This new approach to mathematics --- the
utilization of
advanced computing technology in mathematical
research --- is
often called experimental mathematics. The
computer provides the
mathematician with a "laboratory"
in which she can
perform experiments --- analyzing examples,
testing out new
ideas, or searching for patterns.
This book presents the rationale and historical
context of
experimental mathematics, and includes a
series of examples that
best portray the experimental methodology.
For more examples and
insights, the book, "Experimentation
in Mathematics:
Computational Paths to Discovery" is
a highly recommended
companion. .
To get a taste of the material presented
in both books view the
condensed version.
Year: 2003 ISBN: 1-56881-211-6
350 pages. Hardcover.
A publication of the Theta Foundation.
Description
This volume presents the proceedings of the
conference on
Operator Algebras and Mathematical Physics
held in Constanta,
Romania. The conference gathered experts
to examine and discuss
the interesting connections between these
two areas.
The book contains 24 research and expository
papers reflecting a broad variety of topics
from both domains: C^*-algebras and dynamical
systems, geometric and operator algebraic
quantization, modular invariants, q-commutation
relations, superselection theory, positive
linear maps, groupoids, spectral analysis
of Hamiltonians, random operators, and quantum
systems. The material is suitable for graduate
students and research mathematicians interested
in operator algebras, mathematical physics,
and their interaction.
Contents
E. J. Beggs -- 2-forms and noncommutative
Hamiltonian dynamics
M.-T. Benameur and H. Oyono-Oyono -- Gap-labelling
for quasi-crystals
(proving a conjecture by J. Bellissard)
W. R. Bergmann and R. Conti -- On infinite
tensor products of Hilbert ast-bimodules
M. Buneci -- Haar systems and homomorphisms
on groupoids
M. Choda -- Actions of the matrix groups
on the free group
factors and entropy of automorphisms
M. Dadarlat -- Some remarks on the universal
coefficient theorem
in KK-theory
P. Duclos, O. Lev, P. Stovicek, and M. Vittot
-- Progressive
diagonalization and applications
D. E. Evans -- Critical phenomena, modular
invariants and
operator algebras
C. Ferrari and N. Macris -- Spectral properties
of finite quantum
Hall systems
V. Georgescu and A. Iftimovici -- C^ast-algebras
of quantum Hamiltonians
F. Hiai -- q-deformed Araki-Woods algebras
J. A. Jeong -- Real rank of graph C^ast-algebras
T. Katsura -- On crossed products of the
Cuntz algebra mathcal{O}_infty by quasi-free
actions of abelian groups
B. Kuckert -- Moving quantum systems: particles
versus vacuum
S.-H. Kye -- On the facial structures for
positive linear maps
between matrix algebras
N. P. Landsman -- Quantization and the tangent
groupoid
D. Lenz and P. Stollmann -- Delone dynamical
systems and
associated random operators
W. A. Majewski -- On entanglement of states
and quantum
correlations
M. Mantoiu -- C^ast-algebras, dynamical systems,
spectral analysis
G. Morsella -- The structure of charges in
the ultraviolet and an
intrinsic notion of confinement
D. Pask and S.-J. Rho -- Some intrinsic properties
of simple graph C^ast-algebras
N. C. Phillips -- When are crossed products
by minimal
diffeomorphisms isomorphic?
J. Renault -- AF equivalence relations and
their cocycles
S. Vaes and A. Van Daele -- The Heisenberg
commutation relations,
commuting squares and the Haar measure on
locally compact quantum
groups
Details:
Publisher: Theta Foundation
Series: International Book Series of Mathematical
Texts
Publication Year: 2003
ISBN: 973-85432-2-3
Paging: 400 pp.
Binding: Hardcover
Expected publication date is November 26,
2003
Description
This book, based on the course given by the
author at the College
of Mathematics of the Independent University
of Moscow,
introduces the reader to the language of
generating functions,
which is nowadays the main language of enumerative
combinatorics.
It starts with definitions, simple properties,
and numerous
examples of generating functions. It then
discusses topics, such
as formal grammars, generating functions
in several variables,
partitions and decompositions, and the exclusion-inclusion
principle. In the final chapter, the author
describes
applications of generating functions to enumeration
of trees,
plane graphs, and graphs embedded in two-dimensional
surfaces.
Throughout the book, the reader is motivated
by interesting
examples rather than by general theories.
It also contains a lot
of exercises to help the reader master the
material. Little
beyond the standard calculus course is necessary
to understand
the book. It can serve as a text for a one-semester
undergraduate
course in combinatorics.
Contents
Formal power series and generating functions.
Operations with
formal power series. Elementary generating
functions
Generating functions for well-known sequences
Unambiguous formal grammars. The Lagrange
theorem
Analytic properties of functions represented
as power series and
their asymptotics of their coefficients
Generating functions of several variables
Partitions and decompositions
Dirichlet generating functions and the inclusion-exclusion
principle
Enumeration of embedded graphs
Final and bibliographical remarks
Bibliography
Index
Details:
Series: Student Mathematical Library, Volume:
23
Publication Year: 2003
ISBN: 0-8218-3481-9
Paging: 148 pp.
Binding: Softcover
Expected publication date is December 4,
2003
Description
The central theme of this book is an invariant
attached to an
ideal class of a totally real algebraic number
field. This
invariant provides us a unified understanding
of periods of
abelian varieties with complex multiplication
and the Stark-Shintani
units. This is a new point of view, and the
book contains many
new results related to it.
To place these results in proper perspective
and to supply tools to attack unsolved problems,
the author gives systematic expositions of
fundamental topics. Thus the book treats
the multiple gamma function, the Stark conjecture,
Shimura's period symbol, the absolute period
symbol, Eisenstein series on GL(2), and a
limit formula of Kronecker's type. The discussion
of each of these topics is enhanced by many
examples. The majority of the text is written
assuming some familiarity with algebraic
number theory. About thirty problems are
included, some of which are quite challenging.
The book is intended for graduate students
and researchers
working in number theory and automorphic
forms.
Contents
Introduction
Multiple gamma function and its generalizations
The Stark-Shintani conjecture
Absolute CM-periods
Explicit cone decompositions and applications
Applications of a limit formula of Kronecker's
type
Eisenstein series on GL(2)
On higher derivatives of L-functions
Transcendental property of CM-periods
References
Index
Details:
Series: Mathematical Surveys and Monographs,
Volume: 106
Publication Year: 2003
ISBN: 0-8218-3453-3
Paging: 282 pp.
Binding: Hardcover
Expected publication date is December 24,
2003
Description
This book is an introduction to convex analysis
and some of its
applications. It starts with basic theory,
which is explained
within the framework of finite-dimensional
spaces. The only
prerequisites are basic analysis and simple
geometry. The second
chapter presents some applications of convex
analysis, including
problems of linear programming, geometry,
and approximation.
Special attention is paid to applications
of convex analysis to
Kolmogorov-type inequalities for derivatives
of functions in one
variable. Chapter 3 collects some results
on geometry and convex
analysis in infinite-dimensional spaces.
A comprehensive
introduction written "for beginners"
illustrates the
fundamentals of convex analysis in finite-dimensional
spaces.
The book can be used for an advanced undergraduate
or graduate-level
course on convex analysis and its applications.
It is also
suitable for independent study of this important
area of
mathematics.
Contents
Introduction
Theory
Applications
Appendix
Bibliography
Details:
Series: Translations of Mathematical Monographs,
Volume: 222
Publication Year: 2003
ISBN: 0-8218-3525-4
Paging: 183 pp.
Binding: Softcover