Elliptic Curves, Modular Forms and Fermat's Last Theorem,
Expanded ed.
This is an expanded edition of a prevously published work.
Two chapters have been added to this revised edition. A
conference, on the general theme of "Elliptic Curves and
Modular Forms" was held in the Mathematics Department of the
Chinese University of Hong Kong in December 1993. The impetus for
organizing the conference arose from Andrew Wiles' deep and
spectacular work on the celebrated conjecture that every elliptic
curve over Q is modular, although only some of the lectures at
the conference were specifically related to this theme. At the
time of the conference, the difficulties in the last hurdle in
Wiles' work (the proof of the conjectural upper bound for the
order of the Selmer group attached to the symmetric square of a
modular form) had still not been overcome. It is now history that
Wiles himself, assisted by R. Taylor, found a beautiful proof of
the desired upper bound. As a result, we now know today the
remarkable fact that every semi-elliptic curve over Q is modular.
This proof is not only revolutionary in its own right, but it
also provides a proof of Fermat's Last Theorem. This volume is a
mixture of the texts of some of these lectures, together with a
number of recent articles related to the general theme of the
conference.
1997 340 pp.
1-57146-049-7
International Press
Henneaux, M. / Krasil'shchik, J. / Vinogradov, A. (eds.):
Secondary Calculus and Cohomological Physics
This collection of invited lectures (at the Conference on
Secondary Calculus and Cohomological Physics, Moscow, 1997)
reflects the state-of-the-art in a new branch of mathematics and
mathematical physics arising at the intersection of geometry of
nonlinear differential equations, quantum field theory, and
cohomological algebra. This is the first comprehensive and
self-contained book on modern quantum field theory in the context
of cohomological methods and the geometry of nonlinear PDEs.
Features: * An up-to-date and self-contained exposition of the
newest results in cohomological aspects of quantum field theory
and the geometry of PDEs. * A new look at interrelations between
coho-mology theory, the geometry of PDEs, and field theory.
1998 287 pp.
0-8218-0828-1
A.M.S.
Roussarie, R. :
Bifurcations of Planar Vector Fields and Hilbert's Sixteenth
Problem
In a coherent, exhaustive and progressive way, this book
presents the tools for studying local bifurcations of limit
cycles in family of functions in its ideal of coefficients, and
asymptotic expansion of non-differentiable return maps and
desingularisation. The exposition moves from classical analytic
geometric methods applied to regular limit periodic sets to more
recent tools for singular limit sets. The methods can be applied
to theoretical problems such as Hilbert's 16th problem, but also
for the purpose of establishing bifurcation diagrams of specific
families as well as explicit computations.
May 1998 204 pp.
3-7643-5900-5
Birkhauser
Elias, J. / Giral, J. / Zarzuela, S. (eds.):
Six Lectures on Commutative Algebra
Interest in commutative algebra has surged over the past decades.
In order to survey and highlight recent developments in this rapidly expanding field,
the Center de Recerca Mathematica in Bellaterra organized
the Summer School on Commutative Algebra 1996.
Lecture Series were presented by six high-level specialists,
L. Avramov (Purdue), M. K. Green (UCLA), C. Huneke (Purdue),
P. Schenzel (Halle), G. Valla (Genova) and W. V. Vasconcelos (Rutgers),
providing a fresh and extensive account of the results,
techniques and problems of some of the most active areas of research.
June 1998 408 pp.
3-7643-5951-X
Birkhauer
Facchini, A. :
Module Theory:
Endomorphism Rings and Direct Sum Decompositions in Some
Classes of Modules
The author set out to present the solution of a problem posed by Wolfgang Krull in 1932.
He asked whether what is now called the "Krull-Schmidt Theorem" hold for artinian modules.
A negative answer was published only in 1995 by Facchini, Herbera, Levy and Vlmos.
Second, the author presents the answer to a question posed Warfieldin 1975,
namely, whether the Krull-Schmidt-Theorem holds for serial modules.
