Quicklinks: General Information, Lecture Notes, Final Assignment
The main theme of this course is the rigorous mathematical analysis of probabilistic and combinatorial structures arising from biology, mostly in the study of evolution and genetics. No biology background is required. The course should be of interest to probabilists, combinatorialists, applied mathematicians, theoretical computer scientists, computational biologists, and biostatisticians.
Various stochastic processes on combinatorial structures will be considered, including random trees, Markov models on trees, multitype branching processes, finite Markov chains, random walks, exchangeable partitions, and Kingman's coalescent. Here is a tentative list of topics:
Mathematical Phylogenetics (a.k.a. the mathematics behind the Tree of Life)
Mathematical Population Genetics
Presentations (you may use the following template for your 3-page summary [UPDATED: May 28, 2010])
The optional homework is here. It covers only the phylogenetics part of the course. It is due during class on June 4.
For a final assignment, choose one paper from the following list. Check with me when you have made your choice. The assignment is to write a 3-page summary of the main results and to give a 15-minute (strictly enforced) presentation in class. Most papers are too long to be covered in their entirety. Instead, you should choose a subset of particularly interesting results. Some papers also contain simulations and empirical results, but I expect you to focus on the theoretical parts of the paper.
List of possible papers (a [X] indicates the paper has already been assigned):