What is the best way to self teach yourself math beyond a calculus textbook?
Depends what kind of person you are. Describe your education thus far.
As Gib Z mentioned, it mainly depends on you and your education. Self studying, in general (at least in my experience), requires a lot of will and energy from your side in order to be really efficient.
You can't deny that one.
Also, doing problems as you go along. For example, for Munkres, I just finished reading Chapter 3, last night actually. But I will not go on to Chapter 4 and Chapter 9 (I will do them simultaneously.) until I have completed a minimum of 20-25 problems from Chapter 3 with and an additonal 8 coming from the section on Metric Topology in Chapter 2 because I know personally that is my weakest link right now. So, maybe by next week, I can start reading the next chapter(s).
I do not find it necessary to do all the problems before going to the next chapter though. That can take forever and this can result in lack of motivation to continue because you have so much work to do. So, I just do handful, like I said above, and then move on. I also continue to solve 1 or 2 problems for previous sections as I go along. So, by the time I reach Chapter 5, I hope to have all questions of Chapter 2 done. Which is great because I will always be reacquainted with the definitions and theorems further down the road.
Also, I insist that I don't move on until I fully understand the definitions and the theorems, and I understood the proofs. I don't put too much emphasis on remember them, but merely understanding them. If I tried to remember them, then that would take awhile. I'm just more concerned with the idea that if I read it again later, I will understand it so if I ever needed to remember some, I got the hard part out of the way, which is understanding it.
Note: I'm almost at the Urysohn Metrization Theorem, and the definiton of the Fundamental Group. Those were my first goals, and I'm almost there!
Don't read a calculus book, for starters.
Read analysis. ;0
You have to be very determined. Some books are bad. Some books give absolutely no motivation and will just pile theorems and definitions on you. These kinds of books are hard to digest. On the other hand you have books that are chatty.
I don't want to say you have to be smart to learn math on your own...but you have to be extremely motivated.
He said beyond Calculus, so surely he won't be reading Calculus once again.
Isn't analysis a bit more rigorous? I understand that it varies from course to course, and from book to book etc., but I still got that impression. Perhaps it's a wrong one.
Yes, I would say Analysis is more rigorous.
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