Route from physics to pure maths?

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Discussion Overview

The discussion revolves around the transition from a background in physics to pursuing studies in pure mathematics. Participants explore potential pathways, course recommendations, and the feasibility of company sponsorship for further education in mathematics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant inquires about the best way to transition into pure mathematics after completing a BSc or MSc in physics, considering company sponsorship for further education.
  • Several participants question the rationale behind a company sponsoring pure mathematics studies, suggesting that it would need to be related to the company's work.
  • Another participant expresses skepticism about companies funding courses in abstract algebra, indicating a preference for more applicable mathematics.
  • One participant lists a comprehensive range of mathematical topics covered in their physics courses, suggesting a solid foundation in mathematics.
  • There is a suggestion that learning mathematical logic and proofs is essential before delving into pure mathematics, with recommendations for upper division courses like topology, analysis, and abstract algebra.
  • A participant expresses a personal goal of gaining a mathematical basis for methods used in physics and understanding more abstract mathematics out of personal interest.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the feasibility of company sponsorship for pure mathematics studies, with differing opinions on what types of mathematics might be relevant to companies. There is also no agreement on the specific courses that should be pursued, although there is a shared acknowledgment of the importance of foundational topics like mathematical logic and proofs.

Contextual Notes

Participants express varying levels of familiarity with different areas of mathematics and their relevance to physics, indicating that individual backgrounds may influence their recommendations and perspectives on course selection.

Who May Find This Useful

This discussion may be useful for individuals with a background in physics considering a shift to pure mathematics, as well as those interested in the potential for educational sponsorship by employers in STEM fields.

Stickybees
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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!
 
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Why would a company pay you to do pure math??
 
micromass said:
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
 
Stickybees said:
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.
 
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!
 
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.
 
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
 

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