MATH44020: Advanced Mathematical Biology

• Analysis in Many Variables and Mathematical Biology

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• 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.

• 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.

Subject-specific Knowledge:

• By the end of the module, students will:
• Be able to formulate models of complex biological scenarios, and be able to analyze 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.

• Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
• 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 students progress.
• The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

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

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