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March 14th, 2011, 03:39 PM   #1
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Advise on choosing course (final year undergrad)

I need to pick my module choices for my 3rd and final year, and I am stuck on the final few modules I should choose.

For my final year, I already plan to do courses in complex analysis, functional analysis, stochastic processes, and advanced numerical analysis (Numerical ordinary differential equations//Numerical solutions to PDE's and ODE's), and I plan to do a dissertation on measure theory/lebesgue integration, or Perron–Frobenius theorem.

I am left to choose 2 more modules from the following below, may I ask for advice on choosing my modules? My intention is to do an MSc in financial maths, bearing in mind where universities usually ask for an emphsis in linear algebra, analysis, differential equations and probability theory..
I need to choose from:
1. Lie group and lie algebra
2. Representation Theory
3. Asymptotic analysis
4. Quantum mechanics
5. Algebraic geometry
6. Nonlinear systems with applications to biology (contains stuff on DE's, but related to biology??)

Any advice on which 2 of the 6 i should choose? Im thinking of doing representation theory (as it has stuff on linear algebra) and algebraic geometry, but any advise?
And for my dissertation, i plan to do either measure theory/lebesgue integration OR the perron-frobenius theorem. Any recommendations?
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March 14th, 2011, 04:21 PM   #2
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Re: Advise on choosing course (final year undergrad)

Nonlinear systems and either asymptotic analysis or algebraic geometry. But we should get julien to give his advice here; he's the financial mathematics guru around these parts.

I wouldn't worry about the "for biology" part too much, frankly. It's probably closer to what you want than the equivalent "for mathematicians" course would be.
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March 15th, 2011, 12:21 PM   #3
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Re: Advise on choosing course (final year undergrad)

thanks for your help any more replies?
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March 15th, 2011, 05:07 PM   #4
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Re: Advise on choosing course (final year undergrad)

As much as I would rather take courses in algebraic geometry and representation theory, I think the long-term value of these topics to you is rather limited. If you are looking for courses related to what you hope to do, the asymptotic analysis and the non-linear systems courses will be the most directly applicable. Both of these courses are probably directly related to financial mathematics (and honestly, I would guess that the applications to biology and finance are actually quite similar).

Beyond that, it is really your own personal preference; if you don't want too much of the same things, then you might consider taking other classes. But even then, it depends a lot on how "mathy" you want your classes to be. Lie groups and algebras, algebraic geometry, and representation theory are all very "mathy" topics, whereas the quantum and the bio will use a fair amount of math, but it will have something else in mind (and it's not a bad thing to take classes which show useful ways to apply mathematical knowledge, either). Looking at your course lists, it might be worth mentioning that, while you seem to be analysis-heavy, algebraic geometry and representation theory are probably going to be very algebra intensive while Lie groups and algebras are a bit more in the middle (but really fairly involved in both).
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March 17th, 2011, 07:32 AM   #5
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Originally Posted by CRGreathouse
I wouldn't worry about the "for biology" part too much, frankly.
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