Name: Algebra
ISBN: 9780821847817

Algebra

Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.

What Hacker News says

bananaflagAug 2026

That is research math.

If you read an introductory book (like Algebra: Chapter 0 by Aluffi, yeah the choice is a bit naughty), it doesn't assume (too many) prerequisites.

And after you've read enough of these (e.g. when you have a BSc in math), research papers are more accessible.

thread

phonebucketJan 2023

A lot of recommendations depend on what you're trying to learn.

But I've enjoyed the following texts to a larger extent than others:

- Algebra: Chapter 0 (Aluffi)

- Real Mathematical Analysis (Pugh)

- Mathematics and its History (Stillwell)

- An Introduction to Manifolds (Tu)

- Gauge Fields, Knots and Gravity (Baez)

- A First Look at Rigorous Probability Theory (Rosenthal)

- All of Statistics (Wasserman)

There are some authors I trust and am happy to buy so long as the topic vaguely interests me: VI Arnold, Tristan Needham and John Stillwell.

I really like the list put out by @enriquto in a separate comment, but I've avoided duplicating those recommendations in the list above.

thread

KoshkinFeb 2021

Personally, I wouldn't be that skeptical. By its very nature CT as a foundational theory and is relevant to, and has at least in that sense indeed touched, all corners of mathematics. (Mathematicians had the same skepticism about Set Theory when it first appeared.) Especially the "theoretical" (pure) math. So, sure, "you can read the entire thing without it, with no real loss", but this only says something about the particular textbook and not the subject itself. I assure you, the actual loss, whether you realize it or not, will be very real. Books like Aluffi's Algebra: Chaper 0 have a very good reason behind them. Category Theory is the chapter zero of the modern understanding of mathematics (and not only).

thread

WoahNounMay 2020

I'd love to see a proof of Fermat's or Mazur/Tate without using any category theory. I suppose you could define lifts between categories by being explicit about the morphisms and functors but that's just category theory without the name.

As for the second part, it's not that one single proof or another is easier with category theory. But the entire presentation is very elegant. Thinking of Aluffi Chapter 0 where he uses universal property extensively to simplify a lot of proofs. My personal favorite presentation of Algebra, but everyone has an opinion here.

thread

xyzzyzOct 2019

* (a) lie in an extension of the rationals of degree 2^n; (b) be algebraic, in the sense that its coordinates are roots of rational polynomials.*

(a) implies (b) here, but I’m sure you know this.

From myself, I recommend Aluffi’s “Algebra. Chapter 0”, it’s more modern and I find its style much more matching my taste.

thread

KoshkinJan 2019

Did you mean Aluffi’s Algebra: Chapter 0? What a wonderful book.

thread