V. I. BERNIK
Byelorussian Academy of Sciences
AND M. M, DODSON
University of York

Metric Diophantine Approximation on Manifolds

This book is concerned with Diophantine approximation on smooth manifolds
embedded in Euclidean space, and its aim is to develop a coherent body of theory
comparable with that which already exists for classical Diophantine approximation. In
particular, this book deals with Khintchine-type theorems and with the Hausdorff
dimension of the associated null sets. All researchers with an interest in Diophantine
approximation will welcome this book.

Contents: 1. Diophantine approximation; 2. Khintchine-type manifolds; 3. Hausdorff measure and
dimension; 4. Upper bounds; 5. Lower bounds for Hausdorff dimension; 6. p-adic Diophantine
approximation; 7. Applications.

Subject areas :mathematics (measure theory, geometry)
Market: academic researchers

Series: Cambridge Tracts in Mathematics, 137

0 521 43275 8 Hardback 192pp October 1999



EDITED BY
HOWARD DORWART /Emeritus, Trinity College
AND THOMAS R. BERGER /University of Minnesota

The Geometry of Incidence

The focus in this book is on projective geometry and its roots in -classical geometry', a
pursuit which the authors feel has been largely neglected in the abstract-oriented
mathematics of the twentieth century. Dorwart and Berger quickly lead into a
discussion of the geometry of incidence, tracing its formulation from Euclid through
David Hilbert. The reader is expected to do much of the mathematics within, and the
book wild be suitable for anybody familiar with only a little geometry.


Contents: 1. Fundamental notions; 2. The projective plane; 3. Some theorems; 4. General planes.

Selling Points:
¥ Covers classical material
¥ Enables the reader to actually do the maths
¥ Lots of examples

Subject area :smathematics (geometry)
Market: undergraduate students
Series: New Mathematical Library

0 883 85642 5 Paperback 250pp c October 1999


SHELDON M. ROSS
University of California, Berkeley

Introduction to the Mathematics of Finance
Options and Other Topics

- This textbook explains the modern approach to options pricing, which is based on the
assumption that prices of the underlying security follow a geometric Brownian motion.
lt explains the important concept of arbitrage and shows how this is utilized to derive
the BIack-Scholes option pricing formula. This book is unique in giving a treatment of
the basics of option pricing that is mathematically accurate and yet accessible to
readers with limited mathematical training; it will appeal to professional traders as well
as undergraduates studying the basics of finance.

Contents: 1. Probability; 2. Normal random variables; 3. Geometric Brownian motion; 4. Interest
rates and present value analysis; 5. Pricing contracts via arbitrage; 6. The arbitrage theorem; 7.
The Black-Scholes formula; 8. Valuing by expected utility; 9. Exotic options; 10. Beyond
geometric Brownian motion models; 11. Autoregressive models and mean reversion.

Subject areas: finance, business, economics, statistics, mathematics
Market: professionals, undergraduate students

0521 770432 Hardback I 224pp c October1999
22 line diagrams 15 tables


ANDERS BJORNER /Royal Institute of Techndogy, Stockhdm
MICHEL LAS VERGNAS /Universite Pierre et Marie Curie
BERND STURMFELS /University of California, Berkeley
NEIL WHITE /University of Florida
AND GONTER M. ZEIGLER /Technische Universitat Berlin

Oriented Matroids

Second edition Paperback

This is the second edition of the first comprehensive, accessible account of oriented
matroids, which have applications to areas as diverse as geometry, combinatorics,
operations research, computer science and theoretical chemistry. lt is intended for a
diverse audience: graduate students, researchers from other disciplines and
specialists. A list of exercises and open problems ends each chapter. For the second
edition, the authors have expanded the bibliography greatly to ensure that it remains
comprehensive and up-to-date, and they have also added an appendix surveying
research since the work was first published.

'OveraII this is a book which is a classic of its type; it is a mine of information, which
wiII be the authoritative source for many years to come.'
Bulletin ofthe London Mathematical Society

Contents: Preface; Notation; 1. A first orientation session; 2. A second orientation session; 3.
Axiomatics; 4. From face lattices to topology; 5. Topological models for oriented matroids; 6.
Arrangements of pseudolines: 7. Constructions; 8. Realizability; 9. Convex pdytopes; 10. Linear
programming; Appendix.I Some current frontiers of research; Bibliography; Index.

¥ Second edition contains an up-to-date bibliography and a new appendix
covering research since the first edition
¥ Designed to appeal to graduate students, researchers and specialists

Subject areasmathematics (combinatorics, geometry, topology, operations research) _
Market: academic researchers, graduate students
Series: Encyclopedia of Mathematics and its Applications, 46

0 521 77750 X. Paperback
550pp c October 1999
299 exercises 138 figures


M. PICARDELLO/Universita Roma, Tor Vergata
AND W. WOESS /Universita di Milano-Bicocca

Random Walks and Discrete Potential Theory

This book covers the interplay betvveen the behaviour of a class of stochastic
processes (random walks) and structure theory. Written by leading researchers, this
cdlection of invited papers presents links with spectral theory and discrete potential
theory, besides probabilistic and structure theoretic aspects. Its interdisciplinary .
approach spans several areas of mathematics including geometric group theory,
discrete geometry and harmonic analysis, and wilt be of interest to researchers and
post-graduate students, both in mathematics and statistical physics.

