MATH4105/7105: General Relativity
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):
- Drs. Yao-Zhong Zhang (Mathematics) and Michael Drinkwater
Lecturers and Contact Details
- For the first half: Dr Yao-Zhong Zhang.
- For the second half: Dr. Michael Drinkwater.
You are welcome to ask any questions about the course during consultation
If you have questions about your current or future program of study,
chief academic advisor
, honours coordinator or postgraduate coordinator .
The course profile and course material can be found on the
web at the following address: http://www.maths.uq.edu.au/~yzz/Profile_s2_04.html.
Addtitional material for the second part of the course is at: http://www.physics.uq.edu.au/people/mjd/lectures/math4105/.
Class Contact Hours and Venue: 2 units, 3L, 1T
See also SI-net for class
hours and venue for possible changes.
- Lectures: Tue 10-12am 67-341, Thu 4-5pm 67-342
- Tutorial: Wed 4-5pm 67-342
- A basic knowledge of vector and tensor analysis will be assumed. It is a
student's own responsibility to fill in any gaps in their assumed knowledge.
You may need to undertake background reading to understand the lecture
- Through working problems, the student will have the opportunity to
acquire a basic working knowledge of some important concepts, and
should have the background necessary for the second half of the course,
on Einstein's General Theory of Relativity.
The following graduate attributes will be developed in the course -
In-Depth Knowledge of the Field of Study
- A comprehensive and well-founded knowledge of the field of study: -
through solving problems.
- An understanding of how other disciplines relate to the field of study:
- through applying the mathematical techniques of the course to simple
problems from other disciplines..
- An international perspective on the field of study: - through using
internationally accepted standards of mathematical rigour and notation.
- 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
Independence and Creativity
- The ability to work and learn independently.
- The ability to generate ideas and adapt innovatively to changing
- The ability to identify problems, create solutions, innovate and improve
- 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.
Ethical and Social Understanding
- An appreciation of the philosophical and social contexts of the
- 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
- 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 http://www.uq.edu.au/hupp/contents/view.asp?s1=3&s2=20&s3=5.
Teaching and Learning Methods
- Three hours of lectures and one hour of tutorial per week.
- Lectures and Tutorials: See SI-net.
- There are no tutorials in week 1 and week 13.
- Public holidays: There are no lectures and tutorials on the public
- Examination period: Study week is November 1-7, 2004, Examination
period is 8-21 November, 2004.
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
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)
- Course Notes: Lecture notes must be taken in lectures.
- Text: There is no set textbook.
- References: The reference books for the first half are:
- C.T.J. Dodson & T. Poston, ``Tensor Geometry''.
(QA3.G7 No. 130)
- S. Weinberg, ``Gravitation and Cosmology''. (QC6.W47
- C.J. Isham, ``Modern Differential Geometry for
Physicists''. (QA641.I84 1989)
- M. Dubrovin, A.T. Fomenko & S.P. Novikov,
``Modern Geometry: Methods & Applications, Pt. 1.'' (QA3.G7. No. 93)
S. W. Hawking and G.F. R. Ellis, `` The Large
Scale Structure of Space-Time''. (QC173.59.S65H38 1973)
- J.L. Synge & A. Schild, ``Tensor Calculus''.
- References: The reference books for the second half are:
- C. Misner, K. Thorne and J. Wheeler ``Gravitation''
- S. Weinberg, ``Gravitation and Cosmology''. (QC6.W47
- B.F. Shutz, ``A First Course in General Relativity''
(QC173.6.S38 1985) (good)
- C.M. Will, ``Was Einstein Right?'' (QC173.6.W55
1986) (popular level)
- Library contact: The liaison librarian for Earth
Sciences/Maths/Physics is located in the Physical Sciences and Engineering
Library in the Hawken Building and may be consulted for assistance in the
course: Leith Woodall; Email: mailto:email@example.com;
- Required Assessment Tasks: The final examination will be worth 60%
of the final grade. The assignments will be worth 40% of the final grade.
- The due dates for assignments of the first half of the course are:
Dr. Drinkwater will announce the due dates for assignments of the
second half of the course.
- Assignment 1: due 5pm, Thu August 12.
- Assignment 2: due 5pm, Wed August 16.
- Assignment 3: due 5pm, Wed August 25.
- Assignment 4: due 5pm, Wed September 1.
- Assignment 5: due 5pm, Wed September 8.
