathematics Comes From.

Oct. 2000
0-465-03770-4

When you think about it, it seems obvious: the only mathematical ideas that human beings can have are ideas that the human brain allows. We know a lot about what human ideas are like from research in Cognitive Science. Most ideas are unconscious, and that is no less true of mathematical ideas. Abstract ideas, for the most part, arise via conceptual metaphor --- a mechanism for projecting embodied (that is, sensory-motor) reasoning to abstract reasoning. This book argues that conceptual metaphor plays a central, defining role in mathematical ideas within the cognitive unconscious --- from arithmetic and algebra to sets and logic to infinity in all of its forms: transfinite numbers, points at infinity, infinitesimals, and so on. Even the real numbers are constituted by metaphorical ideas coming out of the way we function in the every day physical world. This book is about mathematical ideas, about what mathemacics means --- and why. It is concerned not just with which theorems are true, but with what theorems mean and why they are true by virtue of what they mean. And it provides an answer to one of the deepest problems of the philosophy of mathematics: how a being with a finite brain and mind can comprehend infinity.

Gourieroux,C.

Econometrics of Qualitative Dependent Variables.

Oct. 2000 384 pp.
0-521-58985-1

This textbook introduces students progressively to various aspects of qualitative models and assumes a knowledge of basic principles of statistics and econometrics. Inferring qualitative characteristics of data on socioeconomic class, education, employment status, and the like - given their discrete nature - requires an entirely different set of tools from those applied to purely quantitative data. Written in accessible language and offering cogent examples, students are given valuable means to gauge real-world economic phenomena. After the introduction, early chapters present models with endogenous qualitative variables, examining dichotomous models, model specification, estimation methods, descriptive usage, and qualitative panel data. Professor Gourieroux also looks at Tobit models, in which the exogenous variable is sometimes qualitative and sometimes quantitative, and changing-regime models, in which the dependent variable is qualitative but expressed in quantitative terms. The final two chapters describe models which explain variables assumed by discrete or continuous positive variables.

Hunt,J./Vassilicos,C.

Turblence Structure and Vortex Dynamics.

Jan. 2001 300 pp.
0-521-78131-0
The articles in this volume, derived from a symposium held at the Newton Institute in Cambridge, examine a number of key questions that have engaged turbulence researchers for many years. Most involve mathematical analysis, but some describe numerical simulations and experimental results that focus on those questions. However, all are addressed to a wide cross-section of the turbulence community, namely mathematicians, engineers and scientists.

Levy,S.(ed.)

The Eightfold Way: the Beauty of Klein's Quartic Curve. (Now in Paperback ed.)

Feb. 2001
0-521-00419-5

The German mathematician Felix Klein discovered in 1879 that the: surface that we now call the Klein quartic has many remarkable properties. Since then, mathematicians have discovered that this object occurs in different guises in many areas of mathematics. This volume explores the tangle of properties and theories surrounding this multiform object. It includes expository and research articles by renowned mathematicians in different fields and a beautifully illustrated essay by the mathematical sculptor Helaman Ferguson. The book closes with the first English translation of Klein's seminal article on this surface.

Gyori,E./Sos,V.(eds.)

Recent Trends in Combinatorics: the Legacy of Paul Erdos.

Feb. 2001 210 pp.

A collection of surveys and research papers on recent topics of interest in combinatorics. Originally published in journal form, it is here reissued as a book due to its special interest. It is dedicated to Paul Erdos, one of the greatest mathematicians of his century, and includes a new preface, written by friends and colleagues, describing his work and containing many anecdotes about his life. Here is a succinct introduction to important recent ideas in combinatorics for researchers and graduate students.

Busa,F./Bouillon,P.(eds.)

The Language of Word Meaning.

Mar. 2001 325 pp.
0-521-78048-9

This volume is a collection of original contributions from outstanding scholars in linguistics, philosophy and computational linguistics exploring the relation between word meaning and human linguistic creativity. The papers present different aspects surrounding the question of what is word meaning, a problem that has been the center of heated debate in all those disciplines that directly or indirectly are concerned with the study of language and of human cognition. The discussions are centered around the newly emerging view of the mental lexicon, as outlined in the Generative Lexicon theory (Pustejovsky, 1995), which proposes a unified model for defining word meaning. The individual contributors present their evidence for a generative approach as well as critical perspectives, which provides for a volume where word meaning is not viewed only from a particular angle or from a particular concern, but from a wide variety of topics, each introduced and explained by the editors.

Hsiao,C./Morimune Kimio / Powell,J.

Nonlinear Statistical Modeling:
Proceedings of the Thirteenth Int'l Symposium in Economic Theory and Econometrics;
Essays in Honor of Takeshi Amemiya.

Mar. 2001 375 pp.
0-521-66246-X

This collection brings together important contributions by leading econometricians on (i) parametric approaches to qualitative and sample selection models, (ii) nonparametric and semi-parametric approaches to qualitative and sample selection models, and (iii) nonlinear estimation of cross-sectional and time series models. The advances achieved here can have important bearing on the choice of methods and analytical techniques in applied research.

Mclaughlin,P.

What Functions Explain: Functional Explanation and Self-Reproducing Systems.

Mar. 2001 272 pp.
0-521-78233-3

This book offers an examination of functional explanation as it is used in biology and the social sciences, and focuses on the kinds of philosophical presuppositions that such explanations carry with them. It tackles such questions as: Why are some things explained functional while others are not? What do the functional explanations tell us about how these objects are conceptualized? What do we commit ourselves to when we give and take functional explanations in the life sciences and the social sciences?

Monahan,J.

Numerical Methods of Statistics.

(Cambridge Series in Statistical and Probabilistic Mathematics,vol.7)

Mar. 2001 416 pp.
0-521-79168-5

This book explains how computer Software is designed to perform the tasks required for sophisticated statistical analysis. The first half of the book provides a basic background in numerical analysis emphasizing issues important to statisticians. The next several chapters cover a broad array of applications, such as maximum likelihood and nonlinear regression, numerical integration and random number generation, Monte Carlo methods, sorting, FFT and the application of other 'fast' algorithms to statistics.

Swinnerton-Dyer,P.

A Brief Guide to Algebraic Number Theory.

(London Mathematical Society Student Texts, Vol. 50)

Mar. 2001 200pp
0-521-80292-X hardcover
0-521-00423-3 softcover

This is an account of Algebraic Number Theory, a field which has grown to touch many other areas of pure mathematics. The book encompasses everything that graduate students and pure mathematicians interested in the subject are likely to need, and assumes only some undergraduate level material and other prerequisites covered in an appendix. The book covers the two basic methods of approaching Algebraic Number Theory and includes a substantial digression on the classical approach to Fermat's Last Theorem.