How do you teach yourself or learn advanced mathematics? Do you

At this level everyone just reads and digests the textbook.

Textbooks(papers on a more advanced level) is the only way. If you are only starting your way then doing exercises is a necessity

bump cuz I have the same doubt. how to read a lets say 500 page textbook and retain information? you people use note taking strategies or what? how not to copy the whole, or mostly, textbook to the paper?

>>9128430
>textbook
>then a different textbook
>then lecture notes
>then problems
>then past exams
T brainlet

>>9128446

Generally, people progress through topics. For instance, one might begin with single variable calculus, progress to multivariate calculus, then begin a serious study of topology.

In that case, the progression is a natural extension of prior concepts, and one can "build a story" in their mind so to speak.

As well, sometimes a topic will require other background knowledge, or would benefit from further reading. For instance, when learning of parametrization of an integral into a rectangular region, it helps to know how a determinant describes a volume expansion factor.

So, it is not necessary to retain all 500 pages of a textbook you might read, but it is necessary to "build a story" in your mind which is memorable. Then, you can retain much more information than you otherwise could through random facts.

>>9128459
>So, it is not necessary to retain all 500 pages of a textbook you might read
It is necessary actually but that depends on your goals and your cognitive abilities.

>>9128430
Interested in this as well. My university doesn't offer a course on Harmonic Analysis, so I'm trying to self teach. The book I'm working through now doesn't really have exercise, but I believe that's common at the higher level.