I never got very far in my math studies; I took zero math in college and had terrible teachers in high school. Fast forward to today and I'm a professional developer who's starting to feel that my lack of a solid grounding in math is holding me back. I can hold my own with basic concepts, etc. but I'd like to start a formal self-education regiment in math. When I take something on, I take it seriously. When I taught myself my programming, I watched lectures from Stanford/MIT/UC Berkeley, read every book, did every exercise etc. I thrive on self-education.
And to my question: can someone recommend some really great resources/books for learning math starting from pre-algebra and beyond? I'd love it if someone could map out a good, structured progression for someone like me who likes math for its own sake, but also wants to use it as a tool for computer science.
Any help would be greatly appreciated.
Best Answer
Although I couldn't provide the sequence you request, I can point two references that can be of great help in gaining a bic-picture view of higher mathematics: The Princeton Companion to Mathematics and Mathematics: Its Content, Methods and Meaning.
Here is a description of the first out of Tim Gowers's web page:
"This is a book I am editing with the help of June Barrow-Green and Imre Leader, which could be thought of as "Mathematics: A Very Long Introduction". It has the aim of being a genuinely useful reference work in mathematics. This is a difficult aim, since mathematics is hard enough to explain at the best of times, and even more so if one has limited space. Is there any point in trying to summarize algebraic geometry in ten pages, for example? Probably not, but the articles in the PCM don't try to summarize , so much as to provide an initial overview and perspective. I like to think of them as "prequels" to textbooks -- things you would read to get an idea of why you were bothering to learn some concept that your lecturer seems to take for granted is interesting. Strenuous efforts have gone into making the book as accessible as possible, which I hope will have been worth it when it comes out, all going well, some time in the first half of 2008."
Hopefully that sounds enticing. (The second book runs somewhat along the same lines).
You mentioned OCW resources, I am sure you will know how to use those after you've gained your motivation and are ready to dive right into the subjects!