Scherk, John
Algebra A Computational Introduction
Description
Adequate texts that introduce the concepts
of abstract algebra
are plentiful. None, however, are more suited
to those needing a
mathematical
background for careers in engineering, computer
science, the
physical sciences, industry, or finance than
Algebra: A
Computational Introduction. Along
with a unique approach and presentation,
the author demonstrates
how software can be used as a problem-solving
tool for algebra.
A variety of factors set this text apart.
Its clear exposition,
with each chapter building upon the previous
ones, provides
greater clarity for the reader. The
author first introduces permutation groups,
then linear groups,
before finally tackling abstract groups.
He carefully motivates
Galois theory by
introducing Galois groups as symmetry groups.
He includes many
computations, both as examples and as exercises.
All of this
works to better prepare
readers for understanding the more abstract
concepts. By carefully integrating the use of Mathematica(r)
throughout the book in examples and exercises,
the author helps readers develop a deeper
understanding and appreciation of the material.
The numerous
exercises and examples along with downloads
available from the
Internet help establish a
valuable working knowledge of Mathematica
and provide a good
reference for complex problems encountered
in the field.
Audience
Undergraduates and professionals in engineering,
computer
science, the physical sciences, industry,
or finance
Contents
CONGRUENCES
PERMUTATIONS
PERMUTATION GROUPS
LINEAR GROUPS
GROUPS
SUBGROUPS
SYMMETRY GROUPS
GROUP ACTIONS
COUNTING FORMULAS
COSETS
SYLOW SUBGROUPS
SIMPLE GROUPS
ABELIAN GROUPS
POLYNOMIAL RINGS
SYMMETRIC POLYNOMIALS
ROOTS OF EQUATIONS
GALOIS GROUPS
QUARTICS
THE GENERAL EQUATION OF THE nth DEGREE
SOLUTION BY RADICALS
RULER-AND-COMPASS CONSTRUCTIONS
APPENDIX: MATHEMATICA COMMANDS
ISBN: 1584880643, No of pages: 336
Publication Date: 06/23/00
Carl, S /
University of Halle-Germany
Heikkila, Seppo /University of Oulu-Finland
Nonlinear Differential Equations in Ordered
Spaces
Description
Extremality results proved in this Monograph
for an abstract
operator equation provide the theoretical
framework for
developing new methods that allow
the treatment of a variety of discontinuous
initial and boundary
value problems for both ordinary and partial
differential
equations, in explicit and implicit
forms. By mean of these extremality results,
the authors prove
the existence of extremal solutions between
appropriate upper and
lower solutions of first
and second order discontinuous implicit and
explicit ordinary and
functional differential equations. They then
study the dependence
of these extremal
solutions on the data.
Contents
OPERATOR EQUATIONS IN ORDERED SPACES AND
FIRST APPLICATIONS
EXTREMALITY RESULTS FOR FIRST ORDER DIFFERENTIAL
EQUATIONS
UNIQUENESS, COMPARISON AND WELL-POSEDNESS
RESULTS FOR QUASILINEAR
DIFFERENTIAL EQUATIONS
SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS
EXTREMALITY RESULTS FOR QUASILINEAR PDE
DIFFERENTIAL INCLUSIONS OF HEMIVARIATIONAL
INEQUALITY TYPE
DISCONTINUOUS IMPLICIT ELLIPTIC AND PARABOLIC
PROBLEMS
APPENDIX
Features
Develops an existence theory for an abstract
operator equation in
ordered spaces
Offers new tools to tackle different kinds
of discontinuous
implicit and explicit differential equations
Presents a unified approach to the existence
of extremal solutions of quasilinear elliptic
and parabolic problems
ISBN: 1584880686, No of pages: 336
Publication Date: 06/14/00
Cox, D.R. /
Nuffield College, Oxford, England
Reid, Nancy /
Univeristy of Toronto
The Theory of the Design of Experiments
Description
Rather than focusing on the analysis of experiment
designs, this
monograph helps researchers understand The
Theory of the Design
of Experiments so
they can easily adapt general principles
to their specialty. The
well-respected authors bring theory to non-statisticians
at a
reasonable mathematical level
so that they can apply and adapt the special
designs. They use
self-contained chapters, illustrated applications,
and examples
to teach the ideas and
concepts needed for sound experiment design
and, consequently,
analysis.
Audience
Researchers in all areas, Statisticians,
and Students in
Statistics
Contents
Some General Concepts. Avoidance of Bias.
Control of Haphazard
Variation. Specialized Blocking Techniques.
Factorial
Experiments: Basic Ideas.
Factorial Experiments: Further Developments.
Optimal Design.
Miscellaneous. Appendix A: Statistical Analysis.
Appendix B: Some
Algebra.
Features
Illustrates applications and examples to
show detailed methods of
analysis without emphasizing any particular
subject matter
Keeps the mathematics simple, creating a
highly accessible
reference
Offers brief, non-technical introductions
to specialized subjects
like block designs, mixture designs, designs
for large variety
trials, and designs based
on spatial stochastic models
Includes appended reviews of necessary background
material
ISBN: 158488195X, No of pages: 336
Publication Date: 06/06/00
Dumitrescu, D. /University of Cluj-Napoca
Lazzerini, Beatrice /Universita' di Pisa
Jain, Lakhmi C. /University of South Australia
Dumitrescu, A /University of Savoie
Evolutionary Computation
Description
Rapid advances in evolutionary computation
have opened up a world
of applications-a world rapidly growing and
evolving. Decision
making, neural
networks, pattern recognition, complex optimization/search
tasks,
scheduling, control, automated programming,
and cellular automata
applications all
rely on evolutionary computation.
Evolutionary Computation provides the basic
principles of
evolutionary computing: genetic algorithms,
evolution strategies,
evolutionary programming,
genetic programming, learning classifier
systems, population
models, and applications. It includes detailed
coverage of binary
and real encoding,
including selection, crossover, and mutation,
and discusses the
(m+l) and (m,l) evolution strategy principles.
The focus then
shifts to applications:
decision strategy selection, training and
design of neural
networks, several approaches to pattern recognition,
cellular
automata, applications of genetic
programming, and more.
Audience
Scientists in any field, engineers, and research
students in AI
and in the industrial design of intelligent
systems
Features
Presents a thorough review of evolutionary
computation techniques
and applications
Includes detailed coverage of encoding, selection
and search
operators, schemata theory, GA parameter
setting, hybridization,
and other genetic
algorithm approaches
Covers techniques beyond the genetic algorithms
Details various evolution strategies
Describes real-world applications
ISBN: 0849305888, No of pages: 424
Publication Date: 06/22/00