Applied and Pure mathematics with focus on modelling

[tavrion]

Hi, I am in need of some expert advice please.

I am enrolling for my honours degree in mathematics next year. I am trying to mix it up in order to have a strong foundation in pure mathematics with specialisation in applied mathematics. My interests are financial mathematics, probability and mathematical modelling.

Below may seem a bit imbalanced on the pure vs. applied, but both measure theory and functional analysis will be covered in depth (two modules each).

For the pure part I have chosen:
>Measure Theory
>Functional Analysis

For the applied, I have gone for:
>Applied functional analysis (which is based on a PDE textbook)
>Optimization theory
>Continuous time stochastic processes
>Fluid mechanics

I still need to choose one of the following for pure mathematics:
>Graph Theory
>Set Theory and Topology
>Nonlinear ODE's

So I guess the question is which would be a stronger choice to ensure a good foundation in pure mathematics with application to mathematical modelling. I can see the advantages of enrolling for set theory (much used in measure theory) but I am not sure what use topology would have from a mathematical modelling point of view.

Perhaps someone has a different view entirely - any guidance would be much appreciated.

Thanks in advance!

 

[MathematicalPhysicist]

The obvious answer is Nonlinear ODE if you into Applied Maths.

If you plan to procceed to a PHD degree in math (either pure or applied), I guess you could take a set theory or graph theory courses as extra classes.

Best of luck, either way.