I've been working through the Abstract Algebra course at Harvard: http://matterhorn.dce.harvard.edu/engage/ui/index.html#/1999... as well as Bartoz's Category Theory courses. I've put that a temporary hold for the last couple of weeks to brush up on algorithms; I'm working through some select chapters of Concrete Mathematics, Programming in the 1990s, How to Solve It, and Algorithms. I find I'm not satisfactory at solving leetcode-style problems in what industry considers a sufficient amount of time so I'm working on improving my skills there. And I'm making progress on my own side projects…
Concrete Mathematics is solidly an undergraduate text. Much of the material in it would already be taught well before graduate school. The preface actually states the book takes comes course material taught to graduates and junior/senior undergraduates and presents it for a “wider audience (including sophomores).” Otherwise I basically agree with your comment. I just take issue with calling Concrete Mathematics a graduate textbook, because I hear people say that as though it’s not an appropriate recommendation for learning. That gives me the impression they’ve not actually opened up a…
There are some decent intro books for adults out there if you don’t care about the branch. Honestly, if you’re looking for intro math books you really shouldn’t care too much about 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
What I understood after studying CS for over 10 years at a few universities regularly ranked highly at ACM ICPC is that math is unnecessarily obfuscated to most people. There is even an excellent book "Concrete Mathematics" from Stanford that tries to bring fun back to math instead of drying people with some formal stuff without explaining how people over the centuries got to that structure. I honestly believe math language is seriously outdated. It's like using COBOL to express everything. Yes, you can do that, but would you really want to given a choice? The most trivial things are so…
I'm not making any claims that I'm a self-taught prodigy. I know what I know and what my limitations are. I can sit through ONAG for fun, have worked my way through Concrete Mathematics and delve into TAOCP when I come across interesting topics, and work out the proof to (\Ax |: P => Q) === {x | P} \subset {x | Q} I'm not kidding myself that I can stand with the best of them and work on bleeding edge problems. The sphere packing problem sounds really cool but it would probably take me quite a while to work my way up to really understanding it. But I believe it's possible if I don't fall…
Concrete Mathematics by Graham/Knuth/Patashnik is still a great resource on the kind of mathematics and mathematical thinking we need in CS, but I'm not sure if it is fully accessible with a high-school level of Maths. To be perfectly honest, I doubt I would've ever gotten through college-level maths without being forced to do it, as it can be very frustrating and difficult in the beginning. Unless you are quite confident in your self-discipline and enthusiasm to learn maths, rather than books I'd recommend something interactive (online course, forums, challenges). If you are interested in…
My recommendations: Hardy, A Course of Pure Mathematics. Knuth, Graham and Patashnik, Concrete Mathematics. Hoffman and Kunze, Linear Algebra (there are several free online books on Linear Algebra and Vector Spaces, Strang, Axler, Lang Halmos and Shilov are also recommended). Feller, An Introduction to Probability Theory and Its Applications. If you're not studying for exams and you have plenty of time on your hands, try the following algorithm: 1. Dive into some random chapter in the book and attempt the first exercise in that chapter. 2. Understand the problem by referring back and…
I've seen a few people recommend The Princeton Companion to Mathematics(PCM) http://press.princeton.edu/titles/8350 I own this book and while I do agree it's a great book for getting a 10000 foot view about topics in mathematics it's not really a book one read to learn the math that the poster is asking for. I agree with another post here that said studying is doing problems and being able to do them again a week later without having to consult the text again. PCM isnt a good book for learning calculus, discrete math, probability or statistics( what the posters wants to learn) simply…
"The topics to study really depend on the programming task" I agree... My day job does not involve any heavy mathematical problem solving, but a good intro to discrete or concrete mathematics (IMHO) proves to be a good foundation for programming in general. I studied in an Indian curriculum and have had a lot of math schooling, but it was always done "wrong", with more emphasis on getting the answer right with no need to understand _why_ that answer is right, hence my reason to ask for a good book that others found an enjoyable read and one that teaches the concepts right. I always found…
I was curious about this as well. The paper you link is providing an extension of the binomial coefficients. Binomial[-1,-1] = 1 isn't the result of an "assumption" per se, but rather the choice of a particular approach to extending the coefficients (which are normally only defined for non-negative integers n, k). The paper does this by writing the coefficient formula in terms of gamma functions, and substituting a finite expression when the gamma function is infinite. Clearly, Knuth does not prefer this generalization. The Knuth-coauthored text "Concrete Mathematics" takes a different…