What Topics Should an Undergraduate Study in Math and Physics for Self-Study?

[bugatti79]

Folks,

I am currently studying undergraduate final year degree in mathematics. I have covered QM's, PDE's and currently studying Functional analysis and vector calculus/complex variables.

I hope to finish the degree middle of next year, however I would like to continue studying math/physics in the form of self study. There are so much interesting topics out there that I don't know what to choose.

I like the weirdness of QM's.
Also think General Relativity/S.R would be interesting.
I also like the visual/graphical representation of vector calculus.
I like to work with math that has physical meaning.
Maybe throw in some speadsheets, mathematica for graphs etc.


Could anyone suggest interesting topics for an undergraduate to take up? I know its a very vague question but at least I might get some ideas? Would like to become knowledgeable in a particular field however small...

 

[ThomasT]

Folks,

I am currently studying undergraduate final year degree in mathematics. I have covered QM's, PDE's and currently studying Functional analysis and vector calculus/complex variables.

I hope to finish the degree middle of next year, however I would like to continue studying math/physics in the form of self study. There are so much interesting topics out there that I don't know what to choose.

I like the weirdness of QM's.
Also think General Relativity/S.R would be interesting.
I also like the visual/graphical representation of vector calculus.
I like to work with math that has physical meaning.
Maybe throw in some speadsheets, mathematica for graphs etc.


Could anyone suggest interesting topics for an undergraduate to take up? I know its a very vague question but at least I might get some ideas? Would like to become knowledgeable in a particular field however small...

The really interesting, and technically solvable, problems are, imho, in condensed matter physics. So, maybe concentrate on QM, and the experimental applied/engineering aspects thereof. But then all the other stuff you mentioned is fascinating also. It's nice to have such choices, eh?