You know, quant school is kicking my arse right now, and I don't have time for much of anything these days, but just to prepare you for how to prepare for grad school in a math-related field, you might want to read an interesting blog post from "Ethan" about his steps for surviving grad school in physics: LINK
But practically, about a third of all students that enter physics graduate schools are gone — having either flunked out or given up — by the end of their second year. And I was worried I was going to be one of them if I didn’t work hard enough. The material was harder than anything I’d encountered before, and I knew that my old study habits weren’t going to cut it. Especially because I wanted to do theory.
So I did something that wound up working for me, and that I suppose I would recommend to any student that was serious about succeeding during their first year in graduate school in physics.
For each class, my study habits actually became outstanding, although they required more time than I’d ever put in before. I would:
* Skim over the sections in the textbook that we were going to be covering in lecture that day.
* I’d go to class, write down everything the instructor wrote down, take the best notes I could, and ask whatever questions I could to make sure I understood the material. And then...
* I’d go through the relevant section in the book, that we just covered in lecture, along with my lecture notes. This time, unlike before class, I’d actually be able to work through it and figure out what the author was talking about. And this step was immensely helpful to me.
* Because when it came time to do the homework, unlike when I was an undergrad, I had an idea of what we were talking about. I knew where to look in the book and my notes for guidance, and I was actually prepared for the next class.
It was really amazing to see that every student that put that kind of work in did just fine in those courses, and every student that failed those classes didn’t put that kind of work in.
It isn’t, of course, the only way to do it, but it was tremendously useful for me, and it helped me turn myself from a student that came in with a deficient background in the upper division undergrad courses, who’d been away from academics for a year, to one ready to take on the most difficult theory courses — general relativity and quantum field theory — with great success in the next year.
So if you’re headed to graduate school in physics, that’s my advice for your first year. Put the work into those core courses, because whatever you want to do after that, that’s work that will pay off. I realize this doesn’t apply to many of you, but I’d also imagine that something very much like this would help in most fields of academic study. Thoughts?
There were some recent letters to grad students in chemistry
(June 2010) and physics
(October 2012) that went viral in the past couple of years, and that were really scary.
Quant finance or financial engineering is a whole different ballgame, chiefly because there are no laboratory research assistantships or anything like that. But the classes themselves are just as brutal, if not more so.
I'm not sure if recommending classic text books is a good idea, because it's pretty damn impossible to crack them until you actually take a class on them, but in general you need to have some acquaintance with Wiener processes
, Ito's lemma
, and formal probability theory, including all the really abstract stuff about sigma algebras, Borel sets/algebras, and Lebesgue measures. Image: http://upload.wikimedia.org/math/f/6/5/f658de4b607351d3bfda98dc68e9b263.png Image: http://upload.wikimedia.org/math/4/7/4/4741446c77941ac175e0266fef2ce99c.png Image: http://upload.wikimedia.org/math/f/8/2/f822e8939551cac1788de9a03fe094e3.png
To get an idea of why in the world anyone would need to learn abstract measure theory before understanding more sophisticated concepts in probability, you can watch this mini-lecture on YouTube by a young math teacher at the University of Missouri: " Mini Lecture #1 - Why use measure theory for probability?
Additionally, probably the most famous young mathematical genius in the world at the current time, Terence Tao
of UCLA, has a free pdf text giving students an introduction to measure theory: " An Introduction to Measure Theory
The idea should probably be to work up to Jacod & Protter's "Probability Essentials," which is a very short & concise book giving in compact form everything an incoming quant student would need to know about the abstract concepts behind probability measure theory... Image: http://bks0.books.google.ch/books?id=OK_d-w18EVgC&printsec=frontcover&img=1&zoom=1&edge=curl&imgtk=AFLRE70SHhwg9mno4Flty39T7R5DjfDSe6GdMf2rh_1PA8YOpVbfgw7GIXgpiQ6oRx6ZidPD5I6kfAZPU1rgov-1kG94Qr1FJbbmtaE0_7JVVOWCQFXrDqCEsnM7R5-qtYW0mg8RSpBw
There are other great texts that bear mentioning, but which might be best left untackled until you arrive at school:
"Stochastic Calculus for Finance I & II" (Shreve)
"Stochastic Finance: An Introduction in Discrete Time" (Föllmer & Schied)
"Limit Theorems for Stochastic Processes" (Jacod & Shiryaev)
"The Mathematics of Arbitrage" (Delbaen & Schachermayer)
"Stochastic Integration and Differential Equations" (Protter)
"Introduction to Stochastic Calculus Applied to Finance" (Lamberton & Lapeyre)
"Stochastic Differential Equations and Diffusion Processes" (Ikeda & Watanabe)
"Brownian Motion and Stochastic Calculus" (Karatzas & Shreve)
"Financial Modeling with Jump Processes" (Cont & Tankov)
"Derivatives in Financial Markets with Stochastic Volatility" (Fouque, Papanicolaou, & Sircar)
"Levy Processes" (Bertoin)
"Finite Elements" (Braess)
"Computational Methods for Quantitative Finance: Finite Element Methods for Derivative Pricing" (Hilber, Reichmann, Schwab, & Winter) ... and from the more practical side, with books that might be useful references for derivatives traders and practitioners...
"Hull-White on Derivatives" (Hull)
"The Mathematics of Financial Derivatives: A Student Introduction" (Wilmott, Howison, & Dewynne)
"Dynamic Hedging: Managing Vanilla and Exotic Options" (Taleb)
"Quantitative Methods in Finance" (vols. 1-5) (Alexander)
This post was edited on 2/23 at 11:27 pm