# Masters Courses in Applied Mathematics

## Studying Applied Mathematics

Students enrolled in Master programme in mathematics can choose amongst a number of courses in applied mathematics. The courses can also be taken as single subject courses.

Applied mathematics courses equip the student with knowledge of mathematical modelling and the tools and techniquies needed to understand systems that display non-linear, stochastic, chaotic or complex behaviour. These tools are applicable in diverse contexts, including physics, biology and economy.

## Selected Courses

**Applied mathematics (5hp or 10hp):** dimension analysis and scaling; perturbation methods; calculus of variation; elementary partial differential equations; generalized Fourier series and Fourier's method; Hamiltonian theory; integral equations.

**Dynamical systems and ordinary differential equations:** We offer a range of course on dynamical systems, including basic courses on ordinary differential equations(I & II), a course on applied dynamical systemsand and an advanced course on chaos and dynamical systems.

**Financial mathematics (various courses):** Diffusion processes, stochastic integration and Ito calculus with applications to pricing financial instruments.

**Partial Differential Equations:** Introductory courses with classification and solution techniques relevant to physical models. Advanced courses with applications in finance and elsewhere.

**Mathematical biology:** The use of mathematical models in biology, ecology and evolution. Modelling tools include several variable calculus, ordinary and partial differential equations, and stochastic modelling.

**Modelling Complex Systems:** Tools from mathematics, physics and computer science used in understanding complex systems. Techniques include: random walks and diffusion approximations; Chaotic dynamical systems; Self-organized critical phenomena; Cellular Automata; and Models of flocking.

## Research Projects

The Centre for Interdisciplinary Mathematics offers Masters research projects (30hp) which cross the boundaries between mathematics and other disciplines.

Here are some examples of such projects:

**Modelling Group dynamics:** Animal groups, from ant colonies, through bird flocks to human societies, produce complex patterns of behaviour. We aim to understand how groups make informed decisions; how ecological interactions produce population dynamics; and other related questions using a combination of laboratory and field experiments, computer simulations and mathematical models.

**Stochastic Models in Molecular Biology:** Molecular processes within biological cells work on very different time scales and display dynamical behaviour ranging from stable steady states, bi-and multistability, to oscillations. Detailed data of how single molecules interact allows stochastic models to be fitted directly to data.

**Computer-Aided Proofs in Analysis:** Numerical simulations of shock waves in materials or chaotic weather dynamics suggest important properties of these systems, but fall short a mathematical proof. This research focuses on rigorously establishing such properties, as well as constructing algorithms to estimate system