Undergraduate Programme and Module Handbook 2023-2024 (archived)

# Module MATH4411: Advanced Mathematical Biology IV

## Department: Mathematical Sciences

### MATH4411: Advanced Mathematical Biology IV

Type | Open | Level | 4 | Credits | 20 | Availability | Available in 2023/24 | Module Cap | None. | Location | Durham |
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#### Prerequisites

- Analysis in Many Variables II (MATH2031) AND Mathematical Biology III (MATH3171)

#### Corequisites

- None

#### Excluded Combination of Modules

- None

#### Aims

- To introduce key areas of modern mathematical modelling.
- To develop an understanding of mathematical models of biological phenomena at different scales.
- To prepare students for future research in Applied Mathematics and Theoretical Biology.

#### Content

- Individual-based models, stochastic simulation algorithms and stochastic resonance.
- Discrete-to-continuum approaches connecting individual-based and stochastic models (mean field theories, multiple-scales asymptotics).
- Applications to problems in population biology such as models of evolution under phenotype selection.
- Continuum mechanical descriptions of biological fluids:
- Non linear elastic phenomena: Expanding bodies and cell cavitation, biofilaments and cell membranes.
- Viscous and viscoelastic phenomena: blood, saliva, semen, mucus, and synovial fluid.

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module, students will:
- Be able to formulate models of complex biological scenarios, and be able to analyse such models in terms of biologically-interpretable predictions.
- Have a systematic and coherent understanding of the mathematical formulation behind individual-based and continuum-mechanical models in biology.
- Have acquired a coherent body of knowledge of modelling in mathematical biology through study of fundamental tools and many particular examples.

Subject-specific Skills:

- Students will develop specialised mathematical skills in mathematical modelling which can be used with minimum guidance.
- They will be able to formulate applied mathematical models for various situations.

Key Skills:

- Students will have basic mathematical skills in the following areas: problem solving, modelling, computation.

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

- Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
- Problem classes show how to solve example problems in an ideal way, revealing also the thought processes behind such solutions.
- Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
- Formatively assessed assignments provide practice in the application of logic and a high level of rigour as well as feedback for the students and the lecturer on the studentsâ€™ progress.
- The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

#### Teaching Methods and Learning Hours

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 42 | 2 per week in Michaelmas and Epiphany; 2 in Easter | 1 hour | 42 | |

Problems Classes | 8 | Fortnightly in Michaelmas and Epiphany | 1 hour | 8 | |

Preparation and Reading | 150 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 100% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

Examination | 3 hours | 100% |

#### 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.

â– Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University