Module code: MATM060

Module Overview

This module introduces the basic concepts and techniques of Einstein’s Special and General Relativity.

Module provider


Module Leader

GUTOWSKI Jan (Maths)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 7

Module cap (Maximum number of students): 30

Overall student workload

Independent Learning Hours: 106

Lecture Hours: 33

Tutorial Hours: 11

Module Availability

Semester 1

Prerequisites / Co-requisites

MAT1036 Classical Dynamics and MAT2011 Linear PDEs.

Module content

This module is divided into three parts:
• Part I: Basics of Special Relativity (such as Minkowski space, Lorentz transformations, and consequences)
• Part II: Basics of semi-Riemannian geometry (such as manifolds, metrics, connections, geodesics, torsion, and curvature)
• Part III: Basics of General Relativity (such as Einstein's field equations, Einstein-Hilbert action, Schwarzschild solution and applications)

Assessment pattern

Assessment type Unit of assessment Weighting
Examination Examination 80
School-timetabled exam/test In-Semester Test 20

Alternative Assessment


Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

That they have learned the basic material in the field, and are able to apply it to examples and problems.

The summative assessment for this module consists of:

• In-Semester Test that constitutes 20% of the final mark;
• Final Examination that constitutes 80% of the final mark.

Formative assessment and feedback:

The students will be given exercise sheets on a regular basis, and it will be suggested that they work through the examples as part of their independent study. This will aid the students with the development of mathematical technique and knowledge. The students will receive feedback on their work in tutorials.

There will be two pieces of unassessed coursework, one early in the semester to help the students prepare for the first in-semester test, the other close to the end of the semester to help them prepare for the second in-semester test. The students will receive detailed feedback on this work in the tutorials.

Module aims

  • The module aims at equipping the students with fundamental knowledge of the concepts of Einstein's theory of gravity.

Learning outcomes

Attributes Developed
001 Demonstrate a thorough understanding of special and general relativity, their postulates and assumptions, and their consequences
002 Master all the mathematical tools underlying general relativity such as differential geometry and pseudo-Riemannian geometry, and be able to perform explicit calculations as well as be able to prove basic statements in these areas
003 Demonstrate a deep understanding of the mathematical formulation of general relativity including the associated variational principle and be able to derive the Newtonian limit
004 Derive solutions of Einstein’s field equations and be able to discuss and analyse in detail their qualitative and quantitative implications for the structure of space-time

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:
• A detailed introduction to Special Relativity, Differential Geometry, and General Relativity
• Experience (through demonstration) of the methods used to interpret, understand and solve problems in Relativity

The learning and teaching methods include:
• 3 x 1 hour lectures per week x 11 weeks interspersed with tutorials when appropriate for 11 weeks, with lecture notes provided;
• Learning is by lectures, exercise sheets and tutorials, coursework, and background reading.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Reading list
Upon accessing the reading list, please search for the module using the module code: MATM060

Other information


Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2019/0 academic year.