MATH4411: Advanced Mathematical Biology IV

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

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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 stochastic models, stochastic differential equations and stochastic simulation algorithms.
• Discrete-to-continuum approaches connecting individual-based and stochastic models.
• Applications to problems in ecology, epidemiology, and population biology.
• Continuum mechanical of biological media, including viscous and ciscoelastic fluids and solids; examples include blood, saliva, DNA, semen, mucus, and proteins.

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 examples from real-world applicatons.

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.
• 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 students progress.
• The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

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