Contemporary Abstract Algebra

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.

• 1 Introduction to Groups2 Groups3 Finite Groups; Subgroups4 Cyclic Groups5 Permutation Groups6 Ismorphisms7 Cosets and Lagrange's Theorem8 External Direct Products9 Normal Subgroups and Factor Groups10 Group Homomorphisms11 Fundamental Theorem of Finite Abelian Groups12 Introduction to Rings13 Integral Domains14 Ideals and Factor Rings15 Ring Homomorphisms16 Polynomial Rings17 Factorization of Polynomials18 Divisibilty in Integral Domains19 Extension Fields20 Algebraic Extensions21 Finite Fields22 Geometric Constructions23 Sylow Theorems24 Finite Simple Groups25 Generators and Relations26 Symmetry Groups27 Symmetry and Counting28 Cayley Digraphs of Groups29 Introduction to Algebraic Coding Theory30 An Introduction to Galois Theory31 Cyclotomic Extensions

"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 exercises2. Many new examples3. New quotes4. A freshening of the discussion portions"- Benjamin Linowitz, Oberlin College, Published in MAA