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Key information

  • Module code:


  • Level:


  • Semester:


  • Credit value:


Module description


Definition and examples of topological spaces and manifolds; functions between manifolds; the tangent space; the tangent bundle; vector fields; Lie derivatives; tensor fields; differential forms; exterior calculus; integration on manifolds; affine connections; torsion; curvature; covariant derivatives; parallel transport; manifolds with metrics; the Levi-Civita connection. If time permits, additional topics such as de Rham cohomology will be discussed.


Knowledge of multivariate calculus, basic linear algebra and topology is sufficient. You are advised to have taken 5CCM211A and 5CCM226A Metric Spaces and Topology. 

Assessment details

2 hour written examination.

Semester 1 only students will be set an alternative assessment in lieu of in-person exams in January.

Full year students will complete the standard assessment.

Educational aims & objectives

The module aims to provide an introduction to differential geometry both for students whose interests are in pure mathematics and for those who are studying theoretical physics and other areas of applied mathematics. The basic objects of study are manifolds, which allow one to translate familiar ideas from vector calculus to curved space. Applications to topology and theoretical physics will be discussed as time allows.

Teaching pattern

Two hours of lectures and one hour of tutorial per week throughout the term

Suggested reading list

Indicative reading list - link to Leganto system where you can search with module code for lists

Module description disclaimer

King’s College London reviews the modules offered on a regular basis to provide up-to-date, innovative and relevant programmes of study. Therefore, modules offered may change. We suggest you keep an eye on the course finder on our website for updates.

Please note that modules with a practical component will be capped due to educational requirements, which may mean that we cannot guarantee a place to all students who elect to study this module.

Please note that the module descriptions above are related to the current academic year and are subject to change.