Abstract Algebra: An Introduction, 3rd Edition

Book Preface

This book is intended for a first undergraduate course in modem abstract algebra. Linear algebra is not a prerequisite. The flexible design makes the text suitable for courses of various lengths and different levels of mathematical sophistication, in­cluding (but not limited to) a traditional abstract algebra course, or one with a more applied flavor, or a course for prospective secondary school teachers. As in previous editions, the emphasis is on clarity of exposition and the goal is to prodooe a book that an average student can read with minimal outside assistance.

New in the Third Edition

Groups First Option Those who believe ( as I do) that covering rings before groups is the better pedagogical approach to abstract algebra can use this edition exactly as they used the previous one&.
Nevertheless, anecdotal evidence indicates that some instructors have used the sec­ond edition for a “groups fir.it” counie,, which pn:swnably means that they liked other aspecill of the book enough that they were willing to take on the burden of adapting it to their needs. To make life easier for them (and for anyone else who prefers “groups first”)
lt is now possil,/e ( though not necessary) to use this text for
a course that corers groups before rings.

See the TO THE INSTRUCTOR section for details.
Much of the rewriting needed to make this option feasible also benefits the “rings first” users. A number of them have suggested that complete proofs were needed in parts of the group theory chapters instead of directions that said in effect “adapt the proof of the analogous theorem for rings”. The full proofs are now there.
Proofs for Beginners Many students entering a first abstract algebra course have had little ( or no) experience in reading and writing proofs. To assist such students ( and better prepared students as well), a number of proofs (especially in Chapters 1 and 2) have been rewritten and expanded. They are broken into several steps, each of which is carefully explained and proved in detail. Such proofs take up more space, but I think it’s worth it if they provide better understanding.
So that students can better concentrate on the essential topics, various items from number theory that play no role in the remainder of the book have been eliminated from Chapters l and 2 (though some remain as exercises).

More Examples and Exercises In the core course (Chapters 1-8), there are 35% more examples than in the previous edition and 13% more exercise& Some older exer­cises have been replaced, so 18% of the exercises are new. The entire text has about 350 examples and 1600 exercises. For easier reference, the examples are now numbered.
Coverage The breadth of coverage in this edition is substantially the same as in the preceding ones, with one minor exception. The chapter on Lattices and Boolean Algebra (which apparently was rarely used) has been eliminated. However, it is avail­able at our website (www.CengageBrain.com) for those who want to use it.