- Collaboration on assignments is allowed, but must write out your own
solutions in your own way. Identical assignment solutions will share the
- Final Examination: Three-hour written examination at the end of the
semester. Anything discussed in lectures is examinable. In addition, problems
from assignments and tutorials as well as similar problems may form part of
the written exam.
- Criteria for the Award of Grades: Your grade in this
subject will be determined by the highest of the following levels of
achievement that you consistently display in the items of summative
- To earn a Grade of 7, a student must demonstrate an
outstanding understanding of the theory of the topics listed in the course
outline, and outstanding ability to apply the associated techniques to solve
- To earn a Grade of 6, a student must demonstrate a
comprehensive understanding of the theory of the topics listed in the course
outline, and proficiency in applying the associated techniques to solve
- To earn a Grade of 5, a student must demonstrate an
adequate understanding of the theory of the topics listed in the course
outline, and the ability to apply the associated techniques to solve
moderately difficult problems.
- To earn a Grade of 4, a student must demonstrate a
basic understanding of the theory of the topics listed in the course
outline, and the ability to apply the associated techniques to solve
- To earn a Grade of 3, a student must demonstrate
some understanding of the theory of the topics listed in the course outline,
and the ability to apply the associated techniques to solve some
- To earn a Grade of 2, a student demonstrates little
understanding of the theory of the topics listed in the course outline, and
little ability to apply the associated techniques to solve problems.
- A student will receive a Grade of 1 if they
demonstrate very little understanding of the theory of the topics listed in
the course outline, and very little ability to apply the associated
techniques to solve problems.
- Assessment Policy: As solutions to assignments are distributed
promptly, credit cannot be given for late assignments. Students who miss
assignments through bereavement or ill health should document their problems
and discuss this with the lecturer of the course. An alternative due date may
be negotiated between the student and lecturer. Allowance cannot be made for
reasons such as sporting or social commitments, or overwork in other courses.
Students should be familiar with the assessment rules in their degrees as
well as general university policy such as found in the General Award Rules.
These are all set out on the Program and Course Information page on the UQ
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.
information on the University policy on plagiarism, please refer to http://www.uq.edu.au/hupp/contents/view.asp?s1=3&s2=40&s3=12
- (a) where paragraphs, sentences, a single sentence or significant part of
a sentence which are copied directly, are not enclosed in quotation marks and
- (b) where direct quotations are not used, but are paraphrased or
summarised, and the source of the material is not acknowledged either by
footnoting or other simple reference within the text of the paper;
- (c) where an idea which appears elsewhere in print, film or electronic
medium is used or developed without reference being made to the author or the
source of that idea.
New University assessment rules relating to supplementary examinations are
accessible at the following URL: http://www.uq.edu.au/student/GeneralRules2003/2003GARs.htm.
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.
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.
More information on the General Award Rules at the University can be
found at http://www.uq.edu.au/student/GeneralRules2003/2003GARs.htm.
More information on the University's assessment policy may be found at http://www.uq.edu.au/hupp/contents/view.asp?s1=3&s2=30&s3=5.
EPSA Faculty policy on the award of special and supplementary exams may be
found at http://www.epsa.uq.edu.au/index.html?id=9329&pid=7564.
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 http://www.uq.edu.au/hupp/contents/view.asp?s1=3&s2=30&s3=5.
EPSA Faculty policy on feedback and re-marking may be found at http://www.epsa.uq.edu.au/index.html?id=7674&pid=7564.
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 http://www.uq.edu.au/hupp/contents/view.asp?s1=3&s2=30&s3=2.
The form may be downloaded from there -- section 3.6 of the policy at http://www.uq.edu.au/hupp-download/Request%20Assessment%20Re_Marking%20Form.pdf.
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 http://www.sss.uq.edu.au/index.html.
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
The Student Liaison officer will be Assoc Prof Peter Adams, Room 547
Priestley building, (email mailto:firstname.lastname@example.org).
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.
- First half: Mathematical tools
- Brief history of non-Euclidean geometry and Einstein
- Pseudo-Riemannian spaces
- Tensors and tensor densities
- Covariant differentiations
- Curvatures, Bianchi identities, Ricci and Einstein
- Second half: Astrophysical applications
- Summary of Special Relativity
- Outline of General Relativity
- Gravitational redshift and time dilation
- Planet orbits in the Suns's gravitational field
- Gravitational deflection of light
- Application to cosmology
- Gravitational radiation
- Any changes to course information will be announced in lectures. It is your responsibility to keep up to date with all information.
MATH4105/7105 Web Page.