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