I have been accepted for a masters course in computational finance that is largely mathematical, and is most suited for students who have studied either mathematics or physics in their bachelor's degree. I however, have done business/finance. I believe the reason why I have been offered a place is because I studied lots of maths in my free time (I really regret not doing maths as my degree, and I am trying to compensate for that by doing it on my own). I would solve STEP questions whenever I had free time off work. I am already week 5 into my course and it has been OK so far. But stochastic processes starts to become a bit too much for me (and it is a core module).
To give you an idea of what I have done so far: for our quantitative module, we derived kolmogorov equation, used similarity methods to solve it; we defined brownian motion; we then learned quickly about stochastic processes; Ito's lemmas and most recently we have derived the Black-Scholes equation. Lecturer mentioned about parabolic and hyperbolic PDEs (I know what a PDE is, but not heard about those classifications).
For linear algebra, I think I am coping, but if you have a nice quick intro book for that, would be awesome; we have "done" (rushed through) SVD and PCA so far (no examples were provided). Even though I understand the concepts of both, I really need to do a few examples (not sure whether they can be manual for PCA?).
And finally, stochastic processes for finance. This is really a disaster. But this is mostly because of the lecturing style than anything else. I have learned chapters 2 to 7 inclusive of Ross's "First Course in Probability". Thus, I have learned about the marginal density functions, convolution etc. To be honest, so far it was basic probability. The last lecture however, started going into Fourier transforms, and I lost the plot at that point.
I am certain it is doable to pass the course, but I want more, I want a somewhat better understanding of what is going on. I study every day from very early until very late, so I hope I can at least partially catch up with other students. Not sure whether this question is appropriate here, and whoever is still reading, I appreciate it. If you have any book recommendations that really are useful for my purposes, please let me know.