A Book of Abstract Algebra
"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."--Publisher's description.
Stats for nerds
25recommend
40mentions
27people
2011–2025years
85% recommend15% neutral
Mentions per year
What Hacker News says
- A book of abstract algebra is very approachable!
- A few years ago, I led a study group through A Book of Abstract Algebra by Charles C Pinter. It culminated in Galois Theory and was one of the best books I've ever used in a math study group.
- Pinter, "A Book of Abstract Algebra", is very nice. It's rigorous but not too terse. It divides the material into many small chapters with many exercises. Chapters are mostly around 10+/-3 pages with about 40-60% of that being text and the rest exercises.
The exercises for each chapter are split into several sections each section covering a different aspect of the chapter's material. Sometimes there is a section of exercises applying the material to some interesting area.
For example, the chapter on groups of permutations has 6 pages of text, then 5 pages of exercises divided into 9 sections. Those sections are: computing elements in S6 (5 problems), examples of groups of permutations (4 problems), groups of permutations in R (4 problems), a cyclic group of permutations (4 problems), a subgroup of SR (4 problems), symmetries of geometric figures (4 problems), symmetries of polynomials (4 problems), properties of permutations of a set A (4 problems), and algebra of kinship structures which consists of 9 problems covering how anthropologists have applied groups of permutations to describe kinship systems in primitive societies.
There are answers in the back for a decent number of the exercises.
It's a Dover republication so is not too hard on the wallet. List price is $30 at Dover but its around $20 on Amazon.
The combination of short chapters and lots of exercises make it easier than most textbooks to fit into a busy adult schedule.
- A Book of Abstract Algebra, Charles Pinter- it’s pretty good, each chapter is has a short description of the math and then many problems to work through. Would recommend
- "How to Think About Analysis" by Lara Alcock (2014) because the first part (half) of the book is specifically dedicated this aim, "[focusing] explicitly on skills and strategies for learning advanced pure mathematics." (from the author's intro). The remaining text demonstrates how to do this for a full first undergraduate course in real analysis.
Also, "A Book of Abstract Algebra" by Charles Pinter (available as a Dover paperback). The introductory sections to each chapter draw motivating lines from earlier definitions / theorems.
Other books that are good mentions, but even better after the above include the 2nd edition of Sheldon Axler's "Linear Algebra Done Right" (it motivates each development similar to Pinter) and "Topology" by K. Janich.
Of all, I have admired how they motivate without compromising rigor, using expository text alongside formal statements of definitions, theorems and proofs.
- A book of abstract algebra - Charles C. Pinter. Each chapter is a few pages of explanation, and the rest you solve yourself by doing exercises that introduce aspects of the theory step by step.
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