Produktdetaljer
Om bidragsyterne
JONATHAN D. H. SMITH is Professor of Mathematics at Iowa StateUniversity. His research interests comprise algebra, combinatorics,and information theory, with applications in computer science,complex systems, physics, and biology. He has published more thansixty research papers and written or edited six books.ANNA B. ROMANOWSKA is Professor of Mathematics at WarsawUniversity of Technology. Her research interests include universalalgebra, lattice theory, and logic, with applications in computerscience and music theory. She has published fifty-five researchpapers and written or edited three books.
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)<br /> <br /> "...an interesting book anyone who works the exercises will obtainan excellent grounding algebraic concepts..." (Zentralblatt MATH,Vol. 946, No. 21)
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.
Algebra: The Central Discipline of Mathematics.
Sets with Structure and Sets Without Structure.
Semigroups and Monoids.
GROUP AND QUASIGROUPS.
Monoid Actions.
Groups and Quasigroups.
Symmetry.
Loops, Nets and Isotopy.
LINEAR ALGEBRA.
General Algebra and Linear Algebra.
Vector Spaces and Modules.
Commutative Algebra.
CATEGORIES AND LATTICES.
Posets, Monoids and Categories.
Limits and Lattices.
Adjoint Functors.
UNIVERSAL ALGEBRA.
Sets with Operations.
Varieties.
Algebraic Theories.
Monads.
Index.
This volume takes an altogether new approach to advanced algebra. Its intriguing title, inspired by the term postmodernism, denotes a departure from van der Waerden's Modern Algebra—a book that has dominated the field for nearly seventy years. Post-Modern Algebra offers a truly up-to-date alternative to the standard approach, explaining topics from an applications-based perspective rather than by abstract principles alone. The book broadens the field of study to include algebraic structures and methods used in current and emerging mathematical research, and describes the powerful yet subtle techniques of universal algebra and category theory. Classical algebraic areas of groups, rings, fields, and vector spaces 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 in university courses.
- A wealth of exercises illustrating concepts and their practical application.
- Effective techniques for solving research problems in the real world.
- Flexibility of presentation, making it easy to tailor material to specific needs.
- Help with elementary proofs and algebraic notations for students of varying abilities.
Post-Modern Algebra is an excellent primary or supplementary text for graduate-level algebra courses. It is also an extremely useful resource for professionals and researchers in many areas who must tackle abstract, linear, or universal algebra in the course of their work.
Produktdetaljer
Om bidragsyterne
JONATHAN D. H. SMITH is Professor of Mathematics at Iowa StateUniversity. His research interests comprise algebra, combinatorics,and information theory, with applications in computer science,complex systems, physics, and biology. He has published more thansixty research papers and written or edited six books.ANNA B. ROMANOWSKA is Professor of Mathematics at WarsawUniversity of Technology. Her research interests include universalalgebra, lattice theory, and logic, with applications in computerscience and music theory. She has published fifty-five researchpapers and written or edited three books.