A Book of Abstract Algebra: Second Edition
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications.
An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.
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Standard structure and content, superb exposition and writing. I own several other books at the same level, and this one is the shortest page-wise, but deepest intuition-wise.
The introductory chapter "Why abstract algebra?" is superb. The parts on groups and rings are lucidly written. The only lacking part is perhaps last chapters that introduce field extensions and Galois theory, and feel a bit sketchy. The reader that enjoys this book will surely be able to read a "proper" (longer, more rigorous and more complete) book on those subjects after reading this.
Easy to read. Best out there for an introduction.