Abstract Algebra Theory and Applications
This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebr...
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| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
[Place of publication not identified]
University of Puget Sound
[2016]
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| Series: | Open textbook library.
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| Subjects: | |
| Online Access: | Access online version |
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Table of Contents:
- Preliminaries
- The Integers
- Groups
- Cyclic Groups
- Permutation Groups
- Cosets and Lagrange's Theorem
- Introduction to Cryptography
- Algebraic Coding Theory
- Isomorphisms
- Normal Subgroups and Factor Groups
- Homomorphisms
- Matrix Groups and Symmetry
- The Structure of Groups
- Group Actions
- The Sylow Theorems
- Rings
- Polynomials
- Integral Domains
- Lattices and Boolean Algebras
- Vector Spaces
- Fields
- Finite Fields
- Galois Theory