This volume is based on lectures on division
algebras given at
a conference held at Colorado State University.
Although division algebras are a very classical
object,
this book presents this "classical"
material in a new way,
highlighting current approaches and new theorems,
and illuminating the connections
with a variety of areas in mathematics.
May 1999 120 pp.
0-8218-0979-2 .
A. M. S.
Proceedings from an international colloquium on Lie groups and ergodic theory held at the TIFR
There were 24 talks given by participants
in Lie groups,
ergodic theory and related fields.
Leading mathematicians from around the world
attended.
Recent developments were presented and a
session was devoted to discussion and problems
for future research.
Distributed worldwide except in India and
neighboring countries.
1998 386 pp.
81-7319-235-9
A. M. S.
Frobenius, Burnside, Schur, and Brauer
The year 1897 was marked by two important
mathematical events:
the publication of the first paper on representations
of finite groups
by Ferdinand Georg Frobenius (1849-1917)
and the appearance of the first treatise
in
English on the theory of finite groups by
William Burnside (1852-1927).
Burnside soon developed his own approach
to representations of finite groups.
In the next few years, working independently,
Frobenius and Burnside explored
the new subject and its applications to finite
group theory.....
An introductory chapter contains some of
the results involving
characters of finite abelian groups by Lagrange,
Gauss, and
Dirichlet, which were part of the mathematical
tradition from
which Frobenius drew his inspiration. This
book presents
the early history of an active branch of
mathmatics.
It includes enough detail to enable readers
to learn
the mathematics along with the history.
1999 319 pp.
0-8218-9002-6
A. M. S.
Algebra and Analysis, I
Kvant Selecta: Algebra and Analysis, I. -
II (MAWRLD/14-15)
are the first volumes of articles published
from 1970 to 1990
in the Russian journal, Kvant.
Articles selected for these two volumes are
written by leading Russian mathematicians
and expositors.
Some articles contain classical
mathematical gems still used in university
curriculae today.
Others feature cutting-edge research from
the 20th Century.
The articles in these books are written so
as to present genuine
mathematics in a conceptual, entertaining,
and accessible way.
* D. B. Fuchs and M. B. Fuchs -- The arithmetic
of binomial coefficients
* M. I. Bashmakov -- Do you like messing
around with integers?
* M. I. Bashmakov -- On Bertrand's conjecture
* D. B. Fuchs and M. B. Fuchs -- On best
approximations. I
* D. B. Fuchs and M. B. Fuchs -- On best
approximations. II
* A. I. Shirshov -- On a certain property
of binomial coefficients
* L. G. Limanov -- On n! and the number e
(Several approaches to a certain problem)
* D. B. Fuchs and M. B. Fuchs -- Rational
approximations and transcendence
* V. N. Vaguten -- Close fractions
* A. I. Shirshov -- On the equation \binom{n}{m}
= \binom{n+1}{m-1}
* A. Kirillov -- On regular polygons, Euler's
function, and Fermat numbers
* B. Bekker, S. Vostokov, and Yu. Ionin --
2-adic numbers
* E. Kuzmin and A. Shirshov -- On the number
e
1999 154 pp.
0-8218-1002-2
A. M. S.
Algebra and Analysis, II
* V. N. Vaguten -- Binomial coefficients,
polynomials, and sequences
(Several approaches to a certain problem)
* Yu. V. Matiyasevich -- Formulas for prime
numbers
* B. Martynov -- Fermat's theorem for polynomials
* I. Yantarov -- Commuting polynomials
* D. B. Fuchs -- On the removal of parentheses,
on Euler,
Gauss, and Macdonald, and on missed opportunities
* N. Vasil'ev and A. Zelevinskii -- Chebyshev
polynomials and recurrence relations
* O. V. Lyashko -- Why resistance does not
decrease
* V. I. Arnol'd -- Evolution processes and
ordinary differential equations
* V. A. Oleinikov -- Irrationality and irreducibility
* V. A. Oleinikov -- Irreducibility and irrationality
* Yu. P. Solov'ev -- The arithmetic of elliptic
curves
* N. B. Vasil'ev -- Pascal's hexagrams and
cubic curves
* V. I. Arnol'd -- Kepler's second law and
the topology of abelian
integrals (According to Newton)
* F. V. Vainstein -- Partitions of integers
* S. Tabachnikov -- Polynomials having least
deviation from zero
1999 159 pp.
0-8218-1915-1
A. M. S.
This volume is based on the author's lecture
courses to
algebraists at Munich and at G?teborg. He
presents,
for the first time in book form,
a unified approach from the point of view
of Frobenius
algebras/extensions to diverse topics, such
as Jones' subfactor theory,
Hopf algebras and Hopf subalgebras, the Yang-Baxter
Equation
and 2-dimensional topological quantum field
theories.
1999 84 pp.
0-8218-1962-3
A. M. S.
This work is at the crossroads of a number
of mathematical areas,
including algebraic geometry, several complex
variables,
differential geometry, and representation
theory.
The authors, both expert mathematicians in
the area of complex manifolds
and representation theory, focus on complex
tori,
which are interesting for their own sake
as
they are the simplest of complex manifolds,
and important in the theory of algebraic
cycles via intermediate jacobians.
Although special complex tori, namely abelian
varieties,
have been investigated for nearly 200 years,
not much is known about arbitrary complex
tori.
There are very few papers on
the subject and no book to date.
July 1999 272 pp.
3-7643-4103-3
Birkhauser
This is a comprehensive and detailed presentation
of the principles and methods of wavelet
theory.
The basic theory of wavelets bases and transforms
are presented
without assuming any knowledge of advanced
mathematics.
The book motivates the central ideas of wavelets
by discussing hoar Series
in depth and then presenting a more generalized
viewpoint.
With many examples, exercises
and through references, this book will be
an essential resource for applied mathematicians
engineers and scientists.
Nov. 1999 465 pp.
3-7643-3962-4
Birkhasuer