Contents: 1. Green's functions, generalized first eigenvalues and perturbation of diffusions or
Markov chains Alano Ancona; 2. Random walks on graphical Sierpinski carpets Martlin T.
BaIlow and Richard F. Bass; 3. Percolation perturbations in potential theory and random walks
ltai Benj'amini, Russell Lyons and Oded Schramm; 4. Twist surfaces Robert Brooks; 5. Harmonic
functions on buildings of type A" Donald Cartwright,. 6... Spectre d'op6rateurs differentiels sur les
graphes Yves Colin de Veriere; 7. Analysis on infinite graphs with regular volume growth
Thierry Coulhon; 8. On the asymptotic spectrum of random walks on infinite families of graphs
Rostislav I. Grigorrchuk and Andizej' Zuk; 9. Stochastic pin-ball Geoffrey R. Gri'mmett; 10. A
discrete time Harnak inequality and its applications Vadim A. Kaimanovich; 11. Multifractal
nature of two dimensional simple random walk paths Gregory F. Lawler; 12. Energy and cutsets
in infinite percolation clusters David Levin and Yuval Peres; 13. On discrete groups and pointwise
ergodic theory Amos Nevo; 14. Random walk and isoperimetry on discrete subgroups of Lie
groups Christophe Pittet and Launent Saloff-Coste,. 15. Distance distortion on Lie groups
Nicholas Th. Varopoulos,

Subject areasmathematics (probability, geometry, combinatorics), statistical physics
Market: academic researchers, graduate students

Series: Symposia Mathematica,,39

0 521 77312 1 Hardback
372pp c October 1999


H.J. STOCKMANN
Philipps-Universitat Marburg

Quantum Chaos

An Introduction

This book introduces the quantum mechanics of classically chaotic systems, or
Quantum Chaos for short. The author's philosophy has been to keep the discussion
simple and illustrate theory, wherever possible, with experimental or numerical
examples. This is the first book treating both experimental and theoretical aspects of
quantum chaos. lt will be of great value to anyone working in quantum chaos.

Contents: 1. Introduction; 2. Billiard experiments; 3. Random matrices; 4. Floquet and
tight-binding systems; 5. Eigenvalue dynamics; 6. Scattering systems; 7. Semiclassical quantum
mechanics; 8. Applications of periodic orbit theory.

Selling Points:
¥ First book treating both experimental and theoretical aspects of quantum chaos
¥ First-hand information on billiard experiments initiated by the author
¥ First introduction on supersymmetry techniques

Subject areasphysics (nonlinear science)
Market: graduate students, academic researchers '{

0 521 59284 4 Hardback 380pp October 1999
6 half-tones 8 colour plates 100figures



JONATHAN GINZBURG /Hebrew University of Jerusalem
LAWRENCE MOSS /University of lndiana
AND MAARTEN DE RIJKE /University of Amsterdam

Logic, Language and Computation
Volume2

The papers contained in this volume by some of the most influential computer
scientists, linguists, logicians and philosophers of today cover many diverse subjects.
The contributions include: Jon Barwise, who shows how the ideas of channel theory fit
in with non-monotonic logic; Jelle Gerbrandy shows how ideas from dynamic logic can
be used to study the notion of common knowledge among groups of agents; and
Wiebe van der Hoek and Maarten de Rijke provide ideas from theoretical computer
science to a more philosophical area, belief revision.

Contents: 1. State spaces, local logics, and non-monotonicity; 2. Presupposition commodation: a
plea for common sense; 3. A dynamic syntax/semantics interface; 4. Dynamic epistemic logic; 5.
Bare plurals, situations and discourse context; 6. lnterleaved contractions; 7. Putting channels on
the map: a channel-theoretic semantics of maps?; 8. Disjunctive information; 9. hnformation,
relevance and social decisionmaking: some principles and results of decision-theoretic
semantics; 10. Hyperproof: abstraction, visual preference and multimodality; 11. Structured
argument generation in a logic-based KB-system; 12. Beliefs, belief revision, and splitting
languages; 13. Prolegomena to a theory of disability, inability and handicap; 14.
ConstraintireSerVing representations; 15. Information, belief and causal role; 16. Takahashi:
proving through commutative diagrams; 17. Topology via constructive logic; 18. Remarks on the
epistemic role of discourse referents; 19, Constrained functions and semantic information.

Selling Points:
Explores the interrelation of logic, linguistics, and computer science
Theories proposed provide tools for the analysis of the specific content of a situation
Papers contained in this volume are by some ofthe most influential people in these fields

Subject areas; Linguistics, logic
Market: academic researchers, graduate students
Series: Center for the Study oT Language and Information Publication Lecture Notes, 96

1 57586181 X Hardback 440pp c October1999
1 575861801 Paperback 440pp c July1999