MATH 320A: Differential Geometry
Course Description
- INSTRUCTOR:
D. Jakobson (TR 11:30-13:00, WONG 1030)
Office: BH1212
Office Hours: Tuesday 4-5pm, Wednesday 1-2pm
Dec. 1 week: Monday, Dec. 1, 1pm-2pm, Tuesday, Dec. 2, 4-5pm
I am away from Dec. 3 to Dec. 12
Finals week: Monday, Dec. 15, 12noon-2pm
Tel: 398-3828
E-mail: jakobson@math.mcgill.ca
Web Page: www.math.mcgill.ca/jakobson
- TEACHING ASSISTANT:
Joseph Malkoun.
He has some nice
articles on his web page.
Office Hours: Monday, 13:30-14:30, BURNSIDE 1036
E-mail: malkoun@math.mcgill.ca
- TEXT: Differential Geometry of Curves and Surfaces
by Manfredo P. do Carmo.
- SYLLABUS:
The course will cover most of chapters 1-4 of
the text. Contents: curves in R3, curvature, torsion,
Frenet formulas. Surfaces: tangent plane, first fundamental
form, area, orientation. Gauss map, second fundamental form,
curvature, ruled and minimal surfaces. Isometries, Gauss theorem,
Christoffel symbols, compatibility equations. Geodesics, parallel
transport, Gauss-Bonnet theorem and other topics may be covered
if time permits.
- HANDOUTS:
ASSIGNMENTS: There will
be several assignments. Due dates will be announced in class and on
the course web page. Late assignments will not be accepted.
MIDTERM: There will an in-class midterm on November 6.
It will be held at the same time and place as the regular lecture.
MIDTERM REVIEW: Tuesday, Novermber 4, at 6pm in Burnside,
room to be announced (tentatively Burnside 1205).
PRACTICE PROBLEMS FOR THE MIDTERM. Don't try to do all
the problems, there are too many of them. Look at 1 or 2 from each
section, esp. at those that have hints in the back (*). DO CARMO:
§1.3 #3,5 (compute the curvature using the corresponding
handout or §1.5 #11); §1.5
#8,11,14; §2.2 #12,13 (compute the 1st fundamental form, angles
between coordinate lines, area form etc); §2.4 # 5,6,10,12;
§2.5 # 2,3,4,6,13. Here are some SOLUTIONS prepared by Jordi for
math 380 last year:
set 1,
set 2,
set 3,
set 4,
set 5.
In addition to the problems in do Carmo, you may look at the following
problems in the differential geometry course taught by C.T.J. Dodson
at the University of Manchester Institute of Science and Technology
(those are pdf files; see also a link to his lecture notes below):
set 1
set 2
Finally, you may go to OLD FINALS link below, download the finals
from math 320 or math 380, and look for problems on curves or on
the first fundamental form.
FINAL EXAM: The final exam will be held on December 17,
14:00-17:00, Room Burnside Hall 1B24 (in the basement)
TAKE-HOME FINAL (due Dec. 13): §1.5 #9; §1.7 #6;
§2.5 #7,13; §3.2 #10,15,17; §3.3 #7abcd,22,24;
§3.5 #9ab,12,14; §4.3 #1,5. DO ANY 11 PROBLEMS (OR AS MANY
AS YOU CAN).
FINAL REVIEW December 13, 6-8pm, room 1205.
Also, here are some some more SOLUTIONS prepared by Jordi for
math 380 last year:
set 6,
set 7,
set 8,
set 9.
OLD FINALS: Go to
SUMS, then click on "Resources" and on "Math Exam Archive."
GRADING: If A = assignment mark, M = midterm mark,
E = exam mark and F = final mark (all out of 100), then F is the
larger of (.75E + .25A)
and (.5E + .25M + .25A)
Reviews of linear algebra, calculus etc
Links in Differential Geometry
HELPDESK is open in Burnside 911 Monday-Friday generally from
12:30-16:30 (see their web page for details); you can also ask questions
by email at
helpdesk@math.mcgill.ca
NOTICE:
McGill University values academic integrity. Therefore, all
students must understand the meaning and consequences of
cheating, plagiarism and other academic offences under the Code
of Student Conduct and Disciplinary Procedures (see McGill web page
on Academic Integrity
for more information).