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MA999: Fundamentals of Mathematical Modelling (15 Cats)

Module leader: Yulia Timofeeva (Computer Science)

Module Aims

This is a core module for the Mathematics for Real-World Systems II CDT. The aim is to introduce students to cutting-edge topics in mathematical modelling that cover the application areas of the CDT: biomedical science, epidemiology, socio-technical systems, and industrial processes and optimization. The topics covered will be used as examples to illustrate fundamental modelling approaches, in particular multiscale modelling and hybrid modelling, which bridges the divide between a-priori and data-driven methods .

Syllabus

The module consists of 4 sets of lecture series by staff (2 weeks each) related to the CDT on Mathematics for Real-World Systems. The module will provide practical examples of the two research themes of the MathSys II CDT: (1) Multiscale Modelling and (2) Hybrid Modelling. These will be demonstrated using practical examples taken from the application areas of the CDT: quantitative biomedical research, mathematical epidemiology, socio-technical systems and advanced modelling and optimisation of industrial processes. Students will learn how to relate and apply the skills learned in the first-term core modules and understand how the various theoretical methodologies can be used to solve real-world problems. The concepts utilised will include: symmetries and constraints, phase transitions, stochastic and deterministic modelling, data-driven modelling, agent-based modelling, course graining, non-linearities and bifurcations and probability.

Illustrative Bibliography

Recent research papers in the field of the 4 lecturers will be made available before the module starts.

Teaching

See main calendar for timetable

  • Per week: 3 hours of lectures, 1 hour of classes
  • Duration: 10 weeks (term 2)

Assessment

For deadlines see Module Resources page.

  • Written homework assignments (20%)
  • Written class test (80%)