Contemporary Abstract Algebra 9th Edition

Book Preface

Although I wrote the first edition of this book more than thirty years  ago, my goals for it remain the same. I want students to receive a solid  introduction to the traditional topics. I want readers to come away with  the view that abstract algebra is a contemporary subject–that its concepts and methodologies are being used by working mathematicians,  computer scientists, physicists, and chemists. I want students to see the  connections between abstract algebra and number theory and geometry.

I want students to be able to do computations and to write proofs. I want  students to enjoy reading the book. And I want convey to the reader my  enthusiasm for this beautiful subject.
Educational research has shown that an effective way of learning  mathematics is to interweave worked-out examples and practice problems. Thus, I have made examples and exercises the heart of the book.

The examples elucidate the definitions, theorems, and proof techniques.
The exercises facilitate understanding, provide insight, and develop the  ability of the students to do proofs. There is a large number of exercises  ranging from straight forward to difficult and enough at each level so  that instructors have plenty to choose from that are most appropriate for  their students. The exercises often foreshadow definitions, concepts,  and theorems to come. Many exercises focus on special cases and ask  the reader to generalize. Generalizing is a skill that students should develop but rarely do. Even if an instructor chooses not to spend class time  on the applications in the book, I feel that having them there demonstrates to students the utility of the theory.
Changes for the ninth edition include new exercises, new examples, new  biographies, new quotes, new appliactions, and a freshening of the historical notes and biographies from the 8th edition. These changes accentuate and enhance the hallmark features that have made previous editions of the  book a comprehensive, lively, and engaging introduction to the subject:
• Extensive coverage of groups, rings, and fields, plus a variety of nontraditional special topics
• A good mixture of more nearly 1700 computational and theoretical  exercises appearing in each chapter that synthesize concepts from multiple chapters
• Back-of-the-book skeleton solutions and hints to the odd-numbered  exercises
• Worked-out examples– totaling more than 300–ranging from routine  computations to quite challenging
• Computer exercises that utilize interactive software available on my  website that stress guessing and making conjectures
• A large number of applications from scientific and computing fields,  as well as from everyday life
• Numerous historical notes and biographies that spotlight the people  and events behind the mathematics
• Motivational and humorous quotations.
• More than 275 figures, photographs, tables, and reproductions of  currency that honor mathematicians
• Annotated suggested readings for interesting further exploration of  topics.
Cengage’s book companion site www.cengage.com/math/gallian includes  an instructor’s solution manual with detailed solutions for all exercises and  other resources. The website www.d.umn.edu/~jgallian also offers a wealth  of additional online resources supporting the book, including:
• True/false questions with comments
• Flash cards
• Essays on learning abstract algebra, doing proofs, and reasons why  abstract algebra is a valuable subject to learn
• Links to abstract algebra-related websites and software packages and much, much more.
Additionally, Cengage offers a Student Solutions Manual, available for  purchase separately, with detailed solutions to the odd-numbered exercises  in the book (ISBN13: 978-1-305-65797-7; ISBN10: 1-305-65797-7) I wish to thank Roger Lipsett for serving as accuracy checker and my  UMD colleague Robert McFarland for giving me a number of exercises  that are in this edition. I am indebted to Spencer Arritt, Content Developer  at Cengage Learning, for his excellent work on this edition. My appreciation also goes to Richard Stratton, Kate Schrumpf, Christina Ciaramella,  Nick Barrows, Brittani Morgan, and Tanya Nigh from Cengage. Finally,  I am grateful for the help of Manoj Chander and the composition work of  the whole team at Lumina Datamatics.