Overview

Lecturer: Professor C M Hull FRS

The course will use examples from mechanics, quantum theory, electromagnetism, general relativity and gauge theory to illustrate these ideas and their application in physics.

Manifolds
The idea of a manifold. Tangent vectors, vector fields and flows. Differential forms and exterior calculus. Differential forms and exterior calculus. 

Integration, Stokes' Theorem and Cohomology
Integration of differential forms. Stokes' theorem. Cohomology and de Rham's theorem.

Riemannian Geometry
Volume forms and non-coordinate bases. The Hodge star. Connections, covariant differentiation, torsion and curvature. Cartan's structure equations. 

Fibre bundles
The idea of a bundle. Vector and principle bundles.


Lecture notes & reading


Examples


Rapid Feedback Sessions

There will be a number of rapid feedback sessions, run by David Tennyson.

These start on 25 October at 12pm and are listed on the following timetable: 2018-19 Term 1

In these, the problems from the examples sheets will be gone over.

If you want your work on the problem sheets marked, please hand your answers in to David by 6pm 2 days before the class; for the first class, they should be handed in by 6pm on Tuesday 23 October. They should be placed in a basket in his office, which is H512.

 These classes are also an opportunity to ask questions and go over any parts of the course, or you want to see further explanation. If there are particular topics you would like covered in the class, please email David at d.tennyson16@imperial.ac.uk in advance so that he can prepare something.


Past papers

  • View past exam papers here. Important: Course material has changed so the content of past papers from 2012 and before is not representative of this year's course. In particular, Lie groups and homology are no longer part of the course.