This course will introduce and develop a number of classical (and some not so classical) methods in mathematical physics, building on the third year courses on complex variables and mathematical physics.

Part 1. Advanced Complex Methods:

• 1.1. Integral representations and complex differential equations.
• 1.2. The hypergeometric equation and hypergeometric functions.
• 1.3. The hydrogen atom

Part 2. Advanced Greens Function Methods:

• 2.1. From integrals to path integrals
• 2.2. Lies, damn lies and statistical mechanics
• 2.3. Perturbation theory - size matters
• 2.4. Correlation functions - 1, 2, 3, many
• 2.5. Topology and integrals Part

3. Advanced other things:

• 3.1. Grassman variables - who ordered that?
• 3.2. Statistical systems in and out of equilibrium
• 3.3. The Ising on the cake - a 2-dimensional solvable system.