Undergraduate Programme and Module Handbook 2011-2012 (archived)
Module MATH3331: GENERAL RELATIVITY III
Department: Mathematical Sciences
MATH3331:
GENERAL RELATIVITY III
Type |
Open |
Level |
3 |
Credits |
20 |
Availability |
Available in 2011/12 and alternate years thereafter |
Module Cap |
None. |
Location |
Durham
|
Prerequisites
- Analysis in Many Variables II (MATH2031) and Mathematical
Physics II (MATH2071); OR Analysis in Many Variables II (MATH2031) and
Foundations of Physics II (PHYS2511).
Corequisites
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
- 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.
- Students will have highly specialised and advanced
mathematical skills which will be used with minimal guidance in the
following ares: spatial awareness, modelling.
- 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% |
|
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