Undergraduate Programme and Module Handbook 2012-2013 (archived)
Module MATH3331: GENERAL RELATIVITY III
Department: Mathematical Sciences
MATH3331: GENERAL RELATIVITY III
| Type | Open | Level | 3 | Credits | 20 | Availability | Available in 2013/14 and alternate years thereafter | Module Cap | None. | Location | Durham |
|---|
Prerequisites
- Analysis in Many Variables II (MATH2031) AND ( Mathematical Physics II (MATH2071) OR Foundations of Physics 2A (PHYS2581) ).
Corequisites
- None.
Excluded Combination of Modules
- General Relativity IV (MATH4051).
Aims
- To appreciate General Relativity, one of the fundamental physical theories.
- To develop and exercise mathematical methods.
Content
- (1) Difference between general and special relativity.
- Experiments showing up the differences.
- Gravity becomes geometry.
- (2) Differential manifold as model of spacetime.
- Coordinates and relations between different systems.
- Curves in spacetime.
- (3) Covariant derivative.
- Partial derivatives are inadequate.
- Properties (linearity, derivative of tensor product, commutation with contraction).
- Geodesic curves.
- Metric connection.
- (4) Distance relations, shape units, light cones, locally inertial coordinate systems.
- Variational principles for geodesics.
- (5) Curvature tensor.
- Symmetries of curvature tensor.
- Einstein tensor.
- Geodesic deviation.
- (6) Newtonian gravity and Einstein's Theory.
- Linear form of Einstein's theory.
- (7) Schwarzschild solution, blackholes with Kruskal-Szekeres coordinates.
- (8) Cosmology.
Learning Outcomes
Subject-specific Knowledge:
- By the end of the module students will: be able to solve complex, unpredictable and specialised problems in General Relativity.
- have an understanding of specialised and complex theoretical mathematics in the field of General Relativity.
- have mastered a coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas: Special relativity.
- Differential manifolds.
- Metric, covariant derivative, curvature.
- General relativity.
- Black holes.
- Cosmology.
Subject-specific Skills:
- Students will have highly specialised and advanced mathematical skills which will be used with minimal guidance in the following ares: spatial awareness, modelling.
Key Skills:
- Students will have enhanced problem solving skills.
Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module
- Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
- Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
- Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
- The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.
Teaching Methods and Learning Hours
| Activity | Number | Frequency | Duration | Total/Hours | |
|---|---|---|---|---|---|
| Lectures | 40 | 2 per week for 19 weeks and 2 in term 3 | 1 hour | 40 | |
| Preparation and Reading | 160 | ||||
| Total | 200 |
Summative Assessment
| Component: Examination | Component Weighting: 100% | ||
|---|---|---|---|
| Element | Length / duration | Element Weighting | Resit Opportunity |
| three-hour written examination | 3 hours | 100% | |
Formative Assessment:
Four written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.
■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University