A good post, and the comments mention some good looking books. Any other suggestions from fellow hackers for math learning books? I have perused MathWorld (http://mathworld.wolfram.com/) but it would be nice to have a book ...
All of the comments here seem to be of the form "I'd like to learn Math". However, it's a pretty huge subject! The topics to study really depend on the programming task. The best introductory book on University style Mathematics from the above range is:
http://www.springer.com/west/home/math/analysis?SGWID=4-1004...
I've spent most of my years coding solver libraries in C++. I am interested mainly in solving Ordinary and Partial Differential Equations, which require a good knowledge of numerical integration techniques. The prerequesites include Real Analysis, Linear Algebra (for the matrix solvers) and Numerical Analysis, for instance.
The best way that I've found to learn a new mathematical topic (or indeed a new programming language) is to give myself a really cool project which requires knowledge of it and then figure out a solution. I used to read Math books on the bus into University, but you just don't get the same level of knowledge that you would if you were making a fun bit of software that needed it.
A great example here is to program your own 3D engine, without using a 3D API! There is no way you would be able to compete with DirectX or OpenGL for quality, but the underlying mathematical knowledge of the graphics pipeline will give you a much better understanding of how the "big" APIs work. It's also great fun too!
"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 math to be interesting, though sadly haven't done much of it since graduation...
Thanks for the link to the Springer series. I have never heard of it, but I will look into them, though honestly, the Knuth book does intrigue me. Looks like a time to hit the local bookstore...
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 so far even if it is a bit slow going for me.
I was browsing Amazon and I came across the same book. I think I certainly will look into this one, though some of the comments (on Amazon) made it sound like the authors jumped from one topic to another, and skirted around a lot of the in-depth discussions that you would normally expect from a book like this... Has this been your experience?
It depends on how much time you devote to it...but the nice thing about that book is that each chapter's exercises are broken up into "Warmup exercises", "Homework exercises", "Exam questions", and "Research problems". It's still well worth working through it though - the authors are shockingly competent.
Linear algebra -- matrices etc. -- is the bit of my undergrad. mathematics that I use most often in programming.
I really liked the informal text by Gilbert Strang, "Introduction to Linear Algebra". The 3rd edition is quite expensive, but Strang's video lectures are available here:
