Physicist Amok

Here’s a post which poses some questions about mathematics training for biologists. I’m close enough where I figured I’d try to answer:

1. Are you a biologist, if so what kind? Sort of. My PhD will be in biology, on the response of mycobacteria to antibiotics. My undergraduate degrees were in physics and math.
2. What math did you take in college? Calculus through multivariable, ordinary differential equations, a two semester course on math methods for physics students covering special functions, complex analysis through contour integration, and some partial differential equations, real analysis through the last course they shove the doctoral students through, the probability course that comes just after, a bit of functional analysis, and a two semester graduate sequence in algebra.
3. What math do you or have you used? My image analysis requires some partial differential equations, a lot of calculus, and a bit of differential geometry. I do some theoretical biology on the side which particularly takes the probability and random processes, and partial differential equations as the limiting cases of the former. My bench work itself doesn’t take more than highschool algebra, but designing and analyzing my experiments requires statistics, which I’ve been teaching myself. Before this, when I was training to be a mathematical physicist, I obviously used everything I knew and it wasn’t enough.
4. What math do you wish you’d studied? I wish I had actually endured the second year of graduate algebra, and a graduate course on combinatorics. A couple semesters of statistics would have saved me a lot of time now, but I can fill in the gaps. I really wish I had taken serious courses on differential geometry and topology.
5. How do you use math in your job (or research)? See above.

I think a case could be made that biologists should take all the math required to take a full scale mathematical statistics course including multivariate and nonparametric methods, and a heavy dose of experimental design. Let’s see: real analysis through measure theory and Lebesgue integration and Stokes’s theorem on manifolds, a hefty course on probability from the axiomatic basis to the beginnings of random processes, and then blast through statistics because a t-test would only require about ten minutes and a homework problem, and so would a U-test. This is four years (two of analysis, one of probability, one of statistics), but it’s only one course a term.

Admittedly, biology departments would suddenly have as many undergraduates as physics departments.