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Math knowledge used in theoretical physics

  1. Sep 12, 2006 #1
    as usual in September I am deciding which courses to take. I am in the second year of my study and so far I am following the more theoretical path, later maybe with focus on quantum mechanics and quantum information proccessing.

    My question is:
    which math courses should I take this year?

    In the first year I had Calculus 1 and 2, Linear Algebra 1,2 and some kind of ODE for physicist, which was rather a cookbook-based-course than a serious mathematical course.

    For sure I will take calculus 3 and 4.

    For the other courses I'm considering these options:

    Abstract Algebra
    Differential Geometry
    Differential Topology
    ODE with theory (is it worth it?)
    Functional analysis

    The criteria are:
    1. I should be able to understand the subject (with my current knowledge)
    2. it should have some application in physics particullarly in qm or qip

    Thank you for your help.
  2. jcsd
  3. Sep 12, 2006 #2
    If you're serious about the theory then I would say : all of the above.

    But in order of preference (i.e. soonest applicability on your physics courses) I would say :

    - Functional Analysis
    - ODE with theory
    - Abstract Algebra
    - Differential Geometry
    - Differential Topology

    Maybe ODE and Algebra could switch places, I'm not certain about that.
  4. Sep 12, 2006 #3
    I would place differential geometry well above abstract algebra, but that's because of my interest in GR.

    I don't remember anything of use for physics in abstract algebra; you just don't get the stuff about group theory there that is of interest in physics.

    Is functional analysis beyond what one gets in a QM class really very useful? (I honestly don't know.) But it would be the most relevant to QM.

    What about complex analysis, Fourier analysis and PDEs, numerical methods, probability theory, and statistics?
  5. Sep 12, 2006 #4
    Any DECENT QM course heavily relies on functional analysis.
    If you want to learn QFT, you need to know about abstract algebra and representation theory. It's also useful in QM (in theory of anglular momentum for example). Besides, it's cool.

    But I agree, you need a good complex analysis course as well.
  6. Sep 12, 2006 #5
    i think it's a good idea to take on the idea of: do i want to have all the possible tools to express my theory or not? you've got to facilitate whatever you need!
  7. Sep 13, 2006 #6


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    Why in these option threads does everyone always play down ODEs, when they have no experience of any of the courses?
  8. Sep 13, 2006 #7
    You should also take a course in combinatorics and lie algebras, the more algebra the better.
  9. Sep 13, 2006 #8


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    These seem like 3rd year level courses.

    For the first two, you would need functional analysis and odes, respectively.

    Probability is second year level, with applied statistics following it in the 3rd.
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