Abstract Algebra: Theory and Applications (Judson)
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Abstract Algebra: Theory and Applications 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. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second-half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.
Front Matter
1: Preliminaries
2: The Integers
3: Groups
4: Cyclic Groups
5: Permutation Groups
6: Cosets and Lagrange's Theorem
7: Introduction to Cryptography
8: Algebraic Coding Theory
9: Isomorphisms
10: Normal Subgroups and Factor Groups
11: Homomorphisms
12: Matrix Groups and Symmetry
13: The Structure of Groups
14: Group Actions
15: The Sylow Theorems
16: Rings
17: Polynomials
18: Integral Domains
19: Lattices and Boolean Algebras
20: Vector Spaces
21: Fields
22: Finite Fields
23: Galois Theory
Back Matter