- #1

tavrion

- 9

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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!