Graduate level Mathematics courses of interest for Biological Physics

[corentin_lau]

I am an incoming graduate student in Theoretical Physics at Universiteit Utrecht, and I struggle to make a choice for one of my mathematical electives. I hope someone can help me out. My main interests lie in the fields of Statistical Physics, phase transitions and collective and critical dynamics with applications to biological and soft matter problems. During my undergrad I did some research on polymer glasses in confined geometries which I found very enjoyable.

I am thinking of taking a mathematics graduate level course in Measure Theory. The course seems very challenging (from my background in physics where mathematics is less rigorous) but it opens up very interesting options such as Stochastic Calculus and Random Walks. Essentially I'd like to know how useful is knowledge of these two sub-fields of mathematics in modern research in Statistical, Biological & Soft Matter Physics ? From my knowledge, the Master Equation formalism includes stochastic terms and random walks are used as polymer models, but i'd like deeper insights ... If you also have any text recommendations ?

If anyone working in the fields of soft matter, biological physics, quantitative biology could give any advice it’d be very much appreciated !

 

[Andy Resnick]

If anyone working in the fields of soft matter, biological physics, quantitative biology could give any advice it’d be very much appreciated !

These fields are progressing rapidly, finding a comprehensive text is difficult. I recommend starting with:

soft matter: Principles of condensed matter physics (Chaikin and Lubensky)
biophysics: Molecular driving forces (Dill and Bromberg)

Picking a book (or 3) for 'quantitative biology' is hard because the term is rather ill-defined, ranging from 'system biology' to quantitative western blots.

In addition, there are several excellent books devoted to the Langevin equation, which you may find useful.

 

[member 587159]

Disclaimer: pure math student here

Measure theory is an absolute necessity if you want to formally understand probability theory. This includes random walks and Brownian motion, which can often be seen as a more general stochastic process that's called martingale.

The prerequisites for such a course would be formal real analysis class in which $\epsilon-\delta$ proofs are treated and where the topology of the real numbers is discussed.