Sorry for the length of this post, but I really want some advice.
I am a freshman in physics. I am confused if I should or not switch to mathematics for next year onwards. We get only one chance to switch in my uni (In India) and there is no double major option.
Please read the following points and offer some advice if you can:
- I wish to pursue a career in THEORETICAL physics or mathematics. I am very sure I don't want to go to experimental physics (Also, I hate lab courses and the ones in my Uni are very unrevised).
- I find the lack of mathematical rigor in physics texts and courses (of undergraduate level) annoying often times.(I know the ‘hand waviness’ is to carry on faster with the relevant physics discussion, but still this is the case for me).
- I am not sure anymore if I currently love physics because of the curiousity to know how things work or because of the impressive mathematical descriptions.
- I find myself curious about any random mathematical idea. But I am not curious about physics research which are of the “applied” kind( like condensed matter physics).I am only very keen about the fundamental ideas.
- I am kind of bad and slow at computation/symbol manipulation in maths. This is what I don’t like in maths. (eg:-I self studied a real analysis book. I liked it very much and found the exercises as nothing too difficult. On the other hand, I am bad at/kind of dislike evaluating integrals. I also have trouble remembering long formulas.)
- I am also interested in mathematical logic and philosophy of mathematics.
I HAVE THESE QUESTIONS:
a) Is enjoyment and performance in higher mathematics dependent on the ability to compute and do smart algebraic manipulations (skills similar to evaluating integrals)? Will point (5) trouble me if I choose mathematics?
b) How to know if maths won’t become too abstract for me? (note that I like physics too)
c) I like proofs as of now. But is all of higher maths just proofs? How to know if it will become too repetitive?
d) Any topic/book I can try to gain some perspective on the questions above? (I am about to start abstract algebra)
e) Is a maths UG better than a physics UG for a THEORETICAL physics career? How feasible is switching to physics for PG after UG in maths and vice versa? (Note that we have no electives in non-major subjects after the second year)
f) Is being a mathematician or theoretical physicist harder? (In terms of- research difficulty, freedom in research, difficulty of getting the job, funding)
Kindly answer atleast some of these questions.