I'm an undergraduate math and econ major and I'm planning on graduating relatively soon and I am very limited to the number of math classes I have left (very sad about this fact). So far I have decided I want to take a (as I'm sure some of you know from previous questions) Mathematical Analysis course, I'm also planning on taking Linear Algebra (of course), Intro to Stochastic Processes, Intro to Brownian Motion and Stochastic Calculus, and a Modern Algebra class. Which means that if there is anything else I want to learn I need to do it on my own by self studying. I have done a little bit of researching different topics and I think I would be interested in Number Theory, Dynamical Systems and Chaos, maybe some Analytical Geometry, and further topics on Stochastic Process.
Is there a certain order that would possibly make these topics come a little easier. If that doesn't make sense I'm just wondering: Should I study topic X before topic Y or vice versa? I know of course Linear Algebra would be the first step since it's so widely used, but what about after that? I really would like to invest my time after graduation, besides having a career, in learning more math. But I don't know what the best order to do it in is. Should I learn Analytical Geometry before Number Theory? Any advice on this would be great. If you know of any other topics too I'm open to suggestions (I do have a particular interest in mathematical finance, but other topics are great too).
Additional Question: Since I have an interest in financial mathematics, are there other topics beisdes the Brownian Motion and Stochastic Calculus that are highly related to finance?
Best Answer
I would recommend contrasting what the graduate math finance program does versus financial programs do, including order, in schools known for these topics.
Example 1:
UoC Mathematics
UoC Financial Mathematics
Example 2:
CME
CME Master Computational Finance
Example 3:PSTAT Ph.D. Courses
Example 4: NYU
I would recommend that you take some time and study the difference between the two types of programs and then to compile a list of math courses which seem to support the direction you wish to pursue.
Regards -A