Pure math courses for mathematical biology? [closed]

Question

For research at the PhD level and beyond in mathematical biology, what math courses come in handy (beyond calculus, ODE, statistics and probability and linear algebra)?

I know it heavily depends on the work one wants to do, nevertheless, courses in PDEs, dynamical systems, control theory, numerical analysis, graph theory and mathematical modeling are bread and butter to the field.

In addition to these subjects, are more pure math topics like complex analysis, real analysis, abstract algebra, functional analysis, etc. used in math bio research?

Answer 1

My take on the matter is that the pure mathematics topics you list tend to have fewer direct applications to mathematical biology itself but can be valuable either to deepen your understanding of some of the mathematics behind the applied mathematics topics or for the occasional direct application. Generally, the more mathematics you know, the better, but this has to be balanced against limits of time, energy, focus, and the need to know enough biology for your research.

As a minor point, one area of pure math you didn't directly mention is topology - now sometimes useful in biology in the form of topological data analysis. (See, for instance, the book Topological Data Analysis for Genomics and Evolution.)

So, as Dave L Renfro recommends in the comment above, look at the background of those currently doing research but take it with a grain of salt. The specialist in a particular mathematical field may be only too happy to find a biological application of their work, but they could be one of only a handful of researchers worldwide using that field of mathematics in that particular way.

Answer 2

Game Theory.

But do not underestimate it. The course in cooperative game theory I took in grad school was, without a single doubt or hesitation, the hardest class I have ever taken in my academic career.

Answer 3

If you want to do more than quantitative storytelling, course (or other activities like internships or hobbies) that will build your biology background and intuition. Otherwise, you will not understand biology well enough to describe biology realistically and will only create mathematically novel, but biologically useless equations.

Also, numerical methods so that you can program your own models and applied statistics or "inverse problem" courses so that you can parameterize your own models.