Hi
I am currently in my fifth semester of studying mathematics, but I'd like to re-study some former material as the only things left from the past semesters are how to calculate derivatives, integrals and differential equations. I'm just mad at myself that I've forgotten all the important theorems, and their proofs too
So what I've planned is (because I already have kind of "specialized" myself into informatics with my studies, so I have more "computer-based" subjects right now and my head wouldn't be really filled with other mathematical subjects from university) to just repeat the past material on my own in my spare time, so I at least can refresh something
But I'd like to go further with all of that (so I'd like to go into "unknown terrain" like Functional Analysis, algebraic Topology etc), and actually make a plan for the upcoming years so I can know what I can be studying on my own.
It's not an ambitious plan, it's more of a hobby because as I'm gonna be heading into informatics professionally I still don't want to abandon mathematics.
And these are my main questions:
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What would "the right order" be? What I mean is: If you'd be the head of a university, how would your personal mathematics curiculum/syllabus look like (from 1st to 5th year)? After completing Real Analysis, what should I be heading to? Complex Analysis, Meassure Theory? What's next? What about the other subjects?
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If I know "my plan" already (created with your help and advice on in which order I should self-study all those subjects), where can I find some good free resources to each subject? A good playlist on YouTube, a good book as a PDF online, etc?
What I am on about is not (only) to learn how to calculate things, or how to use them in an applied way. I want to get to know the theory behind all of that, to learn all the important theorems etc.
I hope you can help me!
Thanks
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