Lectures: This course will be an introduction to the interplay of mathematics with several disciplines, namely biology, ecology and physiology, and it will be taught within the context of modeling complex systems. The applications we shall discuss will range from subcellular molecular systems and cellular behavior to physiological problems, chemical kinetics and population biology. No previous knowledge of these areas will be assumed. The biological background to each problem will be described in sufficient detail to construct and analyze models. The lectures will show how models of complex systems are built up and will provide the mathematical tools indispensable for studying their dynamics. With each topic discussed the scenario will consist of (i) a description of the biological problem; (ii) development of the mathematical model and an assessment of its realism; (iii) mathematical analysis of the model and clues to numerical computations; (iv) biological interpretation of the results from a modeling viewpoint. More specifically, a selection of modeling problems from the following areas will be studied:

I.   Continuous and  discrete models and analyses for interacting populations
II.  Biochemical Reaction Kinetics: Classical versus Stochastic Kinetics Modeling
III. Introduction to reaction diffusion theory in biology and ecology
IV. Spatial pattern formation in biology and ecology
V.  Dynamics of infectious diseases
VI. Selected topics on Modeling Complex Systems in Biology

We shall cover book chapters from Murray and Edelstein-Keshet, and allude to other topics (hand-outs to be provided when necessary) as may be required. The main emphasis of this course will be on techniques of mathematical modeling in biology and ecology, and in the context of mean-field type and stochastic modeling of complex systems (not agent-based modeling of complex systems). Practical implementation of algorithms on computers will be encouraged. Students will be required to complete two term projects.