1st Edition

Abstract Algebra A Gentle Introduction

By Gary L. Mullen, James A. Sellers Copyright 2017
    214 Pages
    by CRC Press

    214 Pages
    by Chapman & Hall


    Abstract Algebra: A Gentle Introduction advantages a trend in mathematics textbook publishing towards smaller, less expensive and brief introductions to primary courses. The authors move away from the ‘everything for everyone’ approach so common in textbooks. Instead, they provide the reader with coverage of numerous algebraic topics to cover the most important areas of abstract algebra.

    Through a careful selection of topics, supported by interesting applications, the authors Intend the book to be used for a one-semester course in abstract algebra. It is suitable for an introductory course in for mathematics majors. The text is also very suitable for education majors

    who need to have an introduction to the topic.

    As textbooks go through various editions and authors employ the suggestions of numerous well-intentioned reviewers, these book become larger and larger and subsequently more expensive. This book is meant to counter that process. Here students are given a "gentle introduction," meant to provide enough for a course, yet also enough to encourage them toward future study of the topic.


    • Groups before rings approach

    • Interesting modern applications

    • Appendix includes mathematical induction, the well-ordering principle, sets, functions, permutations, matrices, and complex nubers.

    • Numerous exercises at the end of each section

    • Chapter "Hint and Partial Solutions" offers built in solutions manual

    Elementary Number Theory


    Primes and factorization 


    Solving congruences 

    Theorems of Fermat and Euler

    RSA cryptosystem 


    De nition of a group 

    Examples of groups


    Cosets and Lagrange's Theorem


    Defiition of a ring 

    Subrings and ideals

    Ring homomorphisms

    Integral domains


    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


    Orthogonal latin squares

    Die/Hellman key exchange

    Vector Spaces

    Definition and examples

    Basic properties of vector spaces




    Unique factorization

    Polynomials over the real and complex numbers

    Root formulas

    Linear Codes


    Hamming codes



    Further study



    Mathematical induction

    Well-ordering Principle





    Complex numbers

    Hints and Partial Solutions to Selected Exercises


    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.