The module has two distinct aspects. First, in a set of lectures and problem solving classes, we develop knowledge and skills over a range of methods of complex analysis used in theoretical physics. This includes integration in the complex plane, analytical continuation, Green functions methods and using complex variables to derive and study special functions. This part of the module is assessed via five assessed problem sheets. Then in parallel, staff will give a series of seminars on the results of recent research. In recent years this has covered topics such as gauge theories, monopoles, quantum computing and quantum vortices. Students are then asked to develop understanding on a topic related to one of the seminars via directed reading.

By the end of the module the student should be able to:

• Use complex variables for calculating definite integrals;
• use Green functions to solve inhomogeneous partial differential equations;
• appreciate some of the most recent advances in theoretical physics;
• display an awareness of the nature of some of the important unsolved problems;
• be able to use LaTeX;
• be able to create a simple webpage;
• be able to give an aural presentation of a research topic.