Non-math Master towards Math PhD

[YuleWalker]

Hi, I will probably get into a thesis-based master program in financial engineering this fall. With the thesis option, it will be very flexible for me to select courses and research topic. As I become more and more interested in mathematics, especially analysis, I am considering applying for a math PhD afterwards. So I plan to select more graduate level pure math courses in addition to my two required finance courses. The courses that I want to take are harmonic analysis, functional analysis, probability theory, stochastic calculus, and operator algebra. I think I can handle these demanding courses because I took some advanced math courses for my bachelor's degree, such as real analysis, measure theory, integration theory, time series, applied probabilities, ect..

My questions are -

1. Will it be realistic, or does it look odd that I want to apply for a math PhD following a financial engineering master program?

2. Will the financial engineering program director allow me to take those pure math courses? (I can choose a demanding thesis topic that requires a lot of pure math knowledge. In that way, I guess I can convince them to allow me to take those courses.)

3. What are my chances of getting into a top 10 math PhD program, like MIT, Princeton, Stanford, Berkeley? (FYI, I have a good undergraduate GPA, 91%-94%, with a major in math/finance, at a quite famous university. For my master thesis, I will probably work on stochastic analysis which will involve a lot of pure math knowledge, and I will try to get around 95% GPA for my master study.)

4. I am thinking of working with a finance professor and try to write some papers, which will involve a lot of math stuffs. Will that be helpful in proving my research ability or just a waste of time considering those are not pure math stuffs?

Thanks in advance for your advice!

[stansfield]

Hi, I will probably get into a thesis-based master program in financial engineering this fall. With the thesis option, it will be very flexible for me to select courses and research topic. As I become more and more interested in mathematics, especially analysis, I am considering applying for a math PhD afterwards. So I plan to select more graduate level pure math courses in addition to my two required finance courses. The courses that I want to take are harmonic analysis, functional analysis, probability theory, stochastic calculus, and operator algebra. I think I can handle these demanding courses because I took some advanced math courses for my bachelor's degree, such as real analysis, measure theory, integration theory, time series, applied probabilities, ect..

My questions are -

1. Will it be realistic, or does it look odd that I want to apply for a math PhD following a financial engineering master program?

2. Will the financial engineering program director allow me to take those pure math courses? (I can choose a demanding thesis topic that requires a lot of pure math knowledge. In that way, I guess I can convince them to allow me to take those courses.)

3. What are my chances of getting into a top 10 math PhD program, like MIT, Princeton, Stanford, Berkeley? (FYI, I have a good undergraduate GPA, 91%-94%, with a major in math/finance, at a quite famous university. For my master thesis, I will probably work on stochastic analysis which will involve a lot of pure math knowledge, and I will try to get around 95% GPA for my master study.)

4. I am thinking of working with a finance professor and try to write some papers, which will involve a lot of math stuffs. Will that be helpful in proving my research ability or just a waste of time considering those are not pure math stuffs?

Thanks in advance for your advice!

You probably can take 1-2 I bet those programs have their cores if it's thesis based.

Given what you said alone, you have basically no chance. Those 4 schools are exactly #2,3,4,5 in pure math. Typically you need about at least a few sequences of grad courses at least need to hit algebra, analysis, and preferably topology, some reu or other form of research, usamo/putnam, stellar letters that vouch for your ability as well as your creativity, 800 quant score and 85%+ gre math subject, and that's still no guarantee into those 4. You can comfortably get into some other top 10 like umich columbia and maybe uchiago given these stats.

Also you have to be careful about your approach because pure math views financial mathematics with some suspicion. Stochastic calculus is anything but pure and more applied than high school algebra or euclidean geometry although there are a few top 30 schools with a flavor for probability/stochastics like nyu, cornell, ucsd, uwashington, rutgers, ucla. berkeley as well but the cores are strict. You need to really tailor each application to its specific program.

Aim for a top 50 research 1 and you would not be limited in any way other than by your own potential.

Edited March 30, 2011 by stansfield

[coffeeintotheorems]

Good God, man, you can't explore professional financial engineering and top-level pure mathematics at the same time, both at the graduate level. I don't care how smart you are; you're going to feel torn on the inside.

Make a decision about which path to explore now. And unless your background is utter perfection, there's no way you could move from an FE masters to a top-level pure maths PhD. It doesn't make sense, and like stansfield commented, the profs in the pure maths programs will look at you suspiciously, wondering where you passions lie. You can't direct your energy both places at once.

[Messed_up_thrice]

They are completely different things.

The only thing they have in common I guess is that both require you know math through about your year-long undergrad Analysis sequence. That's it. MFE programs are PROFESSIONAL degree programs, not preparation for PhD programs in those areas, let alone pure math.

[coffeeintotheorems]

Yule, I just re-read your original post closely, and I may have been a little harsh. I honestly don't know of any FE program that allows quite as much theoretical work as what you are describing; if you don't mind, could you tell us which FE program you're attending?

If you want to get a good idea of what kinds of people get into top 10 pure programs, see this:

http://www.mathematicsgre.com/viewtopic.php?f=1&t=495

Search the profiles there for words like "MIT," "Princeton," etc. and see what kinds of people did and did not get admitted. Best of luck.

[Sleepy]

There are 2 problems here:

1. An FE program from a good school is very costly and very unlikely to receive any funding. I wouldn't defer that much debt for so many years if you do not plan on embarking in a lucrative FE career anyways.

