Series: Discrete Mathematics and Its Applications
ISBN: 1-58488-372-3
Publication Date: 1/14/2005
Number of Pages: 534
" Covers every area of computational group theory
" Summarizes state-of-the-art methods and results and
provides pointers to the literature
" Details the full, underlying theory and correctness proofs
of basic algorithms
" Presents algorithms in pseudocode
" Includes applications both within and outside of group
theory
" Describes the GAP and MAGMA software packages
This handbook covers the whole subject of computational group
theory (CGT) at a level suitable for beginning graduate students
who have some knowledge of group theory and computer algorithms.
It develops the theory of algorithms in full detail, includes
complexity analyses whenever possible, and highlights the
connections between the different aspects of CGT and with other
areas of computer algebra. Several specialist sections provide
pointers to the current state of the art in these areas, and all
sections include exercises of varying difficulty. For each major
collection of algorithms, the book includes a section describing
applications both within and outside of group theory.
Table of Contents
Group Theoretical Preliminaries. History of Computational Group
Theory (CGT) and Its Place Within Computational Algebra. Methods
of Representing Groups on a Computer. Base and Strong Generating
Set Methods in Finite Permutation and Matrix Groups. Coset
Enumeration. Computation in Finite Nilpotent and Solvable Groups.
Representation Theory, Character Theory, and Cohomology.
Algorithms Based on the Normal Structure of Finite Groups.
Libraries and Databases of Groups. The Matrix Group Recognition
Project. Special Techniques for Computing with Very Large Groups
and Their Representations. Quotient Algorithms for Finitely
Presented Groups. Rewriting Systems and the Knuth-Bendix
Completion Process. Automatic Groups (Methods Involving Finite
State Automata)
Series: Monographs & Surveys in Pure & Applied Math
ISBN: 1-58488-459-2
Publication Date: 5/15/2005
Number of Pages: 300
Presents reference material previously only available in Russian
Provides the most serious theoretical treatment of singular
perturbation problems available
Includes complete bibliographic references to the most up-to-date
sources in the field
Grigory Shishkin is well-known for his piecewise uniform meshes
method (Shishkin meshes) developed over the last two decades, and
the author of a Russian-language research thesis thus far
unavailable in English. Difference Methods for Singular
Perturbation Problems includes the reference material featured in
the Russian original, along with a section containing an overview
of recent advances in the field. This volume brings readers up-to-date
in numerical and computational methods for analyzing convection-diffusion,
boundary element, and fluid dynamics problems where the singular
properties of a solution mean that smoothness is limited and
therefore traditional methods would not apply.
Series: Monographs on Statistics and Applied Probability
Volume: 104
ISBN: 1-58488-432-0
Publication Date: 1/27/2005
Number of Pages: 272
Provides a unified treatment of GMRF models from the leading
researchers in the field
Focuses on the computational aspects and provides an online a c-library
for fast and exact simulation
Covers spatial models and state-space models, bringing together
models for spatial and temporal dependence under one umbrella
Gaussian Markov Random Field (GMRF) models are most widely used
in spatial statistics n a very active area of research in which
few up-to-date reference works are available. Gaussian Markov
Random Field: Theory and Applications is the first book on the
subject that provides a unified framework of GMRFs with
particular emphasis on the computational aspects. The book
includes extensive case studies and online a c-library for fast
and exact simulation. With chapters contributed by leading
researchers in the field, this volume is essential reading for
statisticians working in spatial theory and its applications, as
well as quantitative researchers in a wide range of science
fields where spatial data analysis is important.
250 p. 6 x 9 2004
Cloth 1-57586-489-4 Fall 2004
Paper 1-57586-490-8 Fall 2004
Not limited to merely mathematics, probability has a rich and
controversial philosophical aspect. A Philosophical Introduction
to Probability showcases lesser-known philosophical notions of
probability and explores the debate over their interpretations.
Galavotti traces the history of probability and its mathematical
properties and then discusses various philosophical positions on
probability, from the Pierre Simon de Laplace's “classical”
interpretation of probability to the logical interpretation
proposed by John Maynard Keynes. This book is a valuable resource
for students in philosophy and mathematics and all readers
interested in notions of probability.
Subjects:
PHILOSOPHY: Logic and Philosophy of Language
24 x 17 cm. Approx. XV, 417 pages. Cloth.
ISBN 3-11-017447-2 Series: [de Gruyter Proceedings in Mathematics]
This is a volume of research articles related to finite groups.
Topics covered include the classification of finite simple
groups, the theory of p-groups, cohomology of groups,
representation theory and the theory of buildings and geometries.
As well as more than twenty original papers on the latest
developments, which will be of great interest to specialists, the
volume contains several expository articles, from which students
and non-experts can learn about the present state of knowledge
and promising directions for further research.
The Finite Groups 2003 conference was held in honor of John
Thompson. The profound influence of his fundamental contributions
is clearly visible in this collection of papers dedicated to him.
24 x 17 cm. Approx. XII, 452 pages. Cloth.
ISBN 3-11-018346-3
Series: de Gruyter Studies in Mathematics 27
This book is an introduction to financial mathematics.
The first part of the book studies a simple one-period model
which serves as a building block for later developments. Topics
include the characterization of arbitrage-free markets,
preferences on asset profiles, an introduction to equilibrium
analysis, and monetary measures of risk.
In the second part, the idea of dynamic hedging of contingent
claims is developed in a multiperiod framework. Such models are
typically incomplete: They involve intrinsic risks which cannot
be hedged away completely. Topics include martingale measures,
pricing formulas for derivatives, American options, superhedging,
and hedging strategies with minimal shortfall risk.
In addition to many corrections and improvements, this second
edition contains several new sections, including a systematic
discussion of law-invariant risk measures and of the connections
between American options, superhedging, and dynamic risk measures.
24 x 17 cm. Approx. X, 554 pages. Cloth.
ISBN 3-11-016266-0
Series: de Gruyter Expositions in Mathematics 39
The book presents the theory of multiple trigonometric sums
constructed by the authors. Following a unified approach, the
authors obtain estimates for these sums similar to the classical
I. M. Vinogradov´s estimates and use them to solve several
problems in analytic number theory. They investigate
trigonometric integrals, which are often encountered in physics,
mathematical statistics, and analysis, and present purely
arithmetic results concerning the solvability of equations in
integers.