MATH4105/7105: General Relativity

Course Profile

Course Profile for MATH4105/7105 - General Relativity

2nd Semester, 2004

Brief Description (the first half)

This course is jointly taught with Physics. The first half of the course deals with mathematical aspects of General Relativity. It will introduce the basic mathematical tools: pseudo-Riemannian spaces; tensors; covariant differentiation; geodesics; curvature; Bianchi identities; Ricci, Einstein and Weyl tensors. In the second half, these mathematical tools will be used to describe and understand several observable examples of General Relativity in the Universe.

Staff (Course Coordinators):

Lecturers and Contact Details

You are welcome to ask any questions about the course during consultation hours.
If you have questions about your current or future program of study, contact the chief academic advisor , honours coordinator or postgraduate coordinator .

Web Page: The course profile and course material can be found on the web at the following address: Addtitional material for the second part of the course is at:

Class Contact Hours and Venue: 2 units, 3L, 1T

See also SI-net for class contact hours and venue for possible changes.

Assumed Background

Course Goals/Objectives

Graduate Attributes

The following graduate attributes will be developed in the course -

  1. In-Depth Knowledge of the Field of Study

  2. Effective Communication

    • The ability to collect, analyse, and organise information and ideas, and to convey those ideas clearly and fluently, in both written and spoken forms: - through tutorial participation.
    • The ability to interact effectively with others in order to work towards a common outcome: - through cooperative learning strategies in tutorials.
    • The ability to select and use the appropriate level, style and means of communication: - through assignments.
    • The ability to engage effectively and appropriately with information and communication technologies: - through practical use of pen, ink, and computers.
  3. Independence and Creativity

    • The ability to work and learn independently.
    • The ability to generate ideas and adapt innovatively to changing environments.
    • The ability to identify problems, create solutions, innovate and improve current practices.
  4. Critical Judgement

    • The ability to define and analyse problems.
    • The ability to apply critical reasoning to issues through independent thought and informed judgement.
    • The ability to evaluate opinions, make decisions and to reflect critically on the justifications for decisions.
  5. Ethical and Social Understanding

    • An appreciation of the philosophical and social contexts of the discipline.
    • A knowledge and respect of ethics and ethical standards in relation to a major area of Study: - through the experience of a discipline where the concepts of right and wrong are supported by universal and absolute standards.
    • A knowledge of other cultures and times and an appreciation of cultural diversity: - through tutorial participation in a subject taken by students with diverse backgrounds and interests.

For more information on the University policy on development of graduate attributes in courses, refer to the web

Teaching and Learning Methods

Students should attend all the lectures. In truth most people cannot follow immediately all the details of a mathematical lecture; but try to get at least a broad overview of the material. Afterwards work through the material carefully, using lecture notes (on the web) or the reference books. It is important to understand the examples discussed in lectures, and it is good idea to make sure you can do the examples by yourself with the solution covered up. Of course this does not mean memorizing the solution, rather it is a check that you understand the key steps involved.

Assignment sheets will be handed out in tutorials each week. The solutions to each assignment will also be handed out after its due date.

Resources (Textbook and References)



Below is the University's definition of plagiarism Plagiarism is the action or practice of taking and using as one's own the thoughts or writings of another (without acknowledgement). The following practices constitute acts of plagiarism and are a major infringement of the University's academic values:

When a student knowingly plagiarises someone's work, there is intent to gain an advantage and this may constitute misconduct. Students are encouraged to study together and to discuss ideas, but this should not result in students handing in the same or similar assessment work. Do not allow another student to copy your work. While students may discuss approaches to tackling a tutorial problem, care must be taken to submit individual and different answers to the problem. Submitting the same or largely similar answers to an assignment or tutorial problem may constitute misconduct. For more information on the University policy on plagiarism, please refer to

Supplementary examinations

New University assessment rules relating to supplementary examinations are accessible at the following URL: In general, the effect of this rule is to provide for one supplementary examination to a student in his or her final semester of enrolment where a passing grade is required to complete the program. There are, however, exceptions to this rule and transition rules for some cohorts of students. You should check the program rules for your degree program for information on the possible award of supplementary examinations. Applications for supplementary examinations must be made to the Director of Studies in the Faculty within 14 days of the publication of results.

Special examinations

If a student is unable to sit a scheduled examination for medical or other adverse reasons, she/he can and should apply for a special examination. Applications made on medical grounds should be accompanied by a medical certificate; those on other grounds must be supported by a personal declaration stating the facts on which the application relies. Applications for special examinations for central and end-of-semester exams must be made through the Student Centre. Applications for special examinations in school exams are made to the course coordinator.

Further Information

More information on the General Award Rules at the University can be found at

More information on the University's assessment policy may be found at

EPSA Faculty policy on the award of special and supplementary exams may be found at

Feedback on Assessment

You may request feedback on assessment in this course progressively throughout the semester from the course coordinator. Feedback on assessment may include discussion, written comments on work, model answers, lists of common mistakes and the like. ( )

Students may peruse examinations scripts and obtain feedback on performance in a final examination provided that the request is made within six months of the release of final course results. After a period of six months following the release of results, examination scripts may be destroyed.

Information on the University's policy on access to feedback on assessment may be found at

EPSA Faculty policy on feedback and re-marking may be found at

For a remark on the final exam (after viewing the exam on a viewing day), students are to complete a "Request for assessment re-marking form".

The link to the policy is

The form may be downloaded from there -- section 3.6 of the policy at

Students with Disabilities

Any student with a disability who may require alternative academic arrangements in the course is encouraged to seek advice at the commencement of the semester from a Disability Adviser at Student Support Services.

Assistance for Students

Students with English language difficulties should contact the course coordinator or tutors for the course. Students with English language difficulties who require development of their English skills should contact the Institute for Continuing and TESOL Education on extension 56565.

The Learning Assistance Unit located in the Relaxation Block in Student Support Services. You may consult learning advisers in the unit to provide assistance with study skills, writing assignments and the like. Individual sessions are available. Student Support Services also offers workshops to assist students. For more information, phone 51704 or on the web

Student Liaison Officer

The School of Physical Sciences has a Student Liaison Officer as an independent source of advice to assist students with resolving academic difficulties.

The Student Liaison officer will be Assoc Prof Peter Adams, Room 547 Priestley building, (email

Course Schedule: Program of Work for the Semester

The following list of topics is intended as a guide only. It is not a strict list of topics in order, and may be varied at times as the semester proceeds.
  1. First half: Mathematical tools
  2. Second half: Astrophysical applications

Information Changes

MATH4105/7105 Web Page.