This is quite a good book for a first introduction to abstract algebra. The only other algebra book I’ve read in any detail is Fraleigh’s, and Pinter’s is written at a slightly lower level, both in the style of presentation and the mathematical content. The first 30 or so chapters are great and what could have been a major problem with the book—the relatively limited material covered in the chapters themselves—is made up for in the exercise sets, which add greatly to the theoretical material covered in the book. Don’t worry if you don’t think you’re up to proving them yourself; they’re broken down into manageable chunks, sometimes even excessively so that some might call it hand holding. Just about anything covered in a typical first course is included one way or another in this book, and with help available anytime online now, relegating material to the exercises isn’t especially troublesome. There are the usual typos and very minor errors that make their way into just about every math book (one such minor error made the cover!) but nothing too serious. Until...
I was prepared to give it five stars until I got to the later chapters on Galois theory, which seem rushed and a bit sloppy compared to the rest of the book. I did some detective work and checked this edition against the first and I know what happened. In the first edition there were some minor errors in some of the material, for example for one theorem to work he needs to assume that two field extensions are contained in a common extension but he never does, so the theorem he states implies that all splitting fields are equal instead of just isomorphic. Worse, he states a fundamentally incorrect theorem—there’s even an obvious error in the proof—and it looks like he implicitly relies on it a few chapters later. He tries to fix these in the second edition but patching up proofs and inserting some sentences here and there in the chapters instead of redoing them entirely is hard; the result is a hybrid of the old incorrect presentation and the corrected one. This is confusing and results in one theorem that is still technically incorrect (but at least easily fixable) and a VERY confusing proof about polynomials solvable by radicals having solvable Galois groups. The hardest exercise in the book for me was cross-checking with Fraleigh and trying to figure out what Pinter was talking about. I’ll provide the details and some more errata in a comment for anyone interested, which should be everyone planning to go through the entire book.
I view this as a fantastic 30 chapter book with a decent 3 chapter appendix on Galois theory.
- Paperback: 400 pages
- Publisher: Dover Publications; 2 Revised edition edition (14 January 2010)
- Language: English
- ISBN-10: 0486474178
- ISBN-13: 978-0486474175
- Product Dimensions: 14 x 2.5 x 21 cm
- Boxed-product Weight: 481 g
- Average Customer Review: Be the first to review this item
- Amazon Bestsellers Rank: 81,012 in Books (See Top 100 in Books)