How can you learn advanced math if you don't have books or a teacher to consult?

Question

Everyone says to read book "xyz", but I have never found books to helpful for several reasons.

1. You can't ask a book a deep question to do with understanding.
2. No book is perfect.
3. I can't afford them.
4. I have ADHD (although I have no difficulty sitting and thinking about math for hours because it really interests me).
5. This might be different with areas of math I'm not used to, but I've always ended up learning things in the past by finding a missing piece in my understanding at which point I can derive most of everything I need, and end up skipping chapters of the book altogether.

Furthermore, I am not connected to anyone I can ask questions to, although I wish I was. Whenever I meet a mathematician, I try to do everything to make the best of the situation. I have tried using Math Stack Exchange, but it just isn't enough to fully teach yourself a subject (and additionally, I don't always feel safe asking questions here). You can visit my profile to see the kinds of questions I've been asking.

I love math. However, after going through all the regular calculus stuff, as well as multivariable and vector calculus as well as a conceptual understanding of linear algebra, I'm pretty much stuck. I've been putting more time than ever into learning math of a wide variety with almost no results.

What I do have is the internet.

What is general advice for learning math from the internet?

Answer 1

What has worked for me is instead of searching for a "$xyz$" textbook, search for an online free class with an available syllabus. Preferably a class where you have lectures recorded, exercise lists available and a textbook which can be accessed online via a pdf file. This way you won't be intimidated by the volume of the textbook and things that you need to study will already be pinpointed and highlighted by a professor. I know that MIT and Harvard have a nice open course wares.

Good luck !

Answer 2

I have also struggled with mathematics a lot while self-studying. I couldn't understand most the books at starting, and the whole process was quite irreverent. To organise my learning, instead of searching for new books, I looked for the different university curriculums and the books they recommend for courses. It can help you determine which subject would be best suitable for you to study given your present knowledge.
You can also follow online lecture notes like from MIT OCW, Paul's online math notes, etc. if you feel the book to be complicated.

Another critical point is that try to make friends with some mathematics students if you know any. You can also try various social media handles to find. Start asking doubts from them and eventually you will get acquainted with them. It helps a lot as you will get new ways of thinking about concepts.
At last, if nothing works, you can always email professors about your various doubts. I am sure nobody will turn you down. You can also contact any maths professor in you nearby university and take appointments from them to clear your doubts personally.

At last, never give up hope. Keep trying to make contacts, and eventually, everything will get sorted. I am telling you this from my personal experience.
Good luck!