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Thread: Prioritization of math courses

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    Prioritization of math courses

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    The math courses I hope to have finished by undergrad end are:
    - calculus sequence (single var, multi var, linear algebra/differential equations)
    - linear algebra
    - real analysis 1 and 2
    - probability (calculus based)
    - statistical inference
    - mathematical statistics
    - stochastic processes
    - probability (measure theoretic)

    Is there an important math class that I'm neglecting? Are any of these functionally irrelevant for applications and should be replaced?

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    Re: Prioritization of math courses

    Quote Originally Posted by therealslimkt View Post
    The math courses I hope to have finished by undergrad end are:
    - calculus sequence (single var, multi var, linear algebra/differential equations)
    - linear algebra
    - real analysis 1 and 2
    - probability (calculus based)
    - statistical inference
    - mathematical statistics
    - stochastic processes
    - probability (measure theoretic)

    Is there an important math class that I'm neglecting? Are any of these functionally irrelevant for applications and should be replaced?
    For most students, single variable, multiviariable, linear algebra, and real 1 will suffice. I'm on the fence about "calculus-based probability" and real 2.

    If you feel that you must do micro theory, take those courses, and also measure theoretic probability and stochastic processes too. If you feel that you must do econometric theory, I guess I'd take them all, except for ODE/linear algebra.

    I guess I'd emphasize that if you belong to the category of "I must do micro theory in graduate school" or "I must do econometric theory in graduate school", then I'd cut the fat out of those lists and prioritize taking measure theory with the first year (pure) math PHD students at your university.

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    Re: Prioritization of math courses

    Seems like a good list for a typical econ student, except for measure-theoretic probability, which most students should skip. The time is better spent on useful elective courses or research experience, unless they're significantly ahead of schedule on their coursework (e.g. on track to finish all of grad micro/macro/metrics in their 3rd year and have nothing else to take).

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    Re: Prioritization of math courses

    Quote Originally Posted by chateauheart View Post
    unless they're significantly ahead of schedule on their coursework (e.g. on track to finish all of grad micro/macro/metrics in their 3rd year and have nothing else to take).
    My impression was that measure theoretic probability and grad metrics were very complementary? At least my plan was to take both of them together in senior fall.

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    Re: Prioritization of math courses

    Quote Originally Posted by therealslimkt View Post
    My impression was that measure theoretic probability and grad metrics were very complementary? At least my plan was to take both of them together in senior fall.
    At my middle-of-the-road PHD granting institution, there was no measure theory in the first year sequence. I suspect that this might be true at many universities. I don't think that most economists know (or have known) measure theory.

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    Re: Prioritization of math courses

    I've taken PhD metrics at two institutions; measure theory was part of the curriculum in the mid-ranked program (and taught in math camp + first semester metrics) but supplementary material in the high-ranked program. In both cases, problem sets and exams did not really require measure theory, certainly not the proof-writing techniques that you'd learn from PhD math coursework (triangular arrays and all the crazy stuff you do with them). The math behind first-year econometric theory often consists of set theory concepts expressed in measure-theory terms; it's not too difficult to grasp if you did well in undergrad econometrics. Measure theory is used as a bridge to real econometrics research, but few economists will need to read econometrics research for their work.

    From the perspective of an undergrad who's spending most of his time studying math and learning econ theory, it's not wrong to perceive measure theory and econometrics as complementary, just like functional analysis and micro theory might be complementary. But from the perspective of a researcher, the value of prior knowledge in micro theory and econometric theory are generally quite low to begin with, and it's easy to pick up whatever methods you need by perusing reference books when you're actually doing research. In that sense, taking too many math courses as an undergrad is not complementary with doing good work in empirical micro or macro; it may be better to invest in programming skills or general econ knowledge as an undergrad. The exception are those undergrad students who are so academically strong that they don't have *any* meaningful coursework to take by the end of their junior year, and need some extra math/theory coursework to keep their minds sharp.

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