I've been working as a developer for years but all the interesting works seems to require a greater knowledge of computer science than I have. I'm self taught and I am always trying to keep learning.<p>Whenever I start reading a book about algorithms I get lost by the maths.<p>Maths seems to be built on top of maths so I wind back as far as I can and find that my maths education stops at arithmetic (for shame). I've tried using wikipedia whenever I get stuck but it seems to be a maze of interlinked concepts and I quickly get lost again with no solid underpinnings to depend on.<p>Is there a good book or online course you can recommend that can get me to the level needed to take a 1st year CS course? I'm not sure (a) what to learn and (b) in what order, so a list of the subjects to cover and an order that is logical would be enough for me to start learning.
I came back to studying after a 12 year break where I hardly used maths. I bought the Students Survival Guide and found it very useful and easy to dip in to after work:<p><a href="http://www.amazon.com/Maths-Students-Survival-Self-Help-Engineering/dp/0521017076" rel="nofollow">http://www.amazon.com/Maths-Students-Survival-Self-Help-Engi...</a><p>It takes you to the level needed by most Science/Engineering undergraduate courses.
Have a look at <a href="http://www.khanacademy.org" rel="nofollow">http://www.khanacademy.org</a><p>It has a good coverage of topics (including Arithmetic and Pre-algebra)
After arithmetic, the typical order of classes (The ones I took, and the one I believe most often taught in American schools) goes like this:<p>Algebra
Geometry
More Advanced Algebra
Trigonometry
Calculus<p>I don't have any book recommendations and I don't know of any books that would cover all those topics. There are many books on algebra however, and I don't think it will particularly matter which one you use. It should get you up to speed very quickly.<p>The other topics are probably less important for intro CS. I don't think I ever used calculus or trig for any CS classes. Very basic geometry might be used as examples.
Once you get through basic algebra try Exeter's problem sets. I've just started going through them now and it seems pretty fun and well integrated. They even have discrete math!<p><a href="http://www.exeter.edu/academics/84_9408.aspx" rel="nofollow">http://www.exeter.edu/academics/84_9408.aspx</a>
Most of what you want is on the web. But I would suggest an intro to Boolean arithmetic and see if that sparks anything. Just basic operations. Then look at how those simple operations can build bigger ones. It uses math, sure, but is a whole different world from general math. Of course you'll need some algebra in order to program in C++ but not too much. That's sufficient for 1st year CS classes.<p>You'll want Geometry to understand graphics, and you'll want some basic trig and a dash of differential calculus in order to animate.<p>Look around on the web and you'll find all of it.