# Independent math learning

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?

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You should have an easy time finding a self-contained number theory text. The rest should wait until you've finished your course in analysis. – Austin Mohr Dec 11 '12 at 19:08
Well I am planning on taking Analysis next semester and then hopefully summer '13 I will begin doing a little self studying on interests I wont learn in college. At this level of mathematics is there really a "correct" order to learn them? They seem pretty different from each other. – TheHopefulActuary Dec 11 '12 at 19:14
They are all specialty topics. As far as I'm aware, there are no dependencies among them. A solid foundation in algebra and analysis will get you very far. – Austin Mohr Dec 11 '12 at 19:16
Thanks! Now I'm more excited for some self study!! :) – TheHopefulActuary Dec 11 '12 at 19:22
I asked a question very similar to this last week and mine got closed -_- – diimension Dec 11 '12 at 19:45

I do not know much about the course on Brownian Motion and Stochastic Calculus you have taken. Assuming that they are of sufficiently advanced, you can try reading 'Introduction to Analytic Number Theory' by Tom Apostol. You will be able to understand how much you need to know. For analytic geometry, better read Calculus II by Apostol. If it is too easy (seeing the courses you have taken) you can read Differential geometry of Pressley. All the best.

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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

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Helpful, -A! +1 $\;\land\; \ddot\smile$ – amWhy May 12 '13 at 0:25

The following courses make up the preparation program for a PhD in financial mathematics at my university; it might help you get an idea on how to prepare: