Description
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
Sets. Maps. Cartesian Product and Binary Relations. Posets, Lattices, Zorn's Lemma. Peano's Axions. Cardinality. Quotient Sets. Groupoids, Semigroups, Monoids. Groups. The Integers. Congruences. Normal Subgroups. Isomorphism Theorems for Groups. Cyclic Groups. Direct Product of Groups. The Symmetric Group. Further Results on Groups. Rings, Ideals, and Homomorphisms. Quotient Rings. Direct Product of Rings.
