This is what they did at my undergraduate university

Do all of these in order first:

Calculus 1 and 2

Linear algebra and multivariable calculus and an introduction to proofs / logic course (you are ready for some electives at this point)

Ordinary differential equations

Any of these can be done concurrently, choose one Analysis and one algebra :

Advanced calculus (eg “understanding analysis” by Abbott)

Linear algebra in the sense of finite dimensional vector spaces

Easier abstract algebra (senior level classes are eg Artin and rudin, these ones are more elementary textbooks)

Core Senior level courses that you take if you want to get good at math:

Analysis sequence (1 year on baby Rudin)

Algebra sequence (1 year on artin)

Topology (munkres)

Electives:

Probability (can be done after multivariable calc)

Linear optimization (after linear algebra + multivariable calc)

Logic (compactness completeness godel etc whatever, can be done after intro to proofs course but will probably make less sense if you didn’t study some more stuff first)

Numerical analysis (after ODEs I guess or calculus + linear algebra if you want to skip tht stuff)

Statistics (after probability)

Combinatorics - after calc 2 and linear algebra

Geometry - after multivariable calc, linear algebra, proofs

Intro Differential geometry: after advanced calculus

Don’t really have much more knowledge for graduate courses etc. or even some common ones like complex analysis. if you know the senior level core stuff you’re probably “good enough” to make some progress on a lot of things. Each of these classes is 100-200 hours of total study so it seems odd to me that someone will just try to study it on their own by there you go I guess

user:	hnuser355
created:	November 8, 2018
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