ISBN: 0-8493-1708-8
Publication Date: 3/26/2004
Number of Pages: 408
Provides solved problems, historical remarks,
and suggestions for
further reading
Addresses concepts of complex integral calculus
Includes a detailed discussion on the construction
of Riemann
Surfaces for elementary functions, leading
to its abstract
concept
Focuses on step-by-step development of the
most general form of
Cauchy theorem
Effective for undergraduate and postgraduate
students, the single-volume
Complex Analysis functions as both a textbook
and a reference,
depending on the conducted course's structure.
The only
prerequisites are rudiments of real analysis
and linear algebra.
Special features include an integrated approach
to the concept of
differentiation for complex valued functions
of a complex
variable, unified Cauchy Riemann equations,
complex versions of
real intermediate value theorem, and exhaustive
treatment of
contour integration. The book also offers
an introduction to the
theory of univalent functions on the unit
disc, including a brief
history of the Bieberbach's conjecture and
its solutions.
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2004. 24 x 17 cm. XI, 408 pages. Cloth.
ISBN 3-11-018143-6
Series: de Gruyter Series in Nonlinear Analysis
and Applications
10
to be published April 2004
In view of the eminent importance of spectral
theory of linear
operators in many fields of mathematics and
physics, it is not
surprising that various attempts have been
made to define and
study spectra also for nonlinear operators.
This book provides a
comprehensive and self-contained treatment
of the theory,
methods, and applications of nonlinear spectral
theory.
The first chapter briefly recalls the definition
and properties
of the spectrum and several subspectra for
bounded linear
operators. Then some numerical characteristics
for nonlinear
operators are introduced which are useful
for describing those
classes of operators for which there exists
a spectral theory.
Since spectral values are closely related
to solvability results
for operator equations, various conditions
for the local or
global invertibility of a nonlinear operator
are collected in the
third chapter. The following two chapters
are concerned with
spectra for certain classes of continuous,
Lipschitz continuous,
or differentiable operators. These spectra,
however, simply adapt
the corresponding definitions from the linear
theory which
somehow restricts their applicability. Other
spectra which are
defined in a completely different way, but
seem to have useful
applications, are defined and studied in
the following four
chapters. The remaining three chapters are
more application-oriented
and deal with nonlinear eigenvalue problems,
numerical ranges,
and selected applications to nonlinear problems.
The only prerequisite for understanding this
book is a modest
background in functional analysis and operator
theory. It is
addressed to non-specialists who want to
get an idea of the
development of spectral theory for nonlinear
operators in the
last 30 years, as well as a glimpse of the
diversity of the
directions in which current research is moving.
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2004. 24 x 17 cm. VIII, 540 pages.
ISBN 3-11-014211-2
Series: de Gruyter Expositions in Mathematics
38
to be published April 2004
The problem of classifying the finite-dimensional
simple Lie
algebras over fields of characteristic p
> 0 is a long-standing
one. Work on this question during the last
35 years has been
directed by the Kostrikin-Shafarevich Conjecture
of 1966, which
states that over an algebraically closed
field of characteristic
p > 5 a finite-dimensional restricted
simple Lie algebra is
classical or of Cartan type. This conjecture
was proved for p
> 7 by Block and Wilson in 1988. The generalization
of the
Kostrikin-Shafarevich Conjecture for the
general case of not
necessarily restricted Lie algebras and p
> 7 was announced in
1991 by Strade and Wilson and eventually
proved by Strade in 1998.
The final Block-Wilson-Strade-Premet Classification
Theorem is a
landmark result of modern mathematics and
can be formulated as
follows: Every simple finite-dimensional
simple Lie algebra over
an algebraically closed field of characteristic
p > 3 is of
classical, Cartan, or Melikian type .
In the two-volume book, the author is assembling
the proof of the
Classification Theorem with explanations
and references. The goal
is a state-of-the-art account on the structure
and classification
theory of Lie algebras over fields of positive
characteristic
leading to the forefront of current research
in this field. This
first volume is devoted to preparing the
ground for the
classification work to be performed in the
second volume.
