This page enumerates findings and opinions on my path to self-education in higher level mathematics. My goal is to achieve a level of proficiency in mathematics that would give me a fighting chance in a masters program at a top U.S. university.
Attempting to educate oneself to a very strong undergraduate proficiency in a topic such as math is no small task. As such, the decision to do so requires justification.
My intellectual curiosity alone is enough to motivate me. The rigorous thought and exercises are icing on the cake. The fact that most everything I learn will be very useful to me as a computer sciencist: pure gilt.
Since the task is so monumental, and it's largely a lonely road, motivation certainly has to come from within. There's nothing I can say here that's going to give you the steam to learn mathematics on your own. However, since you're reading this, you probably already have that steam. If that's the case, the following is encouraging: Math Every Day , by Steve Yegge. Steve's philosophy on the subject is very different from mine, but that particular essay is valuable and you might find that his philosophy is more in tune with yours than mine is.
Self-educating in math is different from self educating in most other fields in a number of important ways. Being aware of these will help you on your path.
Math has a tendency to build on itself at least as much as any other intellectual field. Without a very strong base in a number of foundational topics, a student has little chance of success at the higher levels. This makes your decisions when you start to study mathematics absolutely critical; it also means that the return on your early investments is huge.
The body of publications surrounding math is absolutely huge. Luckily, there is general concensus on what books are good for a serious student of mathematics for most of the foundational topics.
This page is largely dedicated to relating research into these opinions and relating my experiences with the relevant texts.
The pure versus applied debate gives a student the oppurtunity to set the “theory slider” at a level they're comfortable with. My personal opinion:
As a result of this opinion, I do not shy away from the more theoretical approaches to mathematics, but I do not pursue them solely for the sake of pursuit, or even aesthetic value. My pursuit of theory is grounded in a desire to better understand, and consequently apply, the topics of study.