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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Mathematical Biology (MATH10013)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThis 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.
Course description 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, lectures or screencasts on assigned reading will be augmented through (formal and informal) collaborative discussion, thus implementing a "flipped classroom" setting. Real-time workshops will involve group-based activities to cement concepts, and expand on applications introduced in lectures or screencasts. Opportunities for practice will be provided through worksheets, online quizzes,and biweekly written homework. Additional live support will be available through regularly scheduled drop-in office hours.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Honours Differential Equations (MATH10066) AND Honours Complex Variables (MATH10067)
Prohibited Combinations Other requirements None
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Academic year 2020/21, Available to all students (SV1) Quota:  None
Course Start Semester 1
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 5, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 69 )
Assessment (Further Info) Written Exam 60 %, Coursework 40 %, Practical Exam 0 %
Additional Information (Assessment) The course will be assessed 60% on a final examination and 40% on coursework; the coursework component will consist of biweekly written homework (20%), weekly online quizzes (15%), and an end-of-semester reflection (5%).
Feedback Individual feedback will be provided on homework in writing and orally, in office hours; automated feedback will be given on online quizzes; collective feedback will be given through screencasts, workshops, discussion boards, and worked solutions.
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S1 (December)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Critique and adapt standard dynamical models in mathematical biology, and interpret them in the context of the modelled biological phenomena.
  2. Analyse the qualitative dynamics of these models, with a particular focus on biological oscillation, switching phenomena, and pattern-forming mechanisms.
  3. Apply dynamical systems techniques, such as geometric singular perturbation theory, to difference and differential equation models from mathematical biology.
  4. Evaluate and extend examples studied in the course to solve unseen assignments that illuminate significant concepts in mathematical biology.
  5. Undertake unsupervised reading of course-relevant material, and demonstrate an understanding of key concepts from mathematical biology.
Reading List
1.J.D. Murray. Mathematical Biology I: An Introduction. (Interdisciplinary Applied Mathematics.) Springer-Verlag, 2007.
2.L. Edelstein-Keshet. Mathematical Models in Biology. (Classics in Applied Mathematics.) Society for Industrial and Applied Mathematics, 2005.
3.F. Brauer and C. Castillo-Chavez. Mathematical Models in Population Biology and Epidemiology. (Texts in Applied Mathematics.) Springer-Verlag, 2012.
Additional Information
Graduate Attributes and Skills Not entered
Course organiserDr Nikola Popovic
Tel: (0131 6)51 5731
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
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