About this course
MATH3104/7134 - Mathematical Biology
Course profile, lecture notes and tutorial/assignment sheets.
COURSE CONTENT:
Mathematical biology is a branch of applied mathematics that is growing very rapidly in importance. It deals with mathematical models of biological phenomena in such diverse areas as medicine, neuroscience, physiology, ecology and genetics. Unlike many phenomena in the physical sciences to which mathematics has been widely and successfully applied for a very long time, biological phenomena tend to be characterised by a high degree of variability and complexity. The challenge in modelling them typically lies in identifying a small enough set of variables or aspects for the mathematics to be tractable, without failing completely to capture the essence of what is taking place. Unlike in many mathematics courses where much time is spent on finding solutions to well-defined mathematical problems, in this course a significant amount of time will be spent on the art of constructing models of biological systems, and also on the interpretation of solutions of these new sorts of models.
In the first section of the course we will use mathematics to represent the basic processes of ecology such as birth, death, migration, competition and predation. We start by considering density independent growth in populations, considering exponential growth and stage-structured Leslie matrix models. We then investigate why real populations do not grow unchecked forever, and introduce modelling approaches to capture environmental stochasticity and density dependent Logistic population growth where resources are limited. This leads to a discussion of ecological stability and different approaches to harvesting resources. We then introduce Lotka-Volterra models of competition and predator-prey interactions. Throughout this section of the course we deal with discrete and continuous model implementations. Matlab is used in the lectures and in the four tutorials.
The second section of the course will discuss mathematical models of how the brain works: more specifically the electrical properties of neurons, how information about the world is encoded and decoded by neurons, and how connections between neurons change their strengths. This will involve some electrical circuit theory, ordinary differential equations, Poisson statistics, Bayesian statistics, information theory, and linear algebra.
WHERE IS IT USED:
Mathematical modelling is used increasingly in modern biology and ecology. In this course we introduce some of the key models and modelling methods. The choice of material to be covered inevitably reflects the research interests of the lecturers involved, and will be particularly valuable as an introduction to their research areas, but it will also provide a useful introduction for anyone who wants to go on to a career in the any of the many other areas of modern biological science where mathematical modelling is becoming important.
WHO IS INTERESTED:
Students who want to consider a career working with mathematics in modern biology or ecology will find this course provides useful background. More generally, all students who want to gain an appreciation of the way mathematics can be used to model phenomena in the real world should find this course interesting.
WHAT DO I NEED:
The formal prerequisite for the course is minimal, namely MATH1051. However, a considerable degree of scientific maturity will be expected, given that this is a Level 3 course. Prior study in any or all of MATH1052, 2100, 2200, 2210, and STAT1201 or 2003 will provide useful further background, but is not essential. During the course you will be expected to learn more about programming in MATLAB, beyond what is in MATH1051; to learn something about modelling with ordinary and partial differential equations, as well as difference equations and information theory; and to acquire a general understanding of relevant biological processes. The class is typically quite heterogeneous, with some students having stronger backgrounds in some areas than in others, so an unusually high degree of interaction within the class may occur.
WHEN IS IT AVAILABLE:
MATH3104/7134 is offered in first semester every year.
