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