Differential Geometry
| Code | School | Level | Credits | Semesters |
| MATH4015 | Mathematical Sciences | 4 | 20 | Autumn UK |
- Code
- MATH4015
- School
- Mathematical Sciences
- Level
- 4
- Credits
- 20
- Semesters
- Autumn UK
Summary
The module introduces a number of tools of differential geometry, including manifolds, symmetries, Lie Groups and Lie algebras, differentiation and integration on manifolds.
Target Students
Single and Joint Honours students from the School of Mathematical Sciences. Mathematical Physics students. MSc students on the Gravity, Particles and Fields programme.
Classes
- Three 1-hour lectures each week for 11 weeks
Assessment
- 100% Exam 1 (3-hour): Written exam
Assessed by end of autumn semester
Educational Aims
The course introduces notions of topology and differential geometry which are required for modern research in gravity and other topics involving geometry.Learning Outcomes
A student who completes this course successfully will be able to:
L1 - perform computations involving differential forms, tangent vectors and tensors on manifolds;
L2 - describe mathematical concepts related to topology, manifolds, and Lie groups;
L3 - apply general results such as Stokes Theorem and the rank theorem to particular examples;
L4 - construct submanifolds and give examples of Lie groups and Lie algebras;
L5 - compute the Lie derivative of a tensor.