mathematical topics to study for finance jobs

[vkaul]

I am actually confused about the material I need to read before appearing for finance interview. I am finding there are four principal areas in Mathematics used in Finance:
1) Probability and Stochastic Integration
2) Numerical Methods and PDEs
3) Machine Learning and Time series Analysis
4) Optimization

This is apart from great knowledge of C++ and finance knowledge.
It seems a overwhelming task for me to master all these topics while pursuing PhD.
Area1)For the first area, currently I am taking a course in Advanced Probability( level of Chung) and Stochastic Processes( Shreve-2) and it is quite a lot for me to do besides my PhD.
Area 2) I am familiar with undergraduate level PDEs and basic Numerical Methods, but I am not expert in them. I am focused in using some particluar PDE( Hamilton Jacobi to be precise) and solving them for my application in computer vision. But I in no way expert at the level of Evans in PDES or in Advanced Iterative Methods and Monte Carlo Methods.
Area 3) I have done some time series analysis, machine learning and statistics. But I remember only elementary stuff from each of these courses as I cannot retain them in my memory. Besides I did not apply these statistical tools in large financial data sets. So if I have to master Area 3) I will need to spend a lot more time doing that.
Area 4) I know very basic optimization techniques and I dont think I will be spending too much time doing this area.

I wanted help in somebody guiding me about the first three areas and how I should focus my time in learning them. How much in depth knowledge will be expected in the interview?
Also I am not that great in C++ and I am trying to learn the language better. To top it all, I am trying to also read more finance book( Joshi) so that I know finance stuff little better.

I am overwhelmed by the material required. There are some companies recruiting in Fall for next year. Should I apply right now given my background? If yes, how can I prioritize learning the above material?

I am a Phd in electrical engineering doing Computer Vision/Image processing stuff with some Machine learning and I have MS in Math, EE and AE from Georgia Tech and undergrad from IIT bombay.

 

[atreides]

Maybe you might want to consider getting an MFE to fill in the gaps in knowledge. With 3 masters degrees and a Phd, you should have no troubles getting into any of the top programs like UCB, CMU, Baruch , etc. It will take an extra year or year and half, but might well be worth it in the long run. This is just my uneducated opinion.

 

[buddyforall]

You can try CQF as a way to fill the required gaps.It costs around 18,000$ though.There is a guide at markjoshi.com .

 

[vkaul]

You can try CQF as a way to fill the required gaps.It costs around 18,000$ though.There is a guide at markjoshi.com .

Yes but how much in depth I should know each of the 4 areas below. I dont have money to pay for CQF program. It is way too expensive for me. I will be graduating in June 2010, so when should I apply for jobs?

 

[IlyaKEightSix]

I'm sure that for the first one, a year of stochastic calculus will fill that nicely.

For the second, it varies on the school. All master's of q. finance programs worth anything should have at least one numerical methods course, although I'm sure you can find it in a physical science somewhere...probably in some sort of chemical engineering or physics dept.

For the third it sounds you know where to go...comp sci.

For the fourth, see your local industrial engineering/operations research/management science department.

 

[vkaul]

Do we need to know all of the 4 areas in depth?