
Home Page for MATH 3GP3
Term 2, 2011/12
Geometric Ideas in Physics

Table of Contents
- Announcements and Updates
- Instructor
- Lectures
- Course Description
- Grading Scheme
- Policy Notes
Announcements
and
Updates
There will be a 30-minute quiz in class
on Monday, March 26th
Assignment
#5 (the last one) is due in
class on
Thursday, March 29th, 2012
Here is the link to the paper by Dunajski and Gibbons about "Cosmic
jerk, snap and beyond" that I mentioned in class:
http://arxiv.org/abs/0807.0207v2
Reading assignment for the tenth
and eleventh week
(March 11th to March 24th)
Chapters 23 and 24 from the text book by Hughston
&
Tod
If you love the "the muse Urania" and want to spend about a
year
or two learning more about General Relativity, you can read the "heavy
black book": "GRAVITATION" by Misner, Thorne and Wheeler.
A good book to learn more about differential forms and how they
are used in differential geometry and physics is the Dover book by
Harley Flanders " Differential forms with applications to the physical
sciences"
Click here for an
English translation of Einstein's first paper (1905) on Special
Relativity
Assignment
#4 was due in
class on
Thursday, March 8th, 2012
There was a 30-minute Quiz
during the lecture period on
Thursday, March 1st, 2012
Assignment
#3 was due in
class on
Thursday, February 16th, 2012
Assignment
#2 was due in
class on
Thursday, February 2nd, 2012
There was a 30-minute Quiz
during the lecture period on
Thursday, January 26th, 2012
Assignment
#1 was due in
class on
Thursday,
January 19th, 2012
Reading assignment for the ninth week
(March 4th to March 10th)
Chapters 22 and 23 from the text book by Hughston
&
Tod
Reading assignment for the
eighth week
(February 27th to March 3rd)
Chapters 18, 19 and 20 from the text book by Hughston
&
Tod
Reading assignment for the
reading(sic) week
(February 20th to 26th)
Chapters 16, 17, 18 and 19 from the text book by Hughston
&
Tod
Reading assignment for the
seventh week
(February 13th to 19th)
Chapters 13, 15 and 17 from the text book by Hughston
&
Tod
Reading assignment for the sixth week
(February 6th to 12th)
Chapters 9, 10 and 11 from the text book by Hughston
&
Tod
and Chapters 14, 15 and 19 from the reference book by Penrose
Reading assignment for
the
fifth week
(January 30th to February 5th)
Chapters 5, 6, 7, 8, 9 and 11 from the text book by
Hughston
&
Tod
and Chapters 17, 18 and 19 from the reference book by Penrose
Reading assignment for the
fourth week
(January 23rd to 29th)
Chapters 4, 5 and 8 from the text book by Hughston &
Tod
and Chapters 12 and 14 from the reference book by Penrose
Reading assignment for the
third week
(January 16th to 22nd)
Chapters 2, 3 and 4 from the text book by Hughston &
Tod
and Chapters 10 and 12 from the reference book by Penrose
Reading assignment for the first two
weeks (January 4th to 15th)
Chapters 1, 2 from the text book by Hughston &
Tod
and Chapters 1 to 7 from the reference book by Penrose.
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!)
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Instructor
Lectures
- Mondays, Wednesdays and Thursdays 13:30 -
14:20 in HH/305
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 book on their own
in preparation for the lectures. The five assignments, which are mainly
mathematical in nature form an integral part of the course.
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).
Schedule of Topics (tentative)
- Week 1 and 2 : The Trinity of Classical Geometries:
Euclidean, Spherical and Hyperbolic
- Week 2 and 3: Geometric Calculus (quick
review of vector
fields and their flows, differential forms, Stokes' theorem, Lie
derivatives, divergence, etc.)
- Week 4 and 5: Maxwell's Equations and Lorentz
Transformations, Special Relativity (Algebra and Calculus in
Flat Minkowski Space)
- Week 6: Calculus and Geometry on Riemannian and
Lorentzian Manifolds, Geodesics and Curvature
- Week 7: Einstein's Field Equations and Gravity,
Schwarzschild Geometry
- Week 8: Reading Week
- Week 9 : Schwarzschild Geometry II (perihelion shift,
bending of light and gravitational red-shift)
- Week 10: The Kruskal extension and Penrose diagrams, Kerr
metric
- Week 11: Black Holes and Gravitational Collapse
- Week 12: Cosmological Models (Friedmann-Robertson-Walker)
- Week 13: Selected extra topics, such as Calabi-Yau spaces.
- Week 14: Review
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.
-
Assignment #1
due in class on Thursday,
January 19th, 2012
-
Assignment #2
due in class on Thursday,
February 2nd, 2012
-
Assignment #3
due in class on Thursday,
February 16th, 2012
-
Assignment #4
due in class on Thursday,
March 8th, 2012
- Assignment #5 due in class on
Thursday, March 29th, 2012
3. Quizzes: There will be three 30-minute quizzes
to be held during the lecture period. The dates will be announced in
class and on the course home page
- Quiz #1 during the lecture period on
Thursday, January 26th, 2012
- Quiz #2
during the lecture period on Thursday,
March 1st, 2012
- Quiz #3 during the lecture period
on Monday March 26th, 2012
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:
40%
- Quizzes:
15%
- Final
Exam: 45%
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:
1. Only the standard
McMaster calculator Casio fx 991MS+ can be used for the tests and the
final examination.
2.
If
you
are
absent
from
the
university
for
a
minor
medical
reason,
lasting
fewer
than
5
days,
you
may
report
your absence, once per term, without
documentation, using the McMaster Student Absence Form
Absences
for
a
longer
duration
or
for
other
reasons
must
be
reported
to
your
Faculty/Program
office,
with
documentation,
and
relief
from term work
may not necessarily be granted. When using the MSAF, you must also
report your absence to me (the course instructor M. Min-Oo) immediately
(normally within 2 working days) either by email (minoo@mcmaster.ca) or
by contacting 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 test. 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.
*Important Message*
3.
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.