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Thread: PDEs, Real Analysis II, or Linear Algebra II?

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    kkp318
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    PDEs, Real Analysis II, or Linear Algebra II?

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    I'm currently taking the first semester of Real Analysis, and have already taking a semester of Linear Algebra (as well as the obvious single and multi variable calculus).

    Next semester, I have the option of continuing on to the second semester of Real Analysis, taking the second semester of Linear Algebra, or taking Partial Differential Equations (I have not taken ODEs but they are not a pre-requisite and ODEs is not offered in the spring.).

    I'm wondering which of these classes people think would be the most helpful for getting into a top PhD Economics program, as I'm having trouble deciding, and can only take one of these courses.

    Thanks for the help!

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    Within my grasp! petecheese's Avatar
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    PDEs are mostly useful if you want to do financial economics.
    My vote is take RA2. LA2 is not needed and doesnt signal much beyond LA unless your original LA was not proof based.

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    Is it August yet? moneyandcredit's Avatar
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    Agreed. Real Analysis II, unless your Linear I was just the standard intro and Linear II is the proof-based upper-division course.
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    buzios
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    Could you elaborate on the descriptions of these courses?

    Without knowing anything more about the course content, I'd second Petecheese's vote. Taking a second course in real analysis would generally be the dominant strategy.

    Umm. PDEs have limited use, although this has been the subject of some discussion on this thread.

    I'm not sure what Linear Algebra 2 deals with. If you felt your first course was rigorous enough then that should be fine.

    I'd rank them as RA2>LA2>PDEs (you'd probably also want to have ODEs covered first anyway, it's a pre-req: at least in my department).

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    Eager!
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    what the hell is linear algebra II!! hehe. . if your "linear algebra I" was introduction to LA, maybe you should take the second one too since its pretty much the base of every model and its good to have a solid algebraic base. but without a short content table of those courses its hard for us to guess.. (oh and PDE is strictly dominated imo, unless maybe you want to do finance)

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    Within my grasp! Galoisj's Avatar
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    Anyway, it also depends on which are you interested in. To me, RA2 is the least interesting (if it is talking about multivariate analysis & calculus on manifolds).

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    An Urch Guru Pundit Swami Sage Elliephant's Avatar
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    Quote Originally Posted by Galoisj View Post
    Anyway, it also depends on which are you interested in. To me, RA2 is the least interesting (if it is talking about multivariate analysis & calculus on manifolds).
    Seriously? I'd pick analysis over matrix algebra any day. For enjoyment as well as admissions-value reasons.

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    kkp318
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    Thanks for the help! It looks like it's between RA2 and LA2, so here are the course descriptions for both, as well as for LA1 (sorry I didn't think to post them earlier).

    Linear Algebra I
    Linear equations, matrices, inverses, and determinants. Vector spaces, rank, eigenvalues, and diagonalization. Applications to geometry and ordinary differential equations.

    Linear Algebra II
    Theory of vector spaces, linear transformations, and matrices. Quadratic and bilinear forms. Characteristic polynomials and the Cayley–Hamilton theorem. Similarity and Jordan canonical form.

    Real Analysis II
    Topics include: topology of Rn, derivatives of functions of several variables, inverse and implicit function theorems, multiple integrals, generalized Stokes’s theorem.

    I really appreciate the help from all of you.

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    Is it August yet? moneyandcredit's Avatar
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    Now I think Linear II may be the choice. It has Intro to Mathematical Reasoning (intro to proofs) as a prereq, whereas Linear I doesn't. This tells me that Linear II is the more abstract proof-based course, which will be helpful later on. Still sounds like a bit of a toss-up.
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