Undergraduate courses to get into grad school

[redblacktrees]

Hi.

I'm an undergraduate, and I'm registering for courses for the upcoming fall semester. I'd like to attend a (highly-ranked) graduate program to work in quantitative finance. Which of the following classes is best for me? These are the ones I've been considering:

1. Graduate-level measure theory class
2. Graduate-level mathematical statistics class
3. Graduate-level PDEs class
4. Graduate-level convex optimization class
5. Graduate-level linear programming class

I'll also be taking a grad level probability theory class. I'll have already taken a grad stochastic processes class.

Also, I'm a math+cs double major.

Any advice is appreciated.

EDIT: I thought it should be noted that the convex optimization class is in the electrical engineering department. The linear programming class is offered by the business department. The PDEs, mathematical statistics and measure theory courses are in the math department.

 

[Daniel Duffy]

4. There are many non-convex problems.
5. Not sure how useful LP is, most problems are nonlinear?

Out of curiosity, do you have a list of topics for PDE class?

 

[redblacktrees]

4. There are many non-convex problems.
5. Not sure how useful LP is, most problems are nonlinear?

Out of curiosity, do you have a list of topics for PDE class?

Pretty much, I'd like to take the class that will give me the most marginal value towards getting into a good school.

Here's the description for the graduate PDEs course. I've reworded/summarized it a little bit to maintain my privacy.

Boundary-value problems, Laplace's equation, Heat/wave equation, fourier transforms, maximum principles, fundamental solutions, shock formations, conservation laws, first-order nonlinear PDEs, weak solutions, characteristics, energy methods, Green's functions

Book: Partial Differential Equations by Evans, 2nd edition.

 

[Daniel Duffy]

The PDE course looks good, It is a good foundation.
I would say some exposure to convection-diffusion PDE (e.g. Black Scholes) does no harm and solving PDEs numerically using finite differences. And ODEs are also important,

Here are some extra and comprehensive topics.

Online Courses :: Datasim

www.datasim.nl

 

[Kangaroo]

PDEs would be the most useful. Pricing/hedging can often be boiled down to solving a PDE.

Linear/convex optimization are nice because they give you some inuition behind how to solve some of the basic problems like mean-variance portfolio optimization but they won't be much more useful than that. As mentioned above, most problems you will solve as a quant will be non-linear. Even then, optimization is usually somewhat taken for granted because you can solve most problems in a small number of iterations with algorithms like Levenberg-Marquardt and plain old gradient descent.

Measure theory would look good on a transcript if you do good but if you are taking a probability theory class it may not be useful.

What does the course outline look like for mathematical statistics?

 

[redblacktrees]

@Razvan Ilie Sorry for the late reply. Just wanted to mention that I believe the probability theory course covers some basic measure theory at the start, and it continues to use it throughout the course. Here's a description of the mathematical statistics course:

Noncentral chi-squared distribution, t distribution, F distribution, Sufficiency, factorization, exponential families, completeness, likelihood ratios, Bayesian methods, decision theory, minimax principle, Cramer-Rao theorems, set estimation, point estimation, Lehmann-Scheffe.

Book - Mathematical Statistics by Bickel & Doksum.

What do you think?

 

[Kangaroo]

This class might be as important or more important as PDEs.

These topics are fairly low-level building blocks for a lot of the quant applications of stats and data science.

That being said, if your goal is only to get into a quant program, then fancy courses like measure theory look a bit better if you do well on them (depending on the person who is reviewing your application). However, I would recommend PDEs and stats as they would help you do well in the actual program and do better in interviews once you get there.

 

[redblacktrees]

@Razvan Ilie I think I'll go with grad probability theory & grad measure theory for the reason you described. My immediate goals after college are grad school, and I just want to maximize my chance of getting into a good one. Thanks for your help.

 

[Daniel Duffy]

What's the difference between 'grad measure theory' and just 'measure theory'?
The former suggests almost research level?

 

[redblacktrees]

@Daniel Duffy Yes, that is correct.

 

[Joseph Shamsian]

Data Science and machine learning?

 

[Daniel Duffy]

I

@Daniel Duffy Yes, that is correct.

I'm not sure what gradate level MT means these days but knowing enough in order to understand SDEs and probability theory is a minimum requirement. For the rest, their pervasiveness is limited in the current context. (disclaimer: I had 3 MT courses as undergrad but it was quire a dry subject). Related to MT is Lebesgue integration and Functional Analysis which are the basis for a lot of applied stuff.
Of course, each school will have its own specific requirements.