"Topics in Algebra" by I. N. Herstein is a classic textbook in abstract algebra that has been widely used by students and instructors for decades. First published in 1965, the book provides a thorough introduction to various topics in algebra, including group theory, ring theory, and field theory. In this article, we will review the book's contents, highlighting its strengths and weaknesses, and discuss why it remains a valuable resource for those interested in algebra.
| Feature | Herstein (2nd Ed) | Dummit & Foote | Gallian | | :--- | :--- | :--- | :--- | | | Excellent (300 pages of core text) | Poor (~1000 pages) | Average | | Problem Difficulty | Hard (Proof heavy) | Medium-Hard | Easy-Medium | | Suitability for PDF | Excellent (Linear reading) | Poor (Often requires flipping) | Good | | Why "Better" | Builds maturity fast | Encyclopedic reference | Beginner-friendly | topics in algebra herstein pdf better
The exercises in Topics in Algebra are famous—and infamous. They are not computational drills. They are theoretical mini-lectures. Many problems are actually extensions of the text (e.g., “If G is a group in which every element is of order 2, prove G is abelian”). Working through Herstein’s problems forces you to discover lemmas that are themselves theorems in other books. This is why many professors claim: If you solve 80% of Herstein’s problems, you know algebra better than most first-year graduate students. "Topics in Algebra" by I