I've copied some threads below which I wrote in a different forum which addresses some of the questions regarding these programs. Keep in mind that the other forum in which these comments were posted does not have a nearly as quantitatively oriented audience as this one........For example, Columbia's math finance degree is a one year program. But it assumes a lot of prior mathematical preparation (ode and pde, real analysis, etc.), and the required courses are fairly advanced (basically phd-level stochastics the first semester, etc.). Columbia's financial engineering is also one year, but the required courses are definitely all master's level. So they are designed for somewhat different students. You have to review the specifics of the course offerings (not just the course titles) to help determine what would be best for you. If you select high-level electives, Columbia's math finance would easily be the equivalent to the 2nd year in a 2 year program. Chicago is also a one year program, but you should probably be strong enough in math to be comfortable with all phd level math courses........Since the different programs cater to somewhat different students, the amount of work experience of the "average" student will vary across the programs. Using Columbia again as an example (since it has 2 different programs), the math finance degree will have students with more work experience, on average, than the financial engineering (which will have a lot of people with little or no experience)..........The programs are pretty competitive. Princeton apparently is accepting under 10% this year (I think closer to 6-7% actually); NYU has accepted 12% so far (although they'll probably accept a few more as they figure out their final numbers); Columbia's financial engineering is somewhere between 20-25% this year I think; Columbia's math finance is more competitive (accepting about 10%) than the financial engineering; not sure about Chicago (although I'm sure it's 'competitive') or the other places (CMU, etc.).........Columbia's programs can be what you want to make them be, to a large extent. One could, without too much difficulty, construct the same sequence of coursework within either program. However, the intent of the financial engineering program is to teach more applied material (and the required courses are focused on this), while the financial mathematics program is more theoretical. But Columbia is flexible enough, and offers so many electives across math, stats, engineering, and the business school that you can customize either program fairly well.....Anyways, the math department program is more theoretical than the engineering program, and the coursework is at a higher level. It's also significantly more difficult to get into.Regarding the PhD in finance program, I was trying to be specific about the admissions statistics: either one or two years ago (can't recall which) they had 336 applicants, accepted an unknown (to me) number, and enrolled 6 students. So they accepted more than 6, but many (if not most) people who were accepted would choose to enroll, so I'm guessing they accepted maybe 10-12.Also, try looking around the forums for more information on such programs - a ton has been posted (look around January-March, when people were making decisions regarding where to attend).