1st Edition
Abstract Algebra A Gentle Introduction
Elementary Number Theory
Divisibility
Primes and factorization
Congruences
Solving congruences
Theorems of Fermat and Euler
RSA cryptosystem
Groups
De nition of a group
Examples of groups
Subgroups
Cosets and Lagrange's Theorem
Rings
Defiition of a ring
Subrings and ideals
Ring homomorphisms
Integral domains
Fields
Definition and basic properties of a field
Finite Fields
Number of elements in a finite field
How to construct finite fields
Properties of finite fields
Polynomials over finite fields
Permutation polynomials
Applications
Orthogonal latin squares
Die/Hellman key exchange
Vector Spaces
Definition and examples
Basic properties of vector spaces
Subspaces
Polynomials
Basics
Unique factorization
Polynomials over the real and complex numbers
Root formulas
Linear Codes
Basics
Hamming codes
Encoding
Decoding
Further study
Exercises
Appendix
Mathematical induction
Well-ordering Principle
Sets
Functions
Permutations
Matrices
Complex numbers
Hints and Partial Solutions to Selected Exercises
Biography
Gary Mullen is Professor of Mathematics, The Pennsylvania State University, where he earned his Ph.D. His main interest is finite fields, and is founder of the journal "Finite Fields and Their Introduction." He is also the Editor of The Handbook of Finite Fields published by CRC Press.
James Sellers is Professor and Associate Head for Undergraduate Mathematics, The Pennsylvania State University, where he also earned his Ph.D. He has published many research articles and won awards related to his efforts to advance mathematics education.
