Undergraduate

modules

Modules

MAS3804 : Relativity and Cosmology

Semesters
Semester 1 Credit Value: 10
ECTS Credits: 5.0

Aims

To introduce the concept of spacetime, the theory of special relativity and some preliminary ideas from general relativity. To introduce basic ideas from cosmology and the mathematical model of the expanding universe.

Module Summary

An introduction to spacetime in Special Relativity and Cosmology.

Outline Of Syllabus

Starting from situations such as GPS navigation, where the velocity of light plays an important role, we explore ideas on the fundamental nature of space and time which form the basis of the theory of special relativity.

Lorentz transformations will be introduced and used to explain length contraction and time dilation. Definitions of energy and momentum will lead to the correct version of the famous formula E=mc^2 and Newtonian dynamics will be generalized to be consistent with Special Relativity. The module focuses on a four-dimensional description of special relativity based on spacetime and 4-vectors, and will be making use of the Minkowski line element. The concept of a line element describing geometry will be briefly introduced.

Special Relativity no longer applies in the presence of gravity which requires the theory of General Relativity. We will introduce the equivalence principle as the physical basis of General Relativity and study the line element of weak gravitational fields. The basic mathematical structure of General Relativity will be briefly described.

Cosmology: The aim of cosmology is to construct a mathematical model of the universe. Observational evidence suggests that the universe is an evolving system. General relativity allows the construction of models in the form of ordinary differential equations, which can describe the universe from its origin at the big bang to the present day. The module ends with an elementary exposition of these equations and their consequences.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture11:001:00Class test
Scheduled Learning And Teaching ActivitiesLecture31:003:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture251:0025:00Formal lectures
Guided Independent StudyAssessment preparation and completion16:006:00Revision for class test
Guided Independent StudyAssessment preparation and completion113:0013:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:002:00Unseen exam
Guided Independent StudyIndependent study127:0027:00Studying, practising, and gaining understanding of course material
Guided Independent StudyIndependent study33:009:00Review of coursework assignments and course test
Guided Independent StudyIndependent study26:0012:00Preparation for coursework assignments
Total100:00
Jointly Taught With
Code Title
PHY3022Relativity and Cosmology
MAS8804Relativity and Cosmology
Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
Written Examination1201A90N/A
Written Examination401M5Class test
Exam Pairings
Module Code Module Title Semester Comment
PHY3022Relativity and Cosmology1N/A
MAS8804Relativity and Cosmology1N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M5Written assignments
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. Two written assignments of equal weight and one class test allow the students to develop their problem solving techniques, to practice the methods learnt in the module, to assess their progress and to receive feedback; this is thus formative as well as summative assessment.

Reading Lists

Timetable