Mathematical Biology (MATH10013)
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This course presents an introduction to mathematical biology, with a focus on dynamical (difference and differential equation) models and their interpretation in the context of the modelled biological phenomena. The utility of these models will be showcased in a variety of applications which may include population biology, gene expression, mathematical physiology, enzyme kinetics, virus dynamics, and neuronal modelling.Substantial use will be made of ordinary differential equations and, to a lesser extent, of complex variables; the course hence builds on Honours Differential Equations (MATH10066) and Honours Complex Variables (MATH10067).A suggested syllabus for the course is as follows. Continuous and discrete population models. Perturbations and bifurcations. Interacting populations. Oscillators and switches. Chemical reaction kinetics. Disease dynamics. Reaction-diffusion equations. Waves and fronts. Spatial patterns.
The history of mathematical biology dates back at least to the 1100s, when Fibonacci described the growth of rabbit populations in terms of what is now known as Fibonacci series. Early applied mathematicians focussed mostly on the modelling of population and disease: in the 1700s, Bernoulli modelled the spread of smallpox, while Malthus popularised the concept of exponential growth. Applications in evolutional ecology followed in the 1800s, when Müller investigated mimicry in light of natural selection, thus influencing the later works of Darwin.The field of mathematical biology has since grown considerably, and diverged into a number of specialised areas beyond the traditional ones of ecology and epidemiology. Mathematical modelling has become an indispensable tool in the biomedical sciences as the latter have become increasingly quantitative; in that sense, mathematical biology is a truly interdisciplinary discipline. The focus of this course will be on practical applications of dynamical models which take the form of difference or (ordinary and partial) differential equations. The applications covered may include Michaelis-Menten enzyme kinetics, front propagation in reaction-diffusion equations, competition in predator-prey systems, expression in gene regulatory networks, the dynamics of disease, or relaxation oscillation in the FitzHugh-Nagumo model.Depending on the mode of delivery, live (synchronous) lectures or (asynchronous) screencasts on assigned reading will be augmented through (formal and informal)collaborative discussion, thus implementing a flipped classroom setting. Live workshops will encourage peer interaction to cement concepts and expand on applications introduced in lectures or screencasts. Opportunities for independent practice may be provided through worksheets, online quizzes, and written homework.
Written Exam 60%, Coursework 40%, Practical Exam 0%
Additional Assessment Information
The course will be assessed 60% on a final examination and 40% on coursework. The coursework component may consist of written homework, online quizzes, a written essay, or collaborative reading; specifics will be confirmed in time for the upcoming instance of the course.
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