DavidH,
What level of probability would be enough for say, MFE at Columbia? Would reading a book like Ross's "A First Course in Probability" be enough to understand and excel at the program? Or do you need to know measure theory probability, like Ash's "Probability and Measure Theory" or Billingsley's "Probability and Measure"?
My math background is that of an engineer (CalcI,II,III), Numerical Analysis, Ordinary Diff. Equations, Linear Algebra. I did not take a probability class and I would like to study the topic by myself. Now, I understand that measure theory probability requires more effort, as I would have to study Real Analysis first to gain understanding of measure theory. And then read Ash's or Billingsley's book. Whereas Ross's book I can read now, since I think the only prerequisite for it is the normal Calculus course.
I am interested in the programs at Columbia University, Carnegie Mellon and Berkeley. From what I have read, it seems like Berkeley and CMU are more math intensive than Columbia. I might be wrong. Let me know if Ross's book is enough for all 3 programs or not. If I apply to the program and get accepted, I want to be ready in order to have an smoother year.