This course aims to present a historical development of the subject area, leading to a significant partial proof of Fermat’s Last Theorem.

This course aims to introduce students to classical and quantum mechanics by means of a mathematically rigorous approach. In the first part of the course we shortly introduce Newtonian mechanics and develop Lagrangian and Hamiltonian mechanics on manifolds with a particular emphasis on the underlying variational principles.  The second part introduces Quantum Mechanics in an axiomatic way and is focused on the study of  the spectral properties of the Schrödinger Hamiltonian for different classes of potentials.

Poetically, “Group theory is the branch of mathematics that answers the question “What is symmetry?” (N. C. Carter).  Various physical systems, such as crystals and the hydrogen atom, can be modeled by symmetry groups. Group theory and the closely related representation theory have many applications in physics and chemistry. We first start by consider some main classes of groups such as permutation groups, matrix groups, transformation groups, topological and algebraic groups.

This course aims to introduce students to the fundamental concepts requiring for the description, modeling and forecasting of the time series data.

This course develops the ideas underlying modern, measure-theoretic probability theory, and introduces the various classes of stochastic process, including Markov chains, jump processes, Poisson processes, Brownian motion and diffusions. Their properties and applications are investigated.

This course aims at introducing students to methods of analyzing multivariate data. It introduces students to the notion of principal components factor analysis, various multivariate distributions, analysis of variance, multivariate analysis of variance (MANOVA), multivariate regression and multidimensional scaling and cluster analysis. At the end of the course students would have also considerably improved their knowledge of applied linear algebra and matrix theory and to be somewhat competent with at least one statistical software package.

Each student will work on a mathematical project under the supervision of a faculty member. The project will culminate in an oral presentation to the Department of Mathematics. The topic of the project will agreed upon by the student and supervisor.

This course examines metric and topological spaces, continuity, completeness, and compactness, providing a theoretical foundation for further work in differential equations, probability theory, stochastic processes, differential geometry and mathematical physics.

The course develops the properties of the complex number system, treated as a generalisation of the real number system. We explore the parallel analysis that results, with a particular emphasis on differentiability, analyticity, contour integrals, Cauchy’s  theorem, Laurent series representation, and residue calculus.

This course considers the limitations of the Riemann integral, and shows that it it necessary to develop a precise mathematical notion of ‘length’ and ‘area’ in order to overcome them. Thus we develop the concept of measure, and use it to construct the more powerful Lebesgue integral, and explore its properties. Finally we look at applications of measure and Lebesgue integration in modern probability theory.