Dr Mauro Mobilia
Associate Professor
Applied Mathematics

                            


                                                                                                                                                     
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           





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Teaching qualification: University of Leeds Teaching Award Professional Standard 2 and Fellow of The Higher Education Academy (FHEA)


MATH3567: Evolutionary Modelling & MATH5567M: Advanced Evolutionary Modelling (Jan-May 2018)

General information on MATH3567/5567M: here and on the VLE

Objectives of the courses: Darwin’s natural selection paradigm is a cornerstone of modern evolutionary biology and ecology. Darwinian ideas have applications in social and behavioural science, and have also inspired research in the mathematical and physical sciences. In the last decades, mathematical analysis and theoretical modelling have led to tremendous progress in the quantitative understanding of evolutionary phenomena. Yet, many questions of paramount importance, like the “origin of cooperative behaviour” or “what determines biodiversity”, are subjects of intense research and their investigation requires advanced mathematical and computational tools. The students of the co-taught MATH3567/MATH5567M modules will be exposed to fundamental ideas of evolutionary modelling. These will be introduced through influential models and paradigmatic examples that will be analysed by a combination of methods drawn from the theory of nonlinear dynamics and stochastic processes. The students of these modules will thus be introduced to some areas of applied mathematics that currently give rise to exciting new developments and prominent challenges in mathematical biology and in evolutionary dynamics.

Provisional schedule:
1. Introduction to evolutionary modelling; 2. Modelling with difference equations;  3. Modelling with ordinary differential equations; 4. Introduction to Mendelian genetics; 5. Introduction to game theory; 6. Evolutionary games; 7. Random processes: Discrete-time Markov chains; 8. Random processes: Continuous-time Markov chains 9. Evolutionary game theory in finite populations; 10. Diffusion theory (Fokker-Planck); 11. Application of diffusion processes to population genetics.

Course Resources: Handouts, Questions and Solutions will be available on the VLE



MATH0380: Foundation Applied Mathematics for Business (Jan-May 2018)

Syllabus:
- Graphs of linear equations, elimination methods, supply and demand analysis
- Linear programming.
- Percentages, compound interest, discounting, geometric series, AER
- Addition, subtraction and multiplication of matrices
- The inverse of a matrix
- Evaluation of determinants
- Eigenvalues of a matrix
- Linear difference equations, simple economic models

Practice questions will come here