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Since it's finally the end of the year, I would like to gain some insights about which course should I take that are most helpful to prepare for application to the PHD program in Finance/Financial Economics/Operation Research at top schools (e.g. Columbia's IEOR/Finance departments, NYU, Duke, MIT, Georgia Tech, UNC-Chapel Hill, etc). I'm currently pursuing a MS degree (my first semester btw) in Applied Math in an unknown school, and I learned from my mistake of unsuccessful attempts at top PHD programs to carefully plan my course selection.

Below is the potential list with some extra info about the books that we will use. Keep in mind that I can only choose at most 2 courses to take (since I decided to take these two courses: Fourier Analysis (Stein's book), and Nonlinear Functional Analysis (Philip Ciarlet's book: Linear and Nonlinear FA with application)) with some extra info about the books we will use:

  1. Numerical Linear Algebra (Book: Applied Linear Algebra-Lloyd N. Trefethen)
  2. The Math of Finite Element Method (An Introduction to the Finite Element Method-McGraw Hill)
  3. Topology - Munkres's book
  4. Algebra - Book unknown
  5. Numerical Methods - Scientific Computing (Michael Heath)

I just finish taking Linear Analysis, Linear Programming, Advanced Linear Algebra, and Algebra (undergrad level). I'm leaning towards taking 1 and 2, but I heard that 3 and 5 are quite helpful course for PHD application in Economics. I really don't know which one are the most reasonable ones, in terms of difficulty + helpfulness for admission. Any thoughts would be greatly appreciated.

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  • $\begingroup$ Does anyone know which courses above should I take to be well-prepared for a PHD program in Financial Economics/MS in Computational Finance at CMU? $\endgroup$ – user177196 Dec 18 '14 at 3:11
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Hi I was in a similar position this year:

I would suggest you to take

  1. Linear Algebra
  2. Differential Equations
  3. Statistics (Probability Theory and Stochastic Calculus)
  4. Real Analysis (For FEM and OR it is vital to get through first 6 chapter of Walter Rudin's Principles of Math Analysis)

Hope this helps, and do let me know how has your learning progressed, since this is a late answer.

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Definitely take 1. I think 4 is generally unimportant for econ. The finite element method seems like more technical detail than you're likely to need regarding PDEs, but I could be wrong. It seems that many people end up learning a significant amount of advanced analysis, in particular functional analysis, in an econ PhD, and for that 3 is a necessity, so I'd lean towards 1 and 3.

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  • $\begingroup$ Many thanks for your thought! I also heard that FEM is used a lot in the real world of Finance, but I'm not sure if this is a must-take course for PHD Finance/OR program at schools like Columbia (IEOR department) and NYU. $\endgroup$ – user177196 Dec 17 '14 at 4:11
  • $\begingroup$ It sounds like you know more than I do about its actual use, but I can say pretty confidently that most of your peers won't actually know it, since people come into econ PhDs from a wide range of undergraduate programs. It's more important to learn the fundamentals at this point. $\endgroup$ – Kevin Carlson Dec 17 '14 at 4:12
  • $\begingroup$ Thank you so much! Honestly, I don't know that much about its actual use (only heard from people). May you elaborate on the fundamentals (i.e, why the FEM won't give me the fundamentals that Topology or Numerical LA does?) $\endgroup$ – user177196 Dec 17 '14 at 4:42
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    $\begingroup$ The finite-element method is a particular technique within the field of PDE. Topology is an entire field and one of the most important within math, both for its own sake and for its applications in algebra, geometry, and analysis. Numerical linear algebra is again an application area, although it could be pretty important for you. The general idea is that you should learn subjects which you'll later apply as soon as possible, not that you shouldn't learn these other ideas as soon as possible. $\endgroup$ – Kevin Carlson Dec 17 '14 at 6:59
  • $\begingroup$ So I had a chance to get a reply from the professors who will teach 1 and 4. They said there are some overlaps between these two courses in terms of the materials covered, and the book used in 4 is Scientific Computing by Michael Heath. They both said the courses will focus on the aspects of different numerical algorithms including QR factorization, Least Squares, conditioning/stability, systems of equations, eigenvalue problems, Fast Fourier Transform, FD and FEM (the last 3 topics are only covered in 4). So if you were me, which one would you take, if 4 is one of the "core" courses? $\endgroup$ – user177196 Dec 19 '14 at 3:25

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