Advanced algebra in the service of contemporary mathematicalresearch-- a unique introduction.
This volume takes an altogether new approach to advanced algebra.Its intriguing title, inspired by the term postmodernism, denotes adeparture from van der Waerden's Modern Algebra--a book that hasdominated the field for nearly seventy years. Post-Modern Algebraoffers a truly up-to-date alternative to the standard approach,explaining topics from an applications-based perspective ratherthan by abstract principles alone. The book broadens the field ofstudy to include algebraic structures and methods used in currentand emerging mathematical research, and describes the powerful yetsubtle techniques of universal algebra and category theory.Classical algebraic areas of groups, rings, fields, and vectorspaces are bolstered by such topics as ordered sets, monoids,monoid actions, quasigroups, loops, lattices, Boolean algebras,categories, and Heyting algebras. The text features:
* A clear and concise treatment at an introductory level, tested inuniversity courses.
* A wealth of exercises illustrating concepts and their practicalapplication.
* Effective techniques for solving research problems in the realworld.
* Flexibility of presentation, making it easy to tailor material tospecific needs.
* Help with elementary proofs and algebraic notations for studentsof varying abilities.
Post-Modern Algebra is an excellent primary or supplementary textfor graduate-level algebra courses. It is also an extremely usefulresource for professionals and researchers in many areas who musttackle abstract, linear, or universal algebra in the course oftheir work.
Table of contents
Modern and Post-Modern Algebra.
Algebra: The Central Discipline of Mathematics.
Sets with Structure and Sets Without Structure.
Semigroups and Monoids.
GROUP AND QUASIGROUPS.
Groups and Quasigroups.
Loops, Nets and Isotopy.
General Algebra and Linear Algebra.
Vector Spaces and Modules.
CATEGORIES AND LATTICES.
Posets, Monoids and Categories.
Limits and Lattices.
Sets with Operations.
I found this an interesting book to read, and feel that anyone whoworks though it and works all the exercises, will obtain anexcellent grounding in algebraic concepts, praticularly those whichhave practical applications.(Zentralblatt Math, Volume 946, No 21,2000)
"...an interesting book anyone who works the exercises will obtainan excellent grounding algebraic concepts..." (Zentralblatt MATH,Vol. 946, No. 21)