Concrete mathematics
by Ronald L. Graham, Donald Knuth, Oren Patashnik · first published 1988
65% recommend34% neutral1% critical
Why HN recommends it
Playful, rigorous math for programmers covering recurrences, sums, and asymptotics; margin notes from students add humor. Suits self-learners filling math gaps who want the math side of TAOCP, with exercises.
Common criticism: Harder than it looks; not suited to complete beginners without some proof background
Summarised by Claude from recommending comments
"This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline."
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Many of the list are pop-maths rather than fundamental texts. I do see many in software field recommend Chrystal:Algebra an Elementary Textbook. I also find Don Knuth, 'Concrete Mathematics' a interesting book for software people.
on “Classic Mathematics Books for Lifelong Learners” ↗It's probably too idiosyncratic to meet your needs, but I really like Knuth's "Concrete Mathematics"
on “SICP - summary of 10 months working through the entire book” ↗…course on Linear Algebra, available as a series of video lectures on MIT OCW (http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/Cours...). If you are interested in Discrete mathematics, Knuth's "Concrete Mathematics" is a great book--but it might not count as "basic" enough for your purposes, depending on your background. If by "basics" you mean "the stuff you should have learned in high school or as an undergrad",…
on “Ask HN: Best Mathematics book for complete noobie?” ↗…engineer majors) in college that I truly began to enjoy math once again. I was able to start with concrete ideas and applications, and then work my way back to the theory behind them. I'm now reading "Concrete Mathematics" and really enjoying it. Knuth's ideas on math education are pretty diametrically opposed to those of Lockhart, as far as I can tell, and they give rise to something very close to my ideal learning environment…
on “A Mathematician’s Lament (2002) [pdf] ” ↗…logic, you are using math. If you took a logics and proofs course, it would help you formalize logic better. Every time you write a "for" loop you are essentially using summations. There is a book called Concrete Mathematics and one of the primary authors is Donald Knuth, basically it's "Programmers math" and in my opinion, would make your average developer who completes the text into an exceptional developer.
on “The Math Myth” ↗…the branch. I think what’s more important is to develop mathematical thinking. Here’s some off the top of my head. I really think these will help you build a good foundation for mathematical thinking. Concrete Mathematics by Graham, Knuth, Patashnik Spivak’s Calculus How to Prove It by Velleman Polya’s How to Solve It E.T. Jaynes’ Probability Theory Conceptual Mathematics by Lawvere and Schanuel
on “Book: Mathematics for Machine Learning” ↗…opinion: my favorite math textbook for computer science is Chapter 1, Section 1.2 of The Art of Computer Programming ("Mathematical Preliminaries"). That's pretty dense though, so I usually recommend Concrete Mathematics, which was also (co)authored by Knuth. The benefit of Concrete Mathematics is that it spreads the information out with more examples and better exposition. It also includes an expanded section on probability.…
on “Mathematics for Computer Science: Readings” ↗I'm currently slowly working my way through Concrete Mathematics by Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. It's basically an expanded version of the first bit of Knuth's Art Of Computer Programming. I've found it really fascinating and a lot of fun…
on “Math For Programmers” ↗…:-) I did disagree with the solution (many who see the code would get confused), but it certainly was a positive contribution to the discussion, which is always my bar for upvote/downvote. And I love Concrete Mathematics. I wish people would say Knuth is the author of TAOCP and Concrete Mathematics. And Ronald Graham is another great computer scientist. With that said I do distinguish computer science from programming.
on “The Art of Computer Programming (interview with Don Knuth)” ↗Concrete Mathematics by Graham,Knuth, Patashnik is (explicitly, even) a mini-TAOCP for much* of the mathematical underpinnings of computer science. * I say much rather than most or all since it's focused on asymptotics,…
on “A Software Engineer’s Adventures in Learning Mathematics” ↗I'm going to go a completely different direction from other recommendations and say Concrete Mathematics by Knuth and Patashnik. They will definitely be able to use skills from analysis and calculus here, but there are so many additional tools in this book that it's very much a worthwhile digression. The…
on “Ask HN: Recommend a maths book for a teenager?” ↗Concrete Mathematics by Knuth and Patashnik (already mentioned for u/pmiller2) if the kid likes numbers. That's perhaps the guiding thread of the book -- it's about the beautiful (yet usually very elementary and natural)…
on “Ask HN: Recommend a maths book for a teenager?” ↗…well edited? That's a very bad assumption in this case. The contents of TAOCP are very well edited, just massive in scope and it's one man putting it all together. However, those aren't his only books. Concrete Mathematics is a completed text that expands on, in particular, the math in Chapter 1 of TAOCP. Literate Programming is a collection of papers on topics in programming, and is the first of eight such books. If you…
on “Ask HN: Most interesting, mildly impractical, well-written books on software?” ↗…to: - Discrete Mathematics with Applications, by Susanna Epp, or - Discrete Mathematics and Its Applications, by Kenneth Rosen (both have the same content, choose the style that you prefer), and - Concrete Mathematics, by our lord and savior Donald Knuth. I don't plan on reading TAOCP anymore as I would be dead by the time I finish reading everything else, but those introductory books are very good for beginners.
on “Ask HN: The book that did it for you in math and/or CS?” ↗Concrete Mathematics [1], by Graham, Knuth and Patashnik. Wonderfully written (worth buying for the margin jokes alone) and approachable, but dense with information. Great overview of discrete math and algorithm analysis.…
on “Ask HN: Which books do you consider real gems in your field of work/study?” ↗