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