2. While it may be a rigorous program, an FE program does not cover even 1/4 of what is in the Math Subject GRE. You would have to make up at least 4 courses in order to be considered as having enough of a solid background to pursue a PhD in Math (if you haven't already taken them, obviously). I know that I personally, as someone without a solid background, was not going to bother with any undergrad classes and was not going to take time off from work just to take these classes that may not necessarily guarantee that I even get in to a good school.

But thats just my opinion.

[Xero735]

Also the material we are talking about is baseline. Top tier schools will force you to hit the ground running and if you can't keep up with students that did their undergrad thesis in commutative algebra or simplectic manifolds, you are not gonna make the cut. I currently go to a mid-tier program and even with my math background as a math major undergrad I struggled to keep up. I suggest that if you want to get into a doctorate program you aim low

[YuleWalker]

Thank you all for the advice! Really appreciate it!

I am currently in my third year, and have already taken graduate level analysis courses, which include signed measure, Hahn decomposition, Radon measure, ect. Besides analysis, I have taken two advanced linear algebra, one advanced geometry, so I guess I am not that far behind. Also, I may be able to make up most of the algebra courses and further study graduate analysis by the end of next winter. I think the most unusual thing in my education background is that, I spend my "supposed-to-be" forth year under the name of a FE master degree. But indeed, I will mostly study pure math instead of professional finance courses.

The reason for my strategy is that, by switching to a master program, I can pay one-third of my undergraduate tuition fee and have more research opportunities as well as easier access to graduate courses. Things are flexible because I stay in the same university where I do my undergrad.

I do agree with most of you that my background is not competitive for those prestigious schools. So I wonder what I can do in the following year to improve my profile? Also, if that FE master degree will really have negative effect on my profile, despite my reasoning as above, then shall I just continue my bachelor's degree, in which case I can get a pure math degree with the extended undergraduate study.

Thank you again for your opinions!

[Xero735]

I can tell you moving into something related is very difficult. I am trying to move from pure math to biostats. Partly out of interest, and partly because pure math is VERY difficult to get jobs with, even post-doctorate. You need to be very competitive. I think you have a very solid application for a mid to low tier school but aiming higher and you will waste your money.

[stansfield]

you don't need thesis really adcoms don't really put any weight on them. It's mostly courses and test scores which you're doing well in. Since you're only a junior I say you have a decent shot at a top 15 but FE would kill it almost immediately unless you appeal to specific faculty members very well.

[coffeeintotheorems]

you don't need thesis really adcoms don't really put any weight on them. It's mostly courses and test scores which you're doing well in.

Stansfield, what's your basis for this claim? I would think it would depend greatly on the school and preferences of the adcom. A thesis shows you have research and publication-ready experience. I agree that doing well in lots of graduate-level courses is important, but my impression on test scores is that you mostly just need to make some minimum cutoff and after that a high GRE score carries much less weight than most other factors.

[stansfield]

Stansfield, what's your basis for this claim? I would think it would depend greatly on the school and preferences of the adcom. A thesis shows you have research and publication-ready experience. I agree that doing well in lots of graduate-level courses is important, but my impression on test scores is that you mostly just need to make some minimum cutoff and after that a high GRE score carries much less weight than most other factors.

you don't need super high gre but you need 80+ for those schools he mentioned, really really good scores can help you a bit someone told me. There are two problems with undergrad thesis, 1) they are nothing spectacular, 2) the admission committee is left wondering what percent of the work is done by your advisor. Also college thesis are far from publication ready, they are trivial and heavily padded, most of them are the "a survey of " type. I got in a top 10 without research and most of the people I know didn't have a thesis. You want to pass their quals and for those schools he mentioned lot of international applicants can pass them walking through the door, schools are looking for similar domestic candidates so you want exposure to grad courses. For uchicago, you need at least 7-8 for ex. Your propensity for research is something that your advisor should mention but it won't kill you if it hasn't taken shape yet. Bad grades will kill you however.

[coffeeintotheorems]

There are two problems with undergrad thesis, 1) they are nothing spectacular, 2) the admission committee is left wondering what percent of the work is done by your advisor.

Interesting point. that never occurred to me.

I got in a top 10 without research and most of the people I know didn't have a thesis.

IU Bloomington is great, but I didn't think it was top 10.

Most of the people I've observed getting into top 10 programs at least had either publications in real journals, a senior thesis, or at least a few REUs. Only a few I saw had none.

[stansfield]

Interesting point. that never occurred to me.

IU Bloomington is great, but I didn't think it was top 10.

Most of the people I've observed getting into top 10 programs at least had either publications in real journals, a senior thesis, or at least a few REUs. Only a few I saw had none.

I got into Umich and others...I only mentioned the one I've decided on. 5 people out of my undergrad went to top 20 schools only one had 2 preprints. journals are almost unheard of.

check mathoverflow query undergrad publications, all the DGS say it's not expected and probably not worth it

Edited April 1, 2011 by stansfield

[stansfield]

http://mathoverflow.net/questions/11113/how-important-are-publications-for-undergrads

the opinions of a few esteemed dgs in some R1 schools. It's nice to have to some research but it's secondary to your gpa/scores. some active discussion and participation in seminars and talks will give your advisor an idea of your penchant for doing research both in terms of skills and motivation. If you can get a preprint or something then go for it by all means as long as you can do it on top of grad CORES but I've met 2 people that had journal publications, one went to stanford and one to princeton, and they are not serious journals like annals or jams.