· understanding biological processes by mathematical modeling
· know and understand classical mathematical models
· develop novel mathematical models from scratch
· simulate mathematical models on a computer
· know how to apply local stability analysis (Jacobi matrix)
· know how to apply concepts like hysteresis, periodic behavior, complex systems, chaos, attractor, eigenvalue.
· be able to make and give a verbal presentation in English
· be able to write a succinct paper
Theoretical research plays an important role in biology. The course covers a large number of mathematical models to show how one can describe and understand the dynamics of biological populations. Examples of this population dynamics are: ecological food chains, epidemiological models, bacteria infected by phages and populations of cells. Students are made familiar with the preparation and analysis of mathematical models. After this course, mathematical models should no longer be considered a "black box". Results of models, and their biological consequences, must be critically weighed based on the content, complexity, reality, and formalism of the model.
Classical mathematical models are developed from scratch. By deducing models themselves from simple biological assumptions, the student learns to critically consider such models and gains experience in developing mathematical models themselves. The student learns to translate the results obtained with such models into a biological interpretation. In order to be able to determine the stability of equilibrium we treat a number of new mathematical concepts such as: matrix, eigenvalue, partial derivatives, Jacobi matrix and complex numbers. This first part takes 6 weeks and ends with an exam in week 7.
During the last 3 weeks of the course we will read and discuss a number of classic and recent articles, and you will work in a small group on a project that will be run on the basis of a recent scientific publication. In this assignment you learn to put this knowledge into practice, read primary literature, and go through the research cycle from asking questions, to research, to presenting your results (total 3 weeks, concluded with a symposium and written report in English).
Actual information will be provided via Blackboard and/or on http://tbb.bio.uu.nl/rdb/bm/info.html