Abstract Algebra: Theory and Applications

Abstract

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.