Facchini published a negative answer in 1966.
The solution to the Warfield problem shows an interesting behavior;
in fact, it is a phenomena so rare in the history of Krull-Schmidt type theorems
that its presentation to a wider mathematical audience provides
the third incentive for modules.
When it does hold, any two in decomposable decompositions are uniquely determined up
to one permutation.
June 1998 300 pp.
3-7643-5908-0
Birkhauser
Donkin, S. :
The q-Schur Algebra
This book focuses on the representation theory of q-Schur
algebras and connections with the representation theory of Hecke
algebras and quantum general linear groups. The aim is to
present, from a unified point of view, quantum analogues of
certain results known already in the classical case. The approach
is largely homological, based on Kempf's vanishing theorem for
quantum groups and the quasi-hereditary structure of the q-Schur
algebras. This volume will be primarily of interest to
researchers in algebra and related topics in pure mathematics.
Sep. 1998 235 pp.
0-521-64558-1
Cambridge
Curtis, R. / Wilson, R. :
The Atlas of Finite Groups Ten Years On
This book contains twenty articles by leading experts in the
field, and covers many aspects of group theory and its
applications. The proceedings of a conference organized to mark
the 10th anniversary of the publication of the Atlas, the book
emphasises recent advances in group theory and applications which
have been stimulated by the comprehensive collection of
information contained in the Atlas. It also covers both
theoretical and computational aspects of finite groups, modular
representations, and applications to the study of surfaces. June
1998 320 pp.
0-521-57587-7
Cambridge
Smart, N. P. :
Module Theory:
The Algorithmic Resolution of Diophantine Equations
A coherent modern account of the computational methods
used to solve diophantine equations,
this book's emphasis is on approaches with wide ranging applications.
After a brief introduction, the first section considers basic techniques.
The second section explores problems which can be solved
using Baker's theory of linear forms in logarithms.
The final section looks at problems associated with curves.
Useful exercise and a detailed bibliography are include.
Requiring a basic knowledge of number theory, this book will
appeal to graduate students and research workers.
Oct. 1998 245 pp.
0-521-64156-X/64633-2 13,480./5,040.(Paper ed.)
Cambridge
Pietsch, A. / Wenzel, J. :
Orthonormal Systems & Banach Space Geometry
This book describes the interplay between orthonormal
expansions and Banach space geometry. The text yields a detailed
insight into concepts including type and co-type of Banach
spaces, B-convexity, super-reflexivity, the vector-valued Fourier
transform, the vector-valued Fourier transform, the vector-valued
Hilbert transform and the unconditinality property for martingale
differences (UMD). A long list of unsolved problems is included
as a starting point for research.
Sep. 1998 554 pp.
0-521-62462-2
Cambridge
Miwa, T. / Jimbo, M. / Date, E. :
Mathematics of Solitons
The notion of solitons arose with the study of
partial differential equations at the end of the 19th century.
In more recent times their study has involved ideas from other areas of mathematics
such as algebraic geometry, topology, and in particular infinite dimensional Lie algebras,
and it this approach that is the main theme of this book.
Sep. 1998 180 pp.
0-521-56161-2
Cambridge
Buning, H. / Lettman, T. :
Propositional Logic:
Deduction and Algorithms
This introduction to classical logic emphasises computational aspects.
The authors treat issues of complexity and algorithmic analysis
that have traditionally not been considered the realm of mathematical
logic, but which are vital in areas such as automated reasoning,
knowledge engineering, logic programming and AI.
In order to make the book suited for teaching and for self-study,
the book includes a systematic account of theoretical results,
as well as an exposition of those appropriate algorithms which incorporate them.
Oct. 1998 420 pp.
0-521-63017-7
Cambridge
Bollobas, B. :
Modern Graph Theory
From Contents Fundamentals.- Electrical Networks.- Flows,
Connectivity and Matching.- Extremal Problems.- Colouring.-
Ramsey Theory.- Random Graphs.- Graphs, Groups and Matrices.-
Random Walks on Graphs.- The Tutte Polynomial.
