Route from physics to pure maths?

[Stickybees]

Assuming I finish my study with a BSc or MSc, what are your ideas on the best way to move into more pure maths? I was thinking that getting employed by a company and working out a way for them to pay for it would be good idea, but even so which courses are probably the best? Would I have to return to do undergraduate courses?

Thanks!

 

[micromass]

Why would a company pay you to do pure math??

 

[Stickybees]

Why would a company pay you to do pure math??

The same reason they sponsor you to do a course in the first place? Albiet it would have to be related, but I can think a few which overlap the two a lot. But it's really the route that I was wondering if anyone knows much about :D

 

[micromass]

The same reason they sponsor you to do a course in the first place? Albiet it would have to be related, but I can think a few which overlap the two a lot.

I don't really see any company paying somebody to learn abstract algebra...

But it's really the route that I was wondering if anyone knows much about :D

Ok. So, what math do you already know. What courses have you taken. If we know that, we can comment on your next steps.

 

[Stickybees]

Well I'm assuming that most physics courses do about the same amount of maths alongside them, but so far, essentially everything inside this table of contents: http://www.cambridge.org/gb/knowledge/isbn/item1162976/?site_locale=en_GB

1. Preliminary algebra
2. Preliminary calculus
3. Complex numbers and hyperbolic functions
4. Series and limits
5. Partial differentiation
6. Multiple integrals
7. Vector algebra
8. Matrices and vector spaces
9. Normal modes
10. Vector calculus
11. Line, surface and volume integrals
12. Fourier series
13. Integral transforms
14. First-order ordinary differential equations
15. Higher-order ordinary differential equations
16. Series solutions of ordinary differential equations
17. Eigenfunction methods for differential equations
18. Special functions
19. Quantum operators
20. Partial differential equations: general and particular
21. Partial differential equations: separation of variables
22. Calculus of variations
23. Integral equations
24. Complex variables
25. Application of complex variables
26. Tensors
27. Numerical methods
28. Group theory
29. Representation theory
30. Probability
31. Statistics

Minus a lot of its derivation.

Thanks!

 

[micromass]

OK, cool. Is there anything specific in pure math that you would like to learn??

Anyway, I think it might be best to learn some (very basic) things about mathematical logic and proofs first. You got to know how to do proofs before you can study other pure math topics.

You absolutely won't need to repeat an entire undergrad, you'll just need to take the upper division courses. Things like topology, analysis and abstract algebra come to mind. But it depends a lot on what your eventual goal is.

 

[Stickybees]

Honestly the mathematical logic and proofs is the part that I wanted to do anyway, my goal is just to properly have a mathematical basis for all of the methods I'm using and to be able to understand more abstract maths for personal interest. I could maybe start off with a course with logic and proofs in then? Thanks