Thomas W. Judson: “Abstract Algebra: Theory aand Applications”, 2009, 428p.
“Abstract Algebra: Theory and Applications” is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many nontrivial applications. This version is close to the original, as first published by PWS Publishing Company in 1994. Since then, the copyright has transferred back to the author, making this open-source version possible. There is a tutorial (prepared by Robert Beezer) designed to help instructors and students use SAGE in an introductory course in group theory. While it could be used profitably in any standard course, it has been written to specifically accompany Judson's “Abstract Algebra: Theory and Applications”, it may be downloaded from:
http://abstract.ups.edu/sage-aata.html
SAGE is an open-source program for doing mathematics and is the ideal companion to "Abstract Algebra: Theory and Applications". SAGE is designed to be a free, open-source alternative to Magma, Maple, Mathematica and Matlab. It includes many mature and powerful open-source tools for mathematics, such as GAP for group theory. With a strength in number theory, SAGE also has excellent support for rings and fields.
Contents:
Preface
0 Preliminaries
1 The Integers
2 Groups
3 Cyclic Groups
4 Permutation Groups
5 Cosets and Lagrange's Theorem
6 Introduction to Cryptography
7 Algebraic Coding Theory
8 Isomorphisms
9 Homomorphisms and Factor Groups
10 Matrix Groups and Symmetry
11 The Structure of Groups
12 Group Actions
13 The Sylow Theorems
14 Rings
15 Polynomials
16 Integral Domains
17 Lattices and Boolean Algebras
18 Vector Spaces
19 Fields
20 Finite Fields
21 Galois Theory
Notation
Hints and Solutions
http://ifile.it/bjxt2iu/judson_-_aata.rar
