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:
- Numerical Linear Algebra (Book: Applied Linear Algebra-Lloyd N. Trefethen)
- The Math of Finite Element Method (An Introduction to the Finite Element Method-McGraw Hill)
- Topology - Munkres's book
- Algebra - Book unknown
- 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.
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.