Professor
Mauro
Mobilia
Applied Mathematics |
|
Teaching
qualification:
University of
Leeds Teaching Award Professional Standard 2 and Fellow of
The Higher Education Academy (FHEA)
Course
Resources: Lecture Notes, Example Sheets and Solutions available on Minerva/VLEMATH0390: Foundation Pure and Applied Mathematics (Oct-Dec 2019) General information on MATH0390: here and on Minerva/VLE Syllabus: 1. Linear and quadratic relations: Equations for straight lines; intersection of two lines. Linear relations to model socio-economic scenarios: supply and demand; equilibrium price. Quadratic relations and revenue optimisation. 2. Indices and powers: Index laws; examples and applications. 3. Exponential and logarithm functions: Definition and graphs of exponential functions; the number e and its exponential; definition and graphs of logarithm functions. Logarithm laws and relationship between exponential and logarithm functions; applications. 4. Percentages, geometric series, and applications to interest & savings: Percentages. Simple and compound interest; discounting. Geometric series and application to regular savings. 5. Differentiation and applications: Differentiation from first principles and slope (gradient) of a curve. Tangents and normals to a curve. Maxima and minima of a function; stationary and turning points; distinguishing maxima and minima; application to profit maximisation. 6. Integration and applications: Integration as the reverse of differentiation, indefinite integral. Integration as a summation; definite integral and area under the graph; application to consumer surplus. |
MATH3567/MATH5567M: (Advanced) Evolutionary Modelling (Jan-May 2020) General information on MATH3567/5567M: here and on Minerva/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.
Course
Resources: Handouts, Questions and Solutions will be available on Minerva/VLEProvisional 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. |