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MATH3171: MATHEMATICAL BIOLOGY III

Please ensure you check the module availability box for each module outline, as not all modules will run in each academic year. Each module description relates to the year indicated in the module availability box, and this may change from year to year, due to, for example: changing staff expertise, disciplinary developments, the requirements of external bodies and partners, and student feedback. Current modules are subject to change in light of the ongoing disruption caused by Covid-19.

Type Open
Level 3
Credits 20
Availability Available in 2023/24
Module Cap
Location Durham
Department Mathematical Sciences

Prerequisites

  • Analysis in Many Variables II (MATH2031)

Corequisites

  • None.

Excluded Combinations of Modules

  • None.

Aims

  • Study of non-linear differential equations in biological models, building on level 1 and 2 Mathematics.

Content

  • Introduction to application of mathematics to biological systems and environments.
  • Core applied modelling techniques such as stability analysis, weakly non-linear analysis, travelling wave solutions.
  • ODE models in biology.
  • Reaction diffusion equations.
  • Pattern formation in nature: Turing analysis.
  • Examples taken from the following: diffusion of insects and other species; the formation of spiral wave patterns in nature; hyperbolic models of insect dispersal and migration of a school of fish; glia aggregation in the human brain and possible connection with Alzheimer's disease; enzyme kinetics; the chemostat for bacteria production; branching growth of organisms; modelling the life cycle of the cellular slime mold Dictyostelium discoideum, and the phenomenon of chemotaxis; epidermal and dermal wound healing; epidemic models and the spatial spread of infectious diseases.

Learning Outcomes

Subject-specific Knowledge:

  • By the end of the module students will: be able to solve novel and/or complex problems in Mathematical Biology.
  • have a systematic and coherent understanding of theoretical mathematics in the fields Mathematical Biology.
  • have acquired coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas:
  • Models for diffusion of insect populations.
  • Formation of spiral wave patterns.
  • Mathematics of enzyme kinetics.
  • Mathematics of the Chemostat.
  • Chemostaxis and coalgulation of species.
  • Pattern formation mechanisms.
  • Spread of infectious diseases.

Subject-specific Skills:

  • In addition students will have specialised mathematical skills in the following areas which can be used with minimal guidance: Modelling.

Key Skills:

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

  • Lectures develop technical ideas and methodology and introduce motivating examples.
  • Solution by students of problems in written assignments as part of formative assessment deepens and tests understanding of technical material and helps to develop modelling skills.
  • Students will also be expected on occasion to find additional material from the Internet.
  • Summative assessment by examination measures degree of technical mastery, grasp of basic ideas in modelling and skill carrying through necessary calculations.

Teaching Methods and Learning Hours

ActivityNumberFrequencyDurationTotalMonitored
Lectures422 per week for 20 weeks and 2 in term 31 Hour42 
Problems Classes8Four in each of terms 1 and 21 Hour8 
Preparation and Reading150 
Total200 

Summative Assessment

Component: ExaminationComponent Weighting: 100%
ElementLength / DurationElement WeightingResit Opportunity
Written examination3 Hours100 

Formative Assessment

Eight written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

More information

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