Monday 12:30 - 13:20, Tuesday 13:30 - 14:20 and
Thursday 12:30 - 13:20 in ABB/270
Course Description
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 3 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 universeby
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!)
Schedule of Topics (tentative)
Week 1 and 2 : The Trinity of
Classical Geometries: Euclidean, Spherical and Hyperbolic
Week
3:
Quick review of Maxwell's Equations, Lorentz Transformations and
Special Relativity (Algebra and Calculus in Flat Minkowski
Space)
Week
4:
Geometric Calculus (quick review of vector fields and
their flows, differential forms, Stokes' theorem, Lie
derivatives, divergence, etc.)
Week
5:
Calculus and Geometry on Riemannian and Lorentzian Manifolds,
Geodesics and Curvature
Week
6:
Einstein's Field Equations and Gravity
Week 7 and 8 : Schwarzschild Geometry
(perihelion shift, bending of light and gravitational red-shift)
Week 9 and 10: The Kruskal extension and
Penrose diagrams, Black Holes and Gravitational Collapse, Kerr
metric
Week 11 and 12: Cosmological Models
(Friedmann-Robertson-Walker)
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
20-minute talk during the lecture period. 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
Assignments:
45%
Presentation:
15%
Final
Exam: 40%
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 http://www.mcmaster.ca/academicintegrity
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) immediately (normally within 2
working days) by email (minoo@mcmaster.ca) 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. Here are the
rules:
Requests
for Relief for Missed Academic Term Work for absences from
classes lasting up to 5 days due to a minor medical situation:
Using the McMaster Student Absence Form (MSAF) on-line
self-reporting tool, undergraduate students may report
absences due to minor medical situations lasting up to 5 days
and may also request relief for missed academic work worth
less than 30% of the final grade. The submission of medical
documentation is normally not required. Students may use this
tool to submit a maximum of one request for relief of missed
academic work per term. Students must immediately (e.g. by
e-mail within 2 days) follow up with their course instructors
regarding the nature of the relief. Failure to do so may
negate the opportunity for relief. It is the prerogative of
the instructor of the course to determine the appropriate
relief for missed term work. relief for missed term work.
For
absences from classes lasting more than 5 days: Students who
are absent more than five days cannot use the on-line,
self-reporting tool to request relief. They MUST report to
their Faculty Office to discuss their situation and may be
required to provide appropriate supporting documentation. If
warranted, students will be approved to use a discretionary
version of the MSAF on-line, self-reporting tool.
For
the reporting of more than one request for relief per term:
Students who wish to submit more than one request for relief
of missed academic work per term cannot use the on-line,
self-reporting tool to request relief. They MUST report to the
office office of the Associate Dean (Studies) of their Faculty
within a week of the test date, and may be required to provide
appropriate supporting documentation, e.g. a doctor’s note. If
warranted, students will be approved to use a discretionary
version of the MSAF on-line, self-reporting tool. The
instructor will act on the exemption only after receiving
official communication from the relevant Associate Dean’s
office that the grounds for exemption have been accepted.
For
absences from classes unrelated to a medical situation:
Students who are absent for reasons other than a medical
situation cannot use the on-line, self-reporting tool to
request relief. They MUST report to their Faculty Office to
discuss their situation and may be required to provide
appropriate supporting documentation. If warranted, students
will be approved to use a discretionary version of the MSAF
on-line, self reporting tool.
For
relief from missed work worth 30% or more of the final grade:
Students who have missed a piece of work worth 30% or more
cannot use the on-line, self-reporting tool to request relief.
They MUST report to their Faculty Office to
discuss their situation and may be required to provide
appropriate supporting documentation. If warranted, students
will be approved to use a discretionary version of the MSAF
on-line, self-reporting tool.
For
absences from classes lasting more than five days, for work
worth 30% or more, or for the reporting of more than one
request for relief per term: If the reason was medical, the
approved McMaster University Medical Form covering the
relevant dates must be submitted. The student must be seen by
a doctor at the earliest possible date, normally on or before
the date of the missed work and the doctor must verify the
duration of the illness. Relief will not be considered for
minor illnesses. If the reason is non-medical, appropriate
documentation with verifiable origin covering the relevant
dates must be submitted, normally within five working days. In
some circumstances, students may be advised to submit a
Petition for Special Consideration (Form A) seeking relief for
missed academic work. In deciding whether or not to grant a
petition, adequacy of the supporting documentation, including
the timing in relation to the due date of the missed work and
the degree of the student’s incapacitation, may be taken into
account. If the petition is approved the Faculty Office will
notify the instructor(s) recommending relief. The student must
contact the instructor promptly to discuss the appropriate
relief. Failure to do so may negate the opportunity for
relief. It is the prerogative of the instructor of the course
to determine the appropriate relief for missed term work.
The
MSAF on-line, self-reporting tool cannot be used to apply for
relief for any final examination or its equivalent. Deferrals
for the final exam are handled exclusively by the Associate
Dean’s office.
Calculators:
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.
