Pre: (PH244 or PHYS2100) + (MATH3102 or PH348 or PHYS3050) Inc: ID435

Lecturer: Dr.Yao-Zhong Zhang (see Dr. Michael Drinkwater for the second half).

Teaching Mode: There are three lectures and one tutorial per week.

Lectures: Wednesday 3-5pm 6-232D, Thursday 3-4pm 6-232D

Tutorial: Thursday 4-5pm 6-232D

Assessment: Assignments and (First half of) 3 Hour Final Exam

There is no set textbook for this unit.

Reference Books:
C.T.J. Dodson & T. Poston, ``Tensor Geometry''. (QA3.G7 No. 130)
J.L. Synge & A. Schild, ``Tensor Calculus''. (QA433.S9 1949)
B. Spain, ``Tensor Calculus''. (QA433.S65 1960)
L.P. Eisenhart, ``Riemannian Geometry''. (QA641.E58 1926)
A. Lichnerowicz, ``Elements of Tensor Calculus''. (QA433.L5 1962)
E. Schroedinger, ``Space-Time Structure''. (QC173.59.S65S35 1950)
S. W. Hawking and G.F. R. Ellis, `` The Large Scale Structure of Space-Time''. (QC173.59.S65H38 1973)
H. Weyl, ``Space-Time-Matter''. (QC173.55.W515 1952)
C.J. Isham, ``Modern Differential Geometry for Physicists''. (QA641.I84 1989)
S. Weinberg, ``Gravitation and Cosmology''. (QC6.W47 1972)
M. Dubrovin, A.T. Fomenko & S.P. Novikov, ``Modern Geometry: Methods & Applications, Pt. 1." (QA3.G7. No. 93)

Course Profile:
``In Einstein's theory of gravitation, matter and its dynamical interaction are based on the notion of an intrinsic geometric structure of the space-time continuum. The ideal aspiration, the ultimate aim, of the theory is not more and not less than this: A four-dimensional continuum endowed with a certain intrinsic geometrical structure, a structure that is subject to certain inherent purely geometrical laws, is to be an adequate model or picture of the `real world around us in space and time' with all that it contains and including its total behaviour, the display of all events going on in it.'' (Schroedinger, ``Space-Time Structure''.)
Acceptance of the appropriateness of this notion of ``geometrizing'' all of physics has waxed and waned somewhat since Einstein's time, but the striking achievements of his `General Theory' compel us to study both the theory and the mathematical structure upon which it is founded -- the theory of pseudo-Riemannian geometry. The first half of the course will introduce the basic mathematical tools: pseudo-Riemannian spaces; tensors; covariant differentiation; geodesics; curvature; Bianchi identities; Ricci, Einstein and Weyl tensors; some aspect of special types of space such as space of constant curvature and flat space.
Through working problems, the student will have the opportunity to acquire a basic working knowledge of these concepts, and should have the background necessary for the second half of the course, on Einstein's General Theory of Relativity.

Assessment Criteria: 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 assessment.

Grade of 7: the student demonstrates an outstanding understanding of the theory of the topics listed in the subject outline, and outstanding ability to apply the associated techniques to solve problems.

Grade of 6: the student demonstrates a comprehensive understanding of the theory of the topics listed in the subject outline, and proficiency in applying the associated techniques to solve problems.

Grade of 5: the student demonstrates an adequate understanding of the theory of the topics listed in the subject outline, and the ability to apply the associated techniques to solve moderately difficult problems.

Grade of 4: the student demonstrates an understanding of the theory of the topics listed in the subject outline, and the ability to apply the associated techniques to solve straightforward problems.

Grade of 3: the student demonstrates some understanding of the theory of the topics listed in the subject outline, and the ability to apply the associated techniques to solve some straightforward problems.

Grade of 2: the student demonstrates little understanding of the theory of the topics listed in the subject outline, and little ability to apply the associated techniques to solve problems.

Grade of 1: the student demonstrates very little understanding of the theory of the topics listed in the subject outline, and very little ability to apply the associated techniques to solve problems.

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.