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Courses Which of these math courses important for physics?

  1. May 21, 2012 #1
    I'm planning on taking a bunch of math courses in next year's Fall semester. Here are courses I'm looking into:

    PDE
    Real Analysis
    Abstract Algebra
    Differential Geometry

    There's also Complex Analysis offered in the Spring semester.

    I know PDE is used extensively in physics, but I'm not so sure about the others on the list.
    Which one of these are important for physics?
     
  2. jcsd
  3. May 21, 2012 #2
    Real Analysis and Abstract Algebra as they are presented in undergrad math classes are basically useless for Physics. Knowing the basics of Complex Analysis is really good. Differential Geometry may be worth taking depending on the class.
     
  4. May 21, 2012 #3
    All of them are equally useful.
     
  5. May 21, 2012 #4
    Pde's & diff. geo.
     
  6. May 21, 2012 #5

    Fredrik

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    Differential geometry is very important if you intend to study GR. (If you don't, then it's not that useful). Abstract algebra is less important, because it's easy enough to study the parts you need on your own, when you need them. A PDE course is certainly useful, for example for applications of classical electrodynamics. Real analysis is useful, mainly because it gives you a minimal foundation that you can build on if you ever want to get into mathematical physics, e.g. if you want to study the mathematics of QM. That would also require a course on topology and at least two courses on functional analysis, which would typically have measure and integration theory as a prerequisite. (Yes, the mathematics of QM is crazy hard. So hard that very few physicists actually learn it).

    Linear algebra is more important than anything on that list.

    Edit: kloptok's post below made me realize that I forgot to say something about complex analysis. My opinion is that it's useful, but not essential. There's no physics course that will be significantly harder to pass if you haven't studied it. As kloptok said, it will teach you a new way to solve some difficult integrals. Since I'm more of a theory nerd, I don't care so much about the "how to calculate" stuff. What I like the most about complex analysis is that it gives us a reasonably simple way to prove the fundamental theorem of algebra (every complex polynomial has a root) and the (closely related) theorem that says that the spectrum of a bounded linear operator is non-empty. A course on complex analysis will also teach you useful stuff about power series.
     
    Last edited: May 21, 2012
  7. May 21, 2012 #6
    As a physicist complex analysis is really useful since it gives you new, really quite ingenious, techniques to solve integrals in a way you have probably not done if you have not studied complex analysis. In my opinion it is a very natural addition to the usual single- and multivariable calculus courses taken by all who study physics.

    Haven't read the other subjects on your list but I'm thinking of differential geometry for this fall. My next choice would probably be a PDE course - it can be nice to get a formal mathematical treatment of something which is very much used in physics but not always formally presented.
     
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