Taken from the preface.This edition, in common with previous editions, is intended as a text for a first course in abstract algebra. The goal has continued to be that of making the exposition as simple and clear as possible, but sufficiently precise and thorough to furnish an honest introduction to the methods and results of abstract algebra.  In the present undergraduate curriculum, the first course in abstract algebra often serves several purposes. The student is expected to learn a collection of facts, to learn some methods and ideas, and, in addition, to learn to read and write correct mathematical proofs. All of these requirements have been carefully considered in the preparation of the text.

Introduction to Modern Algebra

Science & Math

McCoy, Neal H.

Mathematics

McGraw-Hill Companies

Rings and Ideals (Carus Mathematical Monographs, No 8)

The Mathematical Association of America

<p>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.</p>

Introduction to Abstract Algebra, 7th Edition

Janusz, Gerald J.

Trustworthy Communications, LLC

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