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Columbia? NYU? Which math phd program would you recommend ?

Joined
3/21/11
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I am foreign students and have applied phd in mathematics for fall 2011.
After all, I am admitted to Columbia(pure math) and NYU Cournat phd.

In fact, I am not sure whetehr I would persue a financial job after phd degree.
I just love math and I am willing to spend about 5 years to study and have a research on it.
(This is the reason why I did not apply MFE programs)

My question is..
If I am interested in studying mathematical finance during phd period, which school looks better?

At first glance, NYU seems one of prestigious school in this and related fields.
There are lots of well known professors working in PDEs and probability (both in theoretical prob and mathematial finance) and it also has a strength in numerical analysis and other applied math.

In Columbia's case, the situation is somewhat different. In math dept, there are some famous professors in mathematical finance, but columbia does not seems to have specialty in analysis (PDE, theoretical probability, numerial and so on). On the other hands, from my search on the internet, they seem to have vibrant co-work atmosphere with other departments such as IEOR or stats. In IEOR and statistics depts, there are several professors in FE or Stochastic process, analysis and so on. I also found some student in math dept who chose their advisors in those departments.

If I decide to study Fin math, I might try to get a job industry.
Then, which school would be better for my career and potential growth as a quant?

I Also have another small question.
In my undergrad university, I have taken several analysis courses related to financial math.
Those courses include graduate real analysis, measure theoretic probability theory, funtional analysis and so on. In mathematical point of view, studying those subjests was interesting.
Proving various convergence or limit theorems and Studying martingale theory was nice.

However, I heard that the most of real work done in industry is not like fancy theories. It mostly deals with numerical results or computational problem. If what the employers expect from phd holders are just some deep math knowledge and quantitative skill (programing sill?), what can be an advantage of studying mathematical finance as specific fields in phd compared to other fields in mathematics or physics?
Can I have more deep sight? give positive signals to employers?

Thank you for reading.
 
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