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Unfortunately, I picked electrical engineering instead of pure maths courses in college and now I can't switch back, but there's still a chance for me to become a pure mathematicians by attempting the GREs. Here's my reading list uptil then:
1)multivariable calc(already done)
2)linear algebra (already done)
3)Ordinary and partial differential equations (studied insofar as it benefits an engineer)
4)abstract algebra
5) Analysis (Rudin, this is where I am right now)
6) I guess more analysis, with going into details about measure theory and functional analysis
7) complex analysis
8) topology
9) more topology
10) even more topology(algebraic topology)
11) differential geometry, but not the elementary course
12) representation theory, with picrel as introduction. Will continue until I have enough knowledge to decipher advanced QFT stuff

Please consider the fact that there is no dearth of time, because I'm basically devoting my entire life to maths and I wanna be able to read PhD level papers on very niche fields with relative ease. This list will serve as just my introduction to maths.
0/10 faggot OP
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Lang is the fucking king of pedagogy. The first advice that comes to mind is that you should try Lang first for everything and only switch if you're some kind of deviant. You can try something else if you don't like Lang, but I don't think you will. It's fast and comprehensive reading.
This seems like a good list, but can Hoffman and kunze be a substitute for both basic and advanced linear algebra?
Also, is Rudin's analysis good enough?
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A fren sent me pic related, got him from either some /sci/ or r/math server
Tobologay where :DDDDDD
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stop making lists and go read a book faggot
I'm already doing it retard, formulating an itinerary helps a lot
I sincerely hope you are trolling
do analysis on manifolds (e.g lees smooth manifolds book) after the first topology course.
if you are interested in qft, i'd recommend abstract harmonic analysis (its basically representation theory of locally compact groups). also some riemannian geometry wouldnt hurt. your study of functional analysis (and i guess pdes) should also include a solid foundation for distribution theory and classical harmonic analysis.

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