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Maths courses for theoretical physics

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  • Thread starter muppet
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  • #1
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Main Question or Discussion Point

I'm choosing 3 maths modules for next year (my third in Maths and Physics, in a UK university) with a view to studying theoretical physics thereafter (starting off with general relativity, quantum field theory and most likely strings, and working outwards from there depending on where I am- possibly to particle theory, black holes, cosmology etc.) The options I'm seriously looking at are courses in differential geometry; topology; solitons; and elliptic functions. I think the first two are all but definite choices (they look interesting, and I understand differential geometry is at the heart of GR, while topology is useful in string theory?), so it's really one from solitons or elliptic functions. My course booklet suggests that elliptic functions have some use in theoretical physics, although precisely what it is eludes me. The relevance of solitions seems more apparent, although the actual maths of elliptic functions seems more interesting (so far as I can tell without actually studying both courses!)
Any thoughts? I'd be particularly appreciative if someone could explain the relevance of elliptic functions to physics. Many thanks.
 

Answers and Replies

  • #2
tmc
289
1
Personally, I'd choose neither and instead opt for a course in some sort of advanced abstract algebra, like advanced group theory or lie groups, unless you're already well-versed in these. Knowing how to play with groups is a very important part of theoretical physics, especially particle physics.
 
  • #3
333
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I second that
 
  • #4
(1) Lie Algebras, Group Representation Theory, Operator Algebras
(2) Differential Geometry and Topology
 
  • #5
604
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Thanks for the responses- Lie Algebras etc aren't options availble to me I'm afraid! These are courses intended for single honours maths undergrads without regard to theoretical physics; the necessary group theory is covered within the specialist particle theory MSc /PhD lecture course. Such pure maths courses as focus on algebra I don't have the necessary prerequisites for from 2nd year.
If anyone is curious as to the complete options list:
http://www.dur.ac.uk/natural.sciences/prospective/msci-maths-phys/ [Broken]
 
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  • #6
tmc
289
1
Your curriculum listed on that website looks awfully incomplete. You'll want to take the courses in stat. thermo and EM for one (this is the first time I've seen a physics program without compulsory EM, not to mention listing EM as a math course); Analysis is also a must. Once you're done with those basics, then you can move on to the nice stuff such as diff geometry, topology, PDE, GR and other such courses.
 
  • #7
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Stat thermo and EM have been covered in 2nd year physics modules; there's also further courses within the 3rd year physics modules. When you say "analysis", I'm guessing you mean to the level of the "analysis III" module about calculus on manifolds?
 
  • #8
What about Algebraic Topology ?
 
  • #9
tmc
289
1
Yes I meant Analysis III (Although I don't get why it's called analysis 3 if it's your first course in analysis, but whatever). Basically, it introduces one-forms, and you absolutely need that everywhere. Not to mention that understanding these manifolds will make things like differential geometry much easier to digest.
 
  • #10
333
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after looking at your list i'd go w/ Diff Geo, topology, and either E&M, PDE or Dynamical Sys
then in year 4 take Alge. topology;
however
I would consult your dep. and see if you can take a pure algebra course ie. Abstract Algebra or some form of Group theory.
Yes I see that those courses aren't part of your modules for joint honours math+ physics however does your school offer a pure mathe degree, I imagine your math dept. must offer an abstract algebra course
 
  • #11
MathematicalPhysicist
Gold Member
4,187
168
Well just a tip.
I too learn maths and physics (but in israel), and i for example asked for permission to learn logic which wasn't part of my modules' options, I think that you can do so as well, i.e request to learn a course not included in your programme.
Although I think that taking an abstract algebra,differential geometry and topology courses are a must for every maths student, due to time constraints and the work load, not everyone can handle this, that's why it's not mandatory.
 
  • #12
Are you thinking of doing an MSc after a BSc or straight to research? Honestly, it'd probably be better to choose modules where you can get the highest marks in.
 

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