10th Edition

Contemporary Abstract Algebra

By Joseph Gallian Copyright 2021
    654 Pages 50 B/W Illustrations
    by Chapman & Hall

    654 Pages 50 B/W Illustrations
    by Chapman & Hall

    Continue Shopping

    Contemporary Abstract Algebra, Tenth Edition

    For more than three decades, this classic text has been widely appreciated by instructors and students alike. The book offers an enjoyable read and conveys and develops enthusiasm for the beauty of the topics presented. It is comprehensive, lively, and engaging.

    The author presents the concepts and methodologies of contemporary abstract algebra as used by working mathematicians, computer scientists, physicists, and chemists. Students will learn how to do computations and to write proofs. A unique feature of the book are exercises that build the skill of generalizing, a skill that students should develop but rarely do. Applications are included to illustrate the utility of the abstract concepts.

    Examples and exercises are the heart of the book. Examples elucidate the definitions, theorems, and proof techniques; exercises facilitate understanding, provide insight, and develop the ability to do proofs. The exercises often foreshadow definitions, concepts, and theorems to come.

    Changes for the tenth edition include new exercises, new examples, new quotes, and a freshening of the discussion portions. The hallmark features of previous editions of the book are enhanced in this edition. These include:

    • A good mixture of approximately 1900 computational and theoretical exercises, including computer exercises, that synthesize concepts from multiple chapters
    • Approximately 300 worked-out examples from routine computations to the challenging
    • Many applications from scientific and computing fields and everyday life
    • Historical notes and biographies that spotlight people and events
    • Motivational and humorous quotations
    • Numerous connections to number theory and geometry

    While many partial solutions and sketches for the odd-numbered exercises appear in the book, an Instructor’s Solutions Manual written by the author has comprehensive solutions for all exercises and some alternative solutions to develop a critical thought and deeper understanding. It is available from CRC Press only. The Student Solution Manual has comprehensive solutions for all odd-numbered exercises and many even-numbered exercises.

    1 Introduction to Groups
    2 Groups
    3 Finite Groups; Subgroups
    4 Cyclic Groups
    5 Permutation Groups
    6 Ismorphisms
    7 Cosets and Lagrange's Theorem
    8 External Direct Products
    9 Normal Subgroups and Factor Groups
    10 Group Homomorphisms
    11 Fundamental Theorem of Finite Abelian Groups
    12 Introduction to Rings
    13 Integral Domains
    14 Ideals and Factor Rings
    15 Ring Homomorphisms
    16 Polynomial Rings
    17 Factorization of Polynomials
    18 Divisibilty in Integral Domains
    19 Extension Fields
    20 Algebraic Extensions
    21 Finite Fields
    22 Geometric Constructions
    23 Sylow Theorems
    24 Finite Simple Groups
    25 Generators and Relations
    26 Symmetry Groups
    27 Symmetry and Counting
    28 Cayley Digraphs of Groups
    29 Introduction to Algebraic Coding Theory
    30 An Introduction to Galois Theory
    31 Cyclotomic Extensions


    Joseph A. Gallian earned his PhD from Notre Dame. In addition to receiving numerous national awards for his teaching and exposition, he has served terms as the Second Vice President, and the President of the MAA. He has served on 40 national committees, chairing ten of them. He has published over 100 articles and authored six books. Numerous articles about his work have appeared in the national news outlets, including the New York Times, the Washington Post, the Boston Globe, and Newsweek, among many others.

    "It has now been 35 years since Gallian's classic textbook Contemporary Abstract Algebra was first published. The book is deservedly popular with instructors of abstract algebra courses. It is written at an appropriate level for junior and senior undergraduates, has lucid coverage of all of the standard topics and several nonstandard ones (Frieze Groups and Crystallographic Groups, Coding Theory, Greek Geometric Construction Problems, etc), is example-driven, and contains thousands of exercises at various levels of difficulty. Moreover, every chapter begins with an interesting quote or two (by as diverse a group of people as Einstein, Miguel de Cervantes, Ralph Waldo Emerson, Bob Dylan, etc) and most conclude with a mini- biography of a mathematician whose work relates to the chapter's content. This is an interesting book that is a pleasure to read.
    According to the Preface, changes made for the tenth edition include:
    1. Approximately 200 new exercises
    2. Many new examples
    3. New quotes
    4. A  freshening of the discussion portions"

    - Benjamin Linowitz, Oberlin College, Published in MAA