Math major looking for advice on phd programs

[cbm39]

Hi guys,

 

I just finished my junior year at Emory, and I'm really interested in a Phd in a quantitative field, but I'm not really sure which programs to apply to. 

I'll give my background and interests and I would really appreciate it if you guys can steer me in the right direction.

 

I'm a Pure math major with a 3.95 GPA. I think I have also completed the Applied Math BS and a minor in CS

 

I'm doing the school's 4 year BS/MS program, so I'll finish with a Math MS next year.

 

I've taken the analysis, algebra, prob stats sequences, complex vars, numerical analysis and all the basics like calc3 diffeq vector spaces etc

 

Doing an REU this summer. Topic is Options Pricing

 

So I've done really well in all of my Math classes, and I really love learning math and taking math classes. I want to keep learning and really develop an expertise and a deep fundamental understanding of a field and learn research skills.

 

BUT I don't see myself doing "math for math's sake" long term.

I want to apply math to model real world things and optimize systems.

So I'm not sure about applying to Pure Math PhD's. And it seems that at most schools (correct me if I'm wrong) there is little separation between Applied Math and Math departments.

 

I have always been interested in quant finance and computers.  Algorithms in general interest me--developing them and optimizing them.

I like doing coding, especially when its implementing a math model.

Scientific computing seems really cool to me.

 

Real Analysis is a class that I absolutely crushed my junior year. I set the curve far and away on every exam.  It just really clicks for me. I'm taking Grad Analysis and Grad Numerical Analysis next year.

So if I were to do anything in pure math it would certainly be in analysis.

 

Coding theory also interest me.  I didn't really enjoy abstract algebra, however finite fields in algebraic coding theory seem pretty cool. Could maybe see myself getting into some silicon valley type things

 

I haven't had time for econometrics or econ forecasting but those are also things I'm interested in

 

I took an Artificial Intelligence class this spring and loved it.

 

Markov Decision Processes and policy/value iteration are really cool

 

So all of these interests have given me these possible Phd programs:

 

Math or Applied Math

 

Stats Phd's? I don't really understand what they do there.

 

Computer Science--focused on AI; not sure if i have enough of a CS background though

 

Computational Math Phd's--Sound really cool, Emory has one, but few other schools do.

 

Operations Research and Industrial Engineering-- this sounds like a really cool interdisciplinary thing that would include all of the things I'm interested in.  programming, algorithms, finance, econ, etc.  But I don't really know much about OR.  And is it too light on the math? Like I really want to learn as much math as I can reasonably apply to real-world phenomena, but I could maybe see myself doing research in complex analysis later in life, post-industry maybe.

 

 

So i just wrote a bunch here, but basically can someone give me some direction?

Is my best bet to just apply to math phd programs, and just focus my thesis on the fields I'm interested in?

 

Also are OR and IE funded as well as math programs are?

 

Is math the most challenging and rigorous out of all of these? And does a math phd garner the most respect out of any of these?--Not that that's a major factor, but if I think I can handle the most rigorous type of program I might as well--I like a challenge in school

Is an OR phd "softer" than a pure math program?

 

Thanks for reading

 

 

[StatsG0d]

Take this with a grain of salt, but from my understanding AI and ML courses are more mathematically-centric than computer science-centric. Given your background, you're likely to be successful at pretty much anything you decide. It seems like the hardest thing for you is deciding.

 

My background is in economics (with a math minor). After I took my first econ course, I thought 100% that I wanted to be an economist. After working as an RA for the last 2.5 years for economists, I decided that it isn't for me. Empirical economists tend to rely on strong assumptions (e.g., rationality) and they tend to use one tool: linear regression. From my viewpoint, there are many relationships which are nonlinear, so I decided to go the statistics route.

 

I think your REU will provide you with a great experience to see if you like quantitative finance. It's an intriguing field, and perhaps will be my preferred research area when I (perhaps I should say if I get accepted) go to grad school.

 

Despite all that, from what I read, it seems like you would be a great mathematician. On the other hand, the best economists are mathematicians. The two need not be mutually exclusive, as virtually all theory of economics comes from mathematical relationships. To play devils advocate a bit, I think you would be successful as a econometrics researcher. You would be able to develop methodologies to advance econometrics.

 

All these opportunities you describe sound fantastic. I wish you luck in your endeavors. Perhaps you should look for research opportunities with professors or with organizations such as the IMF, World Bank, and the Fed if you want to learn more about economics research.