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Which mathematics courses would you recommend?

  1. Apr 26, 2015 #1
    As a quick continuation of the question...what mathematics courses would you (preferably PhD or pursuing a PhD currently) recommend for an undergraduate? I'm interested in high energy/particle physics (I'm working in a lab this summer so we'll see how that goes) and cosmology (no actual experience or coursework experience, just self learning). I do plan on continuing to graduate school and obtaining a PhD although I'm not sure of what topic I want to pursue. Here are some of the courses that I will take for sure:

    Linear Algebra I (I have already taken Elementary Linear Algebra)
    Differential Geometry I and II
    Partial Differential Equations
    Calculus of Variations and Integral Equations

    My university offers a graduate level course to undergraduates called Linear Algebra II. Here is the course description of Linear Algebra I:

    Vector spaces, linear transformations, and matrices. Canonical forms, Determinants. Hermitian, unitary and normal transformations.

    Compared to that of Linear Algebra II:

    A theoretical course on the fundamental concepts and theorems of linear algebra. Topics covered are: vector space, basis, dimension, subspace, norm, inner product, Banach space, Hilbert space, orthonormal basis, positive definite matrix, minimal polynomial, diagonalization and other canonical forms, Cayley-Hamilton, spectral radius, dual space, quotient space.

    Tell me straight; is Linear Algebra II a course worth taking? I am more than willing to provide course descriptions and course planning spreadsheets if necessary. Also, if you have a specific math course in mind, I would love to see if my university has it! So recommend away and I'll get back to you on whether or not it is offered!

  2. jcsd
  3. Apr 26, 2015 #2


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    Gold Member

    There seems to be quite a lot of overlap between these courses, with one concentrating on linear algebra and the other branching into some analysis.

    Both courses are useful. Physics uses a lot of linear algebra. It also uses a lot of infinite dimensional linear spaces. So, if you must chose between them rather than do both, it is a tough decision. I suspect that the theoretical course might turn out to teach you more.

    The linear algebra course looks as if it is aimed principally at computer scientists, but I could be wrong. As a physicist, you should aim eventually to know the content of both courses. Physicists need to know everything.
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