Contemporary Abstract Algebra

Auteur
Joseph A. Gallian earned his Ph.D. from Notre Dame. In addition to receiving numerous national awards for his teaching and exposition, he has served terms as the Second Vice President, and the President of the MAA. He has served on 40 national committees, chairing ten of them. He has published over 100 articles and authored six books. Numerous articles about his work have appeared in national news outlets, including the New York Times, the Washington Post, the Boston Globe, and Newsweek, among many others.

Texte du rabat

CONTEMPORARY ABSTRACT ALGEBRA, 11e stresses the importance of obtaining a solid introduction to the traditional topics, while at the same time presenting abstract algebra as a contemporary and very much active subject which is currently being used by working physicists, chemists, and computer scientists

Résumé
CONTEMPORARY ABSTRACT ALGEBRA, 11e stresses the importance of obtaining a solid introduction to the traditional topics, while at the same time presenting abstract algebra as a contemporary and very much active subject which is currently being used by working physicists, chemists, and computer scientists

Contenu

1 Introduction to Groups
2 Groups
3 Finite Groups; Subgroups
4 Cyclic Groups
5 Permutation Groups
6 Ismorphisms
7 Cosets and Lagrange's Theorem
8 External Direct Products
9 Normal Subgroups and Factor Groups
10 Group Homomorphisms
11 Fundamental Theorem of Finite Abelian Groups
12 Introduction to Rings
13 Integral Domains
14 Ideals and Factor Rings
15 Ring Homomorphisms
16 Polynomial Rings
17 Factorization of Polynomials
18 Divisibilty in Integral Domains
19 Extension Fields
20 Algebraic Extensions
21 Finite Fields
22 Geometric Constructions
23 Sylow Theorems
24 Finite Simple Groups
25 Generators and Relations
26 Symmetry Groups
27 Symmetry and Counting
28 Cayley Digraphs of Groups
29 Introduction to Algebraic Coding Theory
30 An Introduction to Galois Theory
31 Cyclotomic Extensions