In one exceptional volume, Abstract Algebra covers subject matter typically taught over the course of two or three years and offers a self-contained presentation, detailed definitions, and excellent chapter-matched exercises to smooth the trajectory of learning algebra from zero to one. Field-tested through advance use in the ERASMUS educational project in Europe, this ambitious, comprehensive book includes an original treatment of representation of finite groups that avoids the use of semisimple ring theory and explains sets, maps, posets, lattices, and other essentials of the algebraic language; Peano's axioms and cardinality; groupoids, semigroups, monoids, groups; and normal subgroups.
Table of Contents
Cartesian Product and Binary Relations
Posets, Lattices, Zorn's Lemma
Groupoids, Semigroups, Monoids
Isomorphism Theorems for Groups
Direct Product of Groups
The Symmetric Group
Further Results on Groups
Rings, Ideals, and Homomorphisms
Direct Product of Rings
"This is a comprehensive book of over 750 pages, that covers the material of algebra courses in the first two or three years of a bachelor's degree program. …This a nice book is written in a very clear and explanatory style, offering a self-contained presentation and complete proofs, as well as well-chosen exercises, illustrative examples, and some interesting historical notes."
-Mathematical Reviews, Issue 2005e
"Many examples and worked exercises make the text easy to read. Written in a clear and detailed style it will be a valuable basis for students who want to learn algebra from the beginning."
-H. Mitsch, Wien, Monatshefte für Mathematik
"The experience of the authors together with a careful presentation of material makes this book a valuable addition to modern textbooks in algebra."
-EMS Newsletter, June 2005