Algebra
by Paolo Aluffi · first published 2009
92% recommend8% neutral
Why HN recommends it
Clear, modern prose offers a broad sweep through algebra and category theory. It includes many exercises and is accessible to self-learners, including beginners seeking a rigorous text.
Summarised by Claude from recommending comments
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Here are some great books which are meant to be read (and have not been mentioned elsewhere in this thread, i.e. Axler and Pugh). Algebra: Chapter 0 by Paolo Aluffi Measurement by Paul Lockhart The Nature of Computation by Moore & Mertens Ideals, Varieties, and Algorithms by Cox, Little, & O'Shea
on “Ask HN: How or where to begin learning mathematics from first principles?” ↗For those looking for book recommendations, I personally found Aluffi's "Algebra: Chapter 0" quite wonderful. It's available online.
on “Letter to a Young Haskell Enthusiast” ↗…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).
on “Applied Compositional Thinking for Engineers” ↗I'd add to this list Algebra, Chapter 0 by Aluffi. It's very clearly-written, even for a total beginner like me, but not dumbed down at all, and has a boatload of exercises which IMO is very helpful for learning the material. While…
on “Category Theory Reading Lists” ↗…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.
on “Computational Category Theory in Python III: Monoids, Groups, and Preorders” ↗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…
on “Ask HN: Math books that made you significantly better at math?” ↗Did you mean Aluffi’s Algebra: Chapter 0? What a wonderful book.
on “Ask HN: How to self-study mathematics from the undergrad through graduate level?” ↗For anyone interested in another great way of looking into this field, take a look at Aluffi's Algebra Chapter 0[1]. [1] http://www.mimuw.edu.pl/~jarekw/pdf/Algebra0TextboookAluffi....
on “Intro to Group Theory” ↗…listed in Intermediate is fairly/horrendously difficult for someone who hasn't seen elementary treatment of the subject before. Also, there are newer books of comparable quality to old classics like Algebra by Birkhoff/Maclane. If nothing, they have updated prose. Chapter 0 by Aluffi is phenomenal, for example.
on “Chicago undergraduate mathematics bibliography” ↗…good paper about monads in functional programming. It reads quite similarly to a monad tutorial, but with a little more formality. As for actual category theory, I've enjoyed the first few chapters of "Algebra: Chapter 0", by Aluffi. If you're after more type theory, the usual recommendations are "Types and Programming Languages", by Pierce, and "Software Foundations", also by Pierce. [1] http://homepages.inf.ed.ac.uk/wadler/papers/marktoberdorf/ba...
on “Algebraic Patterns – Monoid Morphism” ↗…Kernighan/Pike/Ritchie such as The C Programming Language, The Unix Programming Environment and gopl.io book are all concise and well written books with just exactly the right amount of material it seems. Paolo Aluffi's Algebra Chapter 0 is a good math text as a math example for something that is more than just dumping propositions/theorems and proofs. I liked this draft book as an algorithms book example http://www.parallel-algorithms-book.com/…
on “Textbook manifesto (2016)” ↗* (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…
on “Beware of Cranks: Misguided attempts to solve impossible mathematical problems” ↗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…
on “A digestion of the proof of Sendov's conjecture” ↗…HN article about Concrete Mathematics by Knuth et all. I used this for undergraduate texts, mainly in math that I had collected over the years and never got around to reading, like Calculus (Apostol), Algebra: Chapter 0 (Aluffi), Computer Systems: A Programmer's Perspective (Bryant/O'Halloran), a 1000+ page book I flew through as I found I knew some of the material already and used the exercises to test what…
on “How to Read a Book [pdf]” ↗