This is the classic text for the first undergraduate course in abstract algebra; it follows the “rings before groups” philosophy that relies on the student's familiarity with the ring of integers to make the abstract axioms feel more concrete. The text and exercises are coordinated to help the student learn to read and write mathematical proofs. To achieve an understanding of the methods of proof, the unique factorization theorems are presented several times in different contexts. The integers are covered first, then polynomial rings over a field and, in the final chapter, factorization in principal ideal domains. Results on finite fields up through existence and uniqueness are proved without the use of linear algebra. The material on groups is studied in three chapters, the first giving definitions and examples, including permutation groups; the second gives the classification of finite abelian groups; the third discusses groups acting on sets and gives the proofs of the Sylow theorems. There are many worked examples and a large number of exercises of varying levels of difficulty. By carefully selecting sections to be covered in class lectures, an instructor will find this text suitable for almost any syllabus giving an introduction to abstract algebra.
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4 of 6 people found the following review helpful:
2.0 out of 5 stars
Atrocious....Avoid at ALL COSTS,
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This review is from: Introduction to Abstract Algebra, 7th Edition (Paperback)
This is an atrocious book. If you can avoid it, do not buy. My complaints can be summarized into three points;
1. The concepts are incoherently presented and the exercises require knowledge that was not presented in the tutorial portion of the chapter. 2. There's a lot more to undergraduate level abstract algebra than what this book shows you. 3. The authors presented the material like how a number theorists would present the material, with too much emphasis on proving number theory topics. I recommend the book by Hungerford, or, if you are mathematically mature enough, Dummit & Foote or Artin. You will see the difference.
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