July 1998 375 pp.
3-540-98491-7
Springer
Megginson, R. E. :
An Introduction to Banach Space Theory
Preparing students for further study of both the classical
works and current research, this is an accessible text for
student who have had a course in real and complex analysis and
understand the basic properties of Lp space. It is sprinkled
liberally with examples, historical notes, citations, and
original sources, and over 450 exercises provide practice in the
use of the results developed in the text through supplementary
examples and counterexamples. s From Contents: Basic Concepts.-
The Weak and Weak.- Topologies.- Linear Operators.- Schauder
Bases.- Rotundity and Smoothness.- A: Prerequisites.- B: Metric
Spaces.- C: The Spaces 1_p and 1^{n}_{p}, 1\leq \leq \infty.-
D: Ultranets.
July 1998 615 pp.
3-540-98431-3
Springer
Walter, W. / Thompson, R. :
Ordinary Differential Equations
Based on a translation of the 6th edition of Gewohnliche Differentialgleichungen
by Wolfgang Walter, this edition includes additional treatments of important
subjects not found in the German text as well as material
that is seldom found in textbooks, such as new proofs for a closer look
at contents and methods with an emphasis on
subjects outside the mainstream. Exercises,
which range from routine to demanding, are dispersed throughout the text
and some include an outline of the solution.
Applications from mechanics to mathematical biology are included
and solutions of selected exercises are found at the end of the book.
is suitable for mathematics, physics, and
computer science graduate students to be used as collateral reading
and as a reference source for mathematicians.
Readers should have a sound knowledge of infinitesimal calculus
and be familiar with basic notions from linear algebra;
functional analysis is developed in the text when needed.
July 1998 375 pp.
3-540-98459-3
Springer
Bollobas, B. :
Modern Graph Theory
From Contents Fundamentals.- Electrical Networks.- Flows,
Connectivity and Matching.- Extremal Problems.- Colouring.-
Ramsey Theory.- Random Graphs.- Graphs, Groups and Matrices.-
Random Walks on Graphs.- The Tutte Polynomial.
July 1998 375 pp.
3-540-98491-7
Springer
Megginson, R. E. :
An Introduction to Banach Space Theory
Preparing students for further study of both the classical
works and current research, this is an accessible text for
student who have had a course in real and complex analysis and
understand the basic properties of Lp space. It is sprinkled
liberally with examples, historical notes, citations, and
original sources, and over 450 exercises provide practice in the
use of the results developed in the text through supplementary
examples and counterexamples. s From Contents: Basic Concepts.-
The Weak and Weak.- Topologies.- Linear Operators.- Schauder
Bases.- Rotundity and Smoothness.- A: Prerequisites.- B: Metric
Spaces.- C: The Spaces 1_p and 1^{n}_{p}, 1\leq \leq \infty.-
D: Ultranets.
July 1998 615 pp.
3-540-98431-3
Springer
Walter, W. / Thompson, R. :
Ordinary Differential Equations
Based on a translation of the 6th edition of Gewohnliche Differentialgleichungen
by Wolfgang Walter, this edition includes additional treatments of important
subjects not found in the German text as well as material
that is seldom found in textbooks, such as new proofs for a closer look
at contents and methods with an emphasis on
subjects outside the mainstream. Exercises,
which range from routine to demanding, are dispersed throughout the text
and some include an outline of the solution.
Applications from mechanics to mathematical biology are included
and solutions of selected exercises are found at the end of the book.
is suitable for mathematics, physics, and
computer science graduate students to be used as collateral reading
and as a reference source for mathematicians.
Readers should have a sound knowledge of infinitesimal calculus
and be familiar with basic notions from linear algebra;
functional analysis is developed in the text when needed.
July 1998 375 pp.
3-540-98459-3 11,270.
Springer