We propose to develop and present three short courses over one year, focusing on the mathematical and computational methods necessary to analyze biological complexity. Each short course will be four days in length and will include workshop sessions as well as formal lectures and interactive discussion sections. The overall objective of these short courses is to provide sufficient background that the participants will be able to read with understanding the computationally and quantitatively oriented literature in their area of biology. Additionally, the short courses will provide an entree to the training needed to actually carry out research using these techniques. The first course will provide an overview of mathematical and computational approaches including continuous and discrete dynamical systems, and stochastic models. The second course will focus on the evolution of complex phenotypes, and cover three approaches to the study of complex systems in biology: genetic algorithms, cellular automata, and adaptive landscapes. The third course will focus on nonlinear time series analysis in biology, with an emphasis on irregular and chaotic time series from medicine, epidemiology, and physiology.
