To those in Biology and related fields/majors:
I am looking for both the mathematical and historical background for the following sub-fields that lie at the intersection of mathematics and biology...
- The work of R.A. Fischer on population biology. He invented the ANOVA, as well as the modern notion of "Design of Experiments." I would like to gain some insight into the thought processes that led to these inventions.
- The inference of gene function through "homology." I would like to know what it means for things to be homologous in a mathematical sense, and how exactly, gene functions are inferred from homology. As well as, perhaps, a brief history of how this sub-field developed.
- The study of gene sequences in relation to evolutionary trees. It is my understanding that the modeling here is mathematically intensive. I believe this area of genetics is called coalescent theory. Here I would like a good primer on the biology involved, and perhaps the (possibly mathematical) definitions of things like "gene", "allele", "genetic drift", "gene flow", "population structure," and other such things.
- Cellular Electrophysiology. It is my understanding that this amounts to treating lines of electro-active (a.k.a. nerve?) cells as transmission lines like in electrical engineering (but with lots of discontinuities). But I would like to learn the actual physiology to make sure this conception is accurate.
- Medical Imaging Technology. As I understand it, the signal processing done in this domain is among the trickiest forms of signal processing. For instance you get a bunch of resonances and you need to infer from those signals what was actually on the inside. Any sources on the algorithms used for MRIs and CTs would be very much appreciated.