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Term 1, 2013/14

Geometric Ideas in Physics


Table of Contents

Announcements and Updates
Course Description
Grading Scheme
Policy Notes

Announcements and Updates

Presentations will begin on November 11th.

Assignment #3   is due in class on Tuesday, October 22nd, extended to Tuesday, November 5th

Assignment #4   is due in class on Tuesday, November 19th

Assignment #5  is to write up your presentation (maximum 8 pages)
due in class on Thursday, November 28th

Assignment #1   was due in class on Tuesday, September 24th.

Assignment #2   was due in class on Tuesday, October 8th.

Click  here  for some notes I wrote a long time ago where I defined and proved very basic things about differentiable manifolds, tangent space, vector fields and their flows.
 If you are curious, you can click  here  for an English translation of Einstein's first paper on Special Relativity
For a friendly introduction to the history of non-Euclidean geometry (which will be the topic of the first few lectures) you can check out this lecture on YouTube:

Click  here  for my lecture from Monday, September 9th.
The first lecture was at 12:30 on Thursday,  September 5th, 2013  in ABB/270



Course Description

Here is the description in the undergraduate calendar: Minkowski space, Lorentz metric, Maxwell's equations, General Relativity, geodesics, curvature, black hole geometries and other selected topics.

Course Objective:
To learn the basic geometrical ideas developed over the centuries in the quest to understand the physical world that surrounds us.
  Students are responsible for reading the relevant material from the  textbook and the reference books on their own (that's known as experiential learning) in preparation for the lectures. The five assignments, which are mainly mathematical in nature form an integral part of the course. Students will also be asked to do a presentation (during the last 4 weeks) on material that is related to the course chosen and approved by the instructor.

RECOMMENDED TEXT BOOK:    "An Introduction to General Relativity"  by L.P. Hughston and K.P. Tod,  Cambridge University Press.

Reference Book (fun to read): "The Road to Reality", a  complete guide to the laws of the universe by Sir Roger Penrose, Vintage Books (2005).
Another fun book to read: "Flatterland" by Ian Stewart, which is a modern sequel to the classic Victorian book "Flatland" by Edwin Abbott Abbott (no typo!)

If you prefer "older books" (like me), then here are three books that I read in the 70's when I was a student in Germany:

  1. "GRAVITATION"  by Misner, Thorne and Wheeler  (the big black book!)
  2. "The large scale structure of space-time" by Hawking and Ellis (Hawking then became a very famous theoretical physicist)
  3. "Essential Relativity" by Rindler

Of course, there are a lot of newer books available. R. Wald, B. Schutz, J. Hartle and S. Carroll come to my mind. I have read Wald and Schultz but not Carroll's recent book (I can't afford it, too expensive for me!)

I don't have to tell you that you can also find a lot of material on the Internet  (for example you can check this out: )

Schedule of Topics (tentative)

Course Work:

1. Assignments: There will be five written assignments to be handed in on the due dates that will be announced in class. Late assignments will not be graded.

3. Presentations: Each student will give a 15-minute talk during the lecture period on a topic related to the course chosen by the instructor. The dates will be announced in class and on the course home page
4. Final Examination: There will be a 3-hour final examination scheduled by the Registrar’s office during the exam period in April

Grading Scheme

Academic Dishonesty:  

You are expected to exhibit honesty and use ethical behaviour in all aspects of the learning process. Academic credentials you earn are rooted in principles of honesty and academic integrity. Academic dishonesty is to knowingly act or fail to act in a way that results or could result in unearned academic credit or advantage. This behaviour can result in serious consequences, e.g. the grade of zero on an assignment, loss of credit with a notation on the transcript (notation reads: “Grade of F assigned for academic dishonesty”), and/or suspension or expulsion from the university. It is your responsibility to understand what constitutes academic dishonesty. For information on the various types of academic dishonesty please refer to the Academic Integrity Policy, located at

The following illustrates only three forms of academic dishonesty:

1.  Plagiarism, e.g. the submission of work that is not one’s own or for which other credit    has been obtained.

2.  Improper collaboration in group work.

3.  Copying or using unauthorized aids in tests and examinations.

Other Policy Notes:

MSAF policy:

When using the MSAF, also report your absence to me (the course instructor M. Min-Oo) within 2 working days by email ( and contact me in person to learn what relief may be granted for the work you have missed, and relevant details such as revised deadlines, or time and location of a make-up exam. Please note that the MSAF may not be used for term work worth 30% or more, nor can it be used for the final examination. Please refer to  for the exact rules


Only the standard McMaster calculator Casio fx 991MS+ can be used for the tests and the final examination.

Important Notice: 

The instructor and the university reserve the right to modify or revise information contained in this course during the term. The university may change the dates and deadlines for any or all courses in extreme circumstances. If either type of modification or revision becomes necessary, reasonable notice and communication with the students will be given with explanation and the opportunity to comment on changes. It is the responsibility of the student to check their McMaster email and course websites weekly during the term and to note any changes.