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What math classes should I take?

  1. Nov 13, 2009 #1
    So I'm a second year undergraduate physics major, and I'm taking quantum mechanics and classical mechanics next semester. I have all the basic math requirements completed (calculus and diff eq) Currently, I'm interested in doing PhD work in particle physics/atomic physics once I graduate. And I also need more classes to take and I'm ahead of schedule for graduation, so I was wondering what classes I should take to strengthen my background in other fields relevant to what I want to study. I've talked to some of the professors on my campus briefly and they mentioned classes like complex analysis and partial differential equations. I was just wondering what would be some good classes to take in chemistry or math or CS cuz I need more hours next semester. Thanks guys!
     
  2. jcsd
  3. Nov 13, 2009 #2
    Doesn't particle physics use tons of quantum and quantum field theory? If so, as far as getting ahead in math goes, you need real analysis(rigorous foundations of calculus), topology and probably some statistics. I know you are probably going to be doing a good amount of grad level math if you are going for a phd in physics. Those courses will give you a leg up.

    Also, learning to program couldn't hurt. It might even make it easier to get into doing some lab work with a professor.
     
  4. Nov 13, 2009 #3
    Numerical Analysis in CS

    in maths...

    Have you done Linear Algebra? If not, get that done.
    Second i would say Complex Analysis.
    Then you can go into Vector Calculus and PDE if you like.
     
  5. Nov 14, 2009 #4
    Actually, our calculus II class was actually 60% linear algebra, so I think I have that covered. We have a class called Abstract Vector Spaces, which I feel like would be a good one too. Has anyone taking Physical Chemistry? That was another class I've been interested in taking just because I enjoy chemistry.
     
  6. Nov 14, 2009 #5
    have you done "Mathematical Methods for Physicists" course? If so, taking individual Math course for what was taught in that class is a good idea.

    Also, they prolly have a similar "Mathematical Methods for Physicists" for grad students...check what is covered in that...and if possible take individual Math course on those subjects.
     
  7. Nov 14, 2009 #6
    If you want to do particle physics/atomic physics, then there are a couple of courses you could take. Concerning math, you should consider especially group theory and in particular representation theory, which is inevitable in elementary particle physics. The stuff you'll need is representation theory of the Lorentz and Poincare group as well as the SU(N) groups and this is probably the only case when it is good to take such a course from a physicist, because the mathematicians almost never treat these topics in courses like Abstract algebra or Lie group theory (even though these subjects are interresting as such). In addition, as already suggested, you could take a graduate course on Mathematical Methods for Physicists (covering some PDE's, contour integration, Green's functions,...).

    Now, this was what an ordinary particle physicist needs, but if you want to go further than that and see really the beautiful mathematical structure beyond the physical theories, you might also consider courses like: Differential Geometry (used everywhere in physics, especially GR and also Gauge Theories), Functional Analysis (used for a rigorous formulation of QM and also for advanced methods of solving PDE's), Complex Analysis (especially contour integration, but also for general knowledge (or perhaps complex geometry later on)), Topology (also general knowledge to see the frequently recurring structures in other mathematical fields (esp. diff. geo or later alg. topology)). Advanced calculus should be of course the first on your list if you haven't taken it yet.

    Particle Physicists are also doing a lot of computer simulations, so some knowledge of C++/FORTRAN would be helpful.
     
  8. Nov 14, 2009 #7
    I'm a physics major around the same course level as you. My biggest concern at the start was my mathematical ability, so I've asked just about everyone that would listen what math courses they think would be important. lol
    Here's what I plan to have completed by the time I start grad school (assuming I'm accepted somewhere. lol)

    Calc II
    Calc III
    Linear Algebra
    Differential Equations
    Mathematical proofs
    Vector calc/complex variables
    Advanced differential equations
    Geometry (intro to the non-euclidean stuff)
    Differential Geometry
    Advanced Linear Algebra

    I don't think I'll be able to, but I'd also like to take these courses
    Numerical Analysis
    Intro to Topology
    I'd really like to do an independent study involving the group theory, lie algebra, clifford algebras, that seem to be very exciting.

    Don't know how much that helps you (I'm hoping to do theory btw), but I've asked about everyone I can find and this is what I got out of it.
     
  9. Nov 14, 2009 #8
    We have a class called Mathematical Physics, which I assume is what you guys are talking about. The description is just math you need when encountering problems in QM, EM, thermal physics and mechanics. I'm signed up for a class next semester called program design for engineers. It's a continuation of a class I took last semester which involved programming using matlab, but this one uses mostly C with an introduction to C++

    Anyways thanks for all the advice guys! I have a much better picture of what classes I should be signing up for.
     
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