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hardcover
0-8018-7860-8
2004 928 pp. 9 line drawings
In Contributions to Automorphic Forms, Geometry,
and Number
Theory, Haruzo Hida, Dinakar Ramakrishnan,
and Freydoon Shahidi
bring together a distinguished group of experts
to explore
automorphic forms, principally via the associated
L-functions,
representation theory, and geometry. Because
these themes are at
the cutting edge of a central area of modern
mathematics, and are
related to the philosophical base of Wiles'
proof of Fermat's
last theorem, this book will be of interest
to working
mathematicians and students alike. Never
previously published,
the contributions to this volume expose the
reader to a host of
difficult and thought-provoking problems.
Each of the extraordinary and noteworthy
mathematicians in this
volume makes a unique contribution to a field
that is currently
seeing explosive growth. New and powerful
results are being
proved, radically and continually changing
the field's make up.
Contributions to Automorphic Forms, Geometry,
and Number Theory
will likely lead to vital interaction among
researchers and also
help prepare students and other young mathematicians
to enter
this exciting area of pure mathematics.
Contributors: Jeffrey Adams, Jeffrey D. Adler,
James Arthur, Don
Blasius, Siegfried Boecherer, Daniel Bump,
William Casselmann,
Laurent Clozel, James Cogdell, Laurence Corwin,
Solomon
Friedberg, Masaaki Furusawa, Benedict Gross,
Thomas Hales, Joseph
Harris, Michael Harris, Jeffrey Hoffstein,
Herve Jacquet, Dihua
Jiang, Nicholas Katz, Henry Kim, Victor Kreiman,
Stephen Kudla,
Philip Kutzko, V. Lakshmibai, Robert Langlands,
Erez Lapid, Ilya
Piatetski-Shapiro, Dipendra Prasad, Stephen
Rallis, Dinakar
Ramakrishnan, Paul Sally, Freydoon Shahidi,
Peter Sarnak, Rainer
Schulze-Pillot, Joseph Shalika, David Soudry,
Ramin Takloo-Bigash,
Yuri Tschinkel, Emmanuel Ullmo, Marie-France
Vigneras, Jean-Loup
Waldspurger.
Haruzo Hida is a professor of mathematics
at UCLA. Dinakar
Ramakrishnan is a professor of mathematics
at California
Institute of Technology. Freydoon Shahidi
is Distinguished
Professor of Mathematics at Purdue University.
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hardcover
0-8018-7822-5
June 2004 368 pp. 2 line drawings
With the advent of computers that can handle
symbolic
manipulations, abstract algebra can now be
applied. In this book
David Joyner, Richard Kreminski, and Joann
Turisco introduce a
wide range of abstract algebra with relevant
and interesting
applications, from error-correcting codes
to cryptography to the
group theory of Rubik's cube. They cover
basic topics such as the
Euclidean algorithm, encryption, and permutations.
Hamming codes
and Reed-Solomon codes used on today's CDs
are also discussed.
The authors present examples as diverse as
"Rotation,"
available on the Nokia 7160 cell phone, bell
ringing, and the
game of NIM. In place of the standard treatment
of group theory,
which emphasizes the classification of groups,
the authors
highlight examples and computations. Cyclic
groups, the general
linear group GL(n), and the symmetric groups
are emphasized.
With its clear writing style and wealth of
examples, Applied
Abstract Algebra will be welcomed by mathematicians,
computer
scientists, and students alike. Each chapter
includes exercises
in GAP (a free computer algebra system) and
MAGMA (a
noncommercial computer algebra system), which
are especially
helpful in giving students a grasp of practical
examples.
David Joyner is a professor of mathematics
at the United States
Naval Academy. He is the author of Adventures
in Group Theory:
Rubik's Cube, Merlin's Machine, and Other
Mathematical Toys, also
available from Johns Hopkins. Richard Kreminski
is a professor
and head of the mathematics department at
Texas A & M
University?Commerce. JoAnn Turisco is an
associate professor of
mathematics at the United States Naval Academy.