Christ, Michael, Carlos Kenig, and Cora Sadosky, editors

Harmonic Analysis and Partial Differential Equations: Essays in Honor of Alberto Calderon.

384 p., 12 line drawings. CLM 1999

Cloth 0-226-10456-7 08/99.

Alberto P. Calder?n (1920-1998) was one of this century's leading mathematical analysts. His contributions,
characterized by great originality and depth, have changed the way researchers approach and think about a
wide variety of topics in mathematics and its applications, including harmonic analysis, partial differential equations,
and complex analysis, as well as in more applied fields such as signal processing, geophysics, and tomography.
In addition, he helped define the "Chicago school" of analysis, which remains influential to this day.

In 1995, more than 300 mathematicians from around the world gathered in Chicago for a conference on harmonic
analysis and partial differential equations held in Calderon's honor. This volume originated in papers given there and
presents timely syntheses of several major fields of mathematics as well as original research articles contributed by
some of the finest scholars working in these areas. An important addition to the literature, this book will be welcomed
by researchers in these and other related fields.


Jesseph, Douglas M.

Squaring the Circle: The War between Hobbes and Wallis.

424 p. (est.), 46 line drawings. SCF 1999
Cloth 0-226-39899-4 10/99.
Paper 0-226-39900-1 10/99.

In 1655, the philosopher Thomas Hobbes claimed he had solved the centuries-old problem of "squaring of the circle"
(constructing a square equal in area to a given circle). With a scathing rebuttal to Hobbes's claims, the mathematician
John Wallis began one of the longest and most intense intellectual disputes of all time. Squaring the Circle is a detailed
account of this controversy, from the core mathematics to the broader philosophical, political, and religious issues at stake.

Hobbes believed that by recasting geometry in a materialist mold, he could solve any geometric problem and thereby
demonstrate the power of his materialist metaphysics. Wallis, a prominent Presbyterian divine as well as an eminent
mathematician, refuted Hobbes's geometry as a means of discrediting his philosophy, which Wallis saw as a dangerous mix
of atheism and pernicious political theory.

Hobbes and Wallis's "battle of the books" illuminates the intimate relationship between science and crucial seventeenth-century
debates over the limits of sovereign power and the existence of God.

Table of Contents
Preface
List of Abbreviations
Chapter One: The Mathematical Career of the Monster of Malmesbury
Chapter Two: The Reform of Mathematics and of the Universities
Ideological Origins of the Dispute
Chapter Three: De Corpore and the Mathematics of Materialism
Chapter Four: Disputed Foundations
Hobbes vs. Wallis on the Philosophy of Mathematics
Chapter Five: The "Modern Analytics" and the Nature of Demonstration
Chapter Six: The Demise of Hobbesian Geometry
Chapter Seven: The Religion, Rhetoric, and Politics of Mr. Hobbes and Dr. Wallis
Chapter Eight: Persistence in Error
Why Was Hobbes So Resolutely Wrong?
Appendix: Selections from Hobbes's Mathematical Writings
References
Index

Subjects:

History of Science
Philosophy of Science
History: British History


May, J. P.

A Concise Course in Algebraic Topology.

vii, 247 p., 117 line drawings. CLM 1999
Cloth 0-226-51182-0 09/99.
Paper 0-226-51183-9 09/99.

Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any
advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups.
This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate
students in mathematics either specializing in this area or continuing on to other fields.

J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades,
most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various
topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final
four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts,
and the book concludes with a list of suggested readings for those interested in delving further into the field.


Computational Finance 1999


by Yaser S. Abu-Mostafa, Blake LeBaron, Andrew W. Lo, and Andreas S.
Weigend (eds.)


Computational finance, an exciting new
cross-disciplinary research area, draws extensively on
the tools and techniques of computer science,
statistics, information systems, and financial economics.
This book covers the techniques of data mining,
knowledge discovery, genetic algorithms, neural
networks, bootstrapping, machine learning, and Monte
Carlo simulation. These methods are applied to a wide
range of problems in finance, including risk management,
asset allocation, style analysis, dynamic trading and
hedging, forecasting, and option pricing. The book is
based on the sixth annual international conference
Computational Finance 1999, held at New York
University's Stern School of Business.

forthcoming
October 1999
ISBN 0-262-51107-X
650 pp.
(paper)

forthcoming
September 1999
ISBN 0-262-01178-6
650 pp.
(cloth)


Comparing Financial Systems


by Franklin Allen and Douglas Gale


Financial systems are crucial to the allocation of resources in
a modern economy. They channel household savings to the
corporate sector and allocate investment funds among firms;
they allow intertemporal smoothing of consumption by
households and expenditures by firms; and they enable
households and firms to share risks. These functions are
common to the financial systems of most developed
economies. Yet the form of these financial systems varies
widely. In the United States and the United Kingdom
competitive markets dominate the financial landscape,
whereas in France, Germany, and Japan banks have
traditionally played the most important role.

Why do different countries have such different financial
systems? Is one system better than all the others? Do
different systems merely represent alternative ways of
satisfying similar needs? Is the current trend toward
market-based systems desirable?

Franklin Allen and Douglas Gale argue that the view that
market-based systems are best is simplistic. A more nuanced
approach is necessary. For example, financial markets may be
bad for risk sharing; competition in banking may be inefficient;
financial crises can be good as well as bad; and separation of
ownership and control can be optimal. Financial institutions
are not simply veils, disguising the allocation mechanism
without affecting it, but are crucial to overcoming market
imperfections. An optimal financial system relies on both
financial markets and financial intermediaries.


December 1999
ISBN 0-262-01177-8
584 pp., 32 illus.
(cloth)


Advances in Genetic Programming - Vol. 3


by Lee Spector, William B. Langdon, Una-May O'Reilly, and PeterJ.
Angeline (eds.)


Genetic programming is a form of evolutionary
computation that evolves programs and program-like
executable structures for developing reliable time- and
cost-effective applications. It does this by breeding
programs over many generations, using the principles of
natural selection, sexual recombination, and mutuation.
This third volume of Advances in Genetic Programming
highlights many of the recent technical advances in this
increasingly popular field.

July 1999
ISBN 0-262-19423-6
488 pp.
(cloth)