Advise -choosing final year undergrad courses

[gomes.]

Advise --choosing final year undergrad courses

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? I am thinking of doing representation theory (as it has stuff on linear algebra) and algebraic geometry, but any advise?
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And for my dissertation, i plan to do either measure theory/lebesgue integration OR the perron-frobenius theorem. Any recommendations?

 

[micromass]

What is asymptotic analysis abou? That certainly looks interesting to somebody going for financial math. Also the course on nonlinear systems look could have some benefits for you.

As for the algebraic geometry and representation theory: they are useles for measure theory and financial math. So if you expect your courses to be usable later, then don't take those. However, if it interests you, then take them. It doesn't really matter that much.

 

[gomes.]

Thanks :)

 

[xGAME-OVERx]

What is asymptotic analysis abou?

My understanding from a brief discussion with a lecturer is that it is about the limiting behaviour of functions in special cases. A very simple example might be neglecting parts of an expression proportional to inverse temperature at very high temperatures.

Yes, I suspect non-linear systems will have use in financial modelling, but I wonder if you will cover sufficient material in your Numerical Analysis course - do you know if this treats non-linear DEs?

 

[rezeew]

As a scientist, my advice would be to consider your future career goals and interests when choosing your final year undergraduate courses. Since you are interested in pursuing an MSc in financial maths, it would be beneficial to choose modules that align with this field and strengthen your knowledge in linear algebra, analysis, differential equations, and probability theory.

Based on the modules you have listed, I would recommend choosing representation theory and asymptotic analysis. Representation theory deals with the study of linear transformations and can be applied in various fields, including finance. Asymptotic analysis is also relevant in financial mathematics, as it deals with approximating solutions to complex problems.

For your dissertation, both measure theory/lebesgue integration and the perron-frobenius theorem are interesting and relevant topics. I would suggest considering which one you have a stronger interest in and which one would complement your chosen modules. Additionally, you could also speak with your professors or academic advisors for their input and guidance on choosing a dissertation topic.

Overall, my advice is to choose modules that align with your interests, future career goals, and complement each other to provide a well-rounded education. Good luck with your final year!