A Book of Abstract Algebra
by Charles C. Pinter · first published 1982
93% recommend7% neutral
Why HN recommends it
Gentle, clearly written first course in abstract algebra for self-study. Short expositions open each chapter, then exercises lead readers to discover concepts step by step, building up to Galois theory.
Summarised by Claude from recommending comments
"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. Su
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I don't like the typical definition-theorem-proof approach of most textbook in mathematics, including these. It's great for a classroom, no good for self-study. As an alternative, I highly recommend A Book of Abstract Algebra by Pinter. If you work through that first, you may actually enjoy these two later.
on “Advanced Algebra textbooks” ↗Take a look at "A Book of Abstract Algebra" by Charles Pinter. It's published by Dover, so very affordable. I've seen it criticized as too verbose, but that worked for me.
on “Ask HN: Best resources to gain math intuition?” ↗I tried and quickly stumbled learning abstract algebra from this book. I liked "A Book of Abstract Algebra" by Pinter better because it was lighter on the presentation. But maybe I'm just a wimp. This text by Judson seems to be geared towards graduate studens. From what I can tell it's very thorough, though.
on “Abstract Algebra: Theory and Applications (A Free Textbook)” ↗…I read this before I started my undergrad in CS/Maths. Free Online. - University Calculus (Hass, et. al.). This was reading for my first year, and continued to be useful throughout. Expensive. - A Book of Abstract Algebra (Charles C. Pinter). I read this after my degree, but boy, do I wish I'd had it _during_ my degree. Fairly cheap. - Linear Algebra Done Right (Sheldon Axler). Moderately priced. I can't remember which…
on “Ask HN: How or where to begin learning mathematics from first principles?” ↗goofy suggestion. those are both either grad or senior undergrad books depending on where you are. much better suggestion is A Book of Abstract Algebra by Pinter (really gentle) or A First Course in Abstract Algebra by Fraleigh
on “Ask HN: How to self-study mathematics from the undergrad through graduate level?” ↗…acting on the tangent space). You might also be interested in various 'dual' concepts, like that between tangent spaces and cotangent spaces in differential geometry. For algebra, I'd recommend Pinter's Book of Abstract Algebra.
on “Ask HN: What OR Are there some multiple perspective books in mathematics?” ↗…Discrete Mathematics, Hefferon's Linear Algebra, Colley's Vector Calculus, Dudley's Elementary Number Theory, Spivak or Apostol's Calculus (these go far beyond ordinary freshman calculus), Pinter's A Book of Abstract Algebra, among many others. Some of these books are expensive to buy new, but just buy older editions. Resources like Khan Academy and 3blue1brown are also fantastic, and I have shared some of these with my…
on “Ask HN: Is there a website specialized in mathematics courses?” ↗For abstract algebra self-study, I highly recommend "A Book of Abstract Algebra" by Charles Pinter. Each chapter starts with a few definitions and examples, and the rest of the chapter is a series of exercises meant to help you discover algebraic concepts for yourself.
on “How to Study Mathematics (2017)” ↗I recommend "How to Think About Abstract Algebra" by Lara Alcock and "A Book of Abstract Algebra" by Charles Pinter.
on “Galois Groups and the Symmetries of Polynomials” ↗…the same material several times and struggle with it. Furthermore, even the same subject within "advanced" mathematics can have wildly different depths of coverage depending on the author. Pinter's A Book of Abstract Algebra is probably approachable for anyone currently reading this comment, or even high school students. Dummit-Foote is a step beyond that, and appropriate for undergraduates who are already immersed in a math…
on “How to Study Mathematics (2017)” ↗Pinter's A Book of Abstract Algebra is one of the best math books I've ever read. It's short, to the point, and doesn't assume you're an idiot. I learned a lot from it and I can't recommend it enough.
on “A Path to Enlightenment in Programming Language Theory” ↗For abstract algebra, take a look at Pinter's "A Book of Abstract Algebra" [1]. It's a Dover republication, so is not expensive. It has a lot of exercises...in many chapters more than half the pages are exercises. It does not provide answers to every exercise--maybe 10% tops--but…
on “Books I Recommend” ↗I quite like Pinter’s “A Book of Abstract Algebra”. He writes very cleanly, is aimed at beginners, but doesn’t cut corners. If you’re already pretty serious about math (i.e., you already write proofs; maybe you took an analysis class), then I recommend…
on “Rust implementations of abstract algebraic structures” ↗…I was only able to do from finding like minded people in the mathematics sub reddit and did basically a mock semester class on discord. specific to algebra, I really like the classic Pinter book, "A book of Abstract Algebra", which does a great job of mixing in exposition and history that was really beneficial for self study.
on “Galois Groups and the Symmetries of Polynomials” ↗A pretty good book for abstract algebra is Pinter's "A Book of Abstract Algebra". It's rigorous but not overly terse and provides enough examples and applications as it goes to motivate the student. Chapters are fairly short and end with a large number of exercises, organized by…
on “Ask HN: The book that did it for you in math and/or CS?” ↗