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Thread: Math Requirements for Theory

  1. #11
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    Re: Math Requirements for Theory

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    Quote Originally Posted by Zilch View Post
    Most courses on measure theory really just teach you the basic tools. Most parts of advanced mathematics use these tools without even mentioning them so in that sense it is a very basic course in the grand scheme of things.

    I took an analysis course once during my undergrad and this was the syllabus :

    Banach and Hilbert spaces, theorems of Hahn-Banach and Banach-Steinhaus, open mapping theorem,closed graph theorem, Fredholm theory, spectral theorem for compact self-adjoint operators, spectral theorem for bounded selfadjointoperators. Additional topics to be chosen from: Lorentz spaces and interpolation, Banach algebras and the Gelfandtheory, distributions and Sobolev spaces, The von Neumann-Schatten classes, symbolic calculus of Hilbert space operators,representation theory and harmonic analysis, semigroups of operators, Krein-Milman theorem, tensor products of Hilbert spacesand Banach spaces, fixed point theorems.

    I think what cheatuheart was getting at is that most theory applicants would have had several courses like the one above.
    I don't think your example is a good one since it's WAY beyond just measure theory. A good example would be a probability theory class with measure theory, or a functional analysis class that goes in-depth into Lp spaces or even a harmonic analysis class.

  2. #12
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    Re: Math Requirements for Theory

    I ask this question for a theory professor once. There is some basic knowledge and the rest is pick as you go.

    By base knowledge i mean: You need to know well Linear Algebra and Real Analysis, and you need some introduction to Optimization, Measure Theory, Functional Analysis and maybe some Stochastic Process.

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