The course in biomathematics is a course in applied dynamical systems with applications to areas in biology. It applies discrete and continuous, linear and non-linear, dynamical systems to problems mainly in ecology, but also to physiology and epidemics of infectious diseases. Such models are crude (nature is infinitely more complicated than we can capture in a few equations) but gives good insight into the possible dynamics of the real systems. A key feature here is how to investigate how the system changes behaviour as we change one or more of the parameters in the model. Most problems discussed need numerical computer investigations to be fully comprehended. During the course you will learn both how pure mathematical analysis provides an initial qualitative description of the dynamics, and to take the next step and carry out numerical investigations.This part of the course looks at time evolution of whole populations, but in the later part of the course a spatial component is added to the model and we will discuss how this leads to traveling waves (in one space dimension) and pattern formation (like the stripes of zebras and leopards spots) in two space dimension.
The course consists of 18 sessions ā 2 hours spread over the full spring term. These sessions will be used as lecture time and as problem solving classes.
To pass the course you need to pass on three compulsory assignments (handins) and a short oral exam at the end of the course. For students with active participation during the course, the oral exam may be redundant and not performed. Such decisions are made by the course responsible alone. To get one of the higher grades you will also have to do a written take-home-exam as well as an oral exam.
Hand-in dates are February 19, March 26 and April 25. The actual projects can be found in the column to the right. Projects should be handed in as PDF-files by e-mail to firstname.lastname@example.org
If you want to opt for a higher grade than 3, which is what you get when you have three approved handins, please send the course responsible an e-mail. It means to take an home-exam and an oral exam.
The following table contain links to planned outlines for the lectures.
These outlines will not be adhered to strictly. I particular discussion about hand-ins will be included when appropriate.
Läs om matematikhistoria på: MacTutor
History of Mathematics.
Matematikintresserade studenter rekommenderas att besöka Lunds Matematiska Sällskaps möten.