[drablyechoes]

It is really hard to truly self-study in mathematics. Going through the opencourseware and reading textbooks (working as many exercises as you can, of course) will get you only so far. It is important to have someone (ideally with a PhD-level education in mathematics) who you can meet with to guide your study, correct mistakes and answer questions.

[gnulinux]

I strongly disagree actually. I think mathematics is the best field to self-study. There is nothing in mathematics that cannot be explained on the paper. There are many textbooks that are very good that in most universities professors won't be that good anyway. I went to UC Berkeley to study mathematics (ended up studying CS though) which is supposed to be a top department, but most of my textbooks were better teachers than my professors. I still prefer reading textbook to people explaining me math. I don't even think I understand math when people explain me. I need to first teach it to myself. Then occasionally people offering different perspectives is very beneficial, which, again, can be done on paper.

I don't think you need a PhD level educator. You need mathematical maturity. Mathematics follows a very specific logical structure that needs you to shift the way you think. Human brain simply doesn't work the way mathematics needs it to work. But this is a constant time overhead. Once you understand how to approach mathematical problems, I can't see why you cannot learn everything from a textbook.

[jack_h]

As someone who did study both math and CS at university I disagree. I think there are numerous courses that can more easily be self-taught[1], mostly what one would encounter in their first ~2 years in a math degree. After that things get conceptually a lot more difficult.

For me personally I didn't really need an instructor for most of my calculus courses, or ordinary differential equations, or most of the linear algebra stuff. It was a bit more difficult around real/complex analysis, non-linear dynamics, and courses of that nature. The classes that taught me the value of having an instructor were abstract algebra and topology. Those were such a massive shift away from what I had perceived math to be that an instructor being able to impart intuition, correct my own incomplete or incorrect assumptions, and generally just help guide me to a different mode of thinking was invaluable.

The problem with books/texts in this instance is they are not reactive, they have no idea what you're thinking and can't steer you in the right direction. Worse is that as the person trying to learn the subject matter you don't know where to look to get on the right track and correct your own assumptions because you don't know enough yet.

Now I'm not saying you need an instructor per se, but having some place to ask questions where someone far more knowledgeable than you can help might be a good substitute. I'm sure there are some websites like this, although I don't know of any since I graduated a long time ago.

[1]This does somewhat depend on a person's skillset going into this.

[NegativeK]

I didn't realize the value of this until after I was done with my undergraduate studies.

Textbooks and lectures will teach you what math is. The concepts, the different proof methods can all come from a book.

The value from an instructor is that they'll give you feedback on the _how_ of math. A halfway decent professor will edit your proof just like an English professor will -- from the level of word choice all the way to the method you constructed and presented your argument. And, just as importantly, they'll tell you when you fucked up and didn't notice.

[maxxxxx]

I agree, I would not have survived math in school without being able to ask other people.

I learned programming on my own from books but I don't think I could do that with advanced math.