# 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:
• Linear algebra review: A short blurb about determinants in ps and pdf
• Computing curvature and torsion for curves that are NOT parametrized by arclength (solution of Problem 12abc on p. 25 in do Carmo): ps and pdf
• Proof of THEOREMA EGREGIUM of Gauss: ps and pdf
• 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.
• Assignment 1 (due Thursday, September 25): §1.2 # 2,5; §1.3 #4,6,10; §1.4 # 11,13; §1.5 # 1,4,7,18(extra credit). Scanned pages: page 1, page 2, page 3, page 4, page 5, page 6, page 7.
• Assignment 2: (due Thursday, October 16): §2.2 # 11,15,16 (p. 67); §2.3 # 3,4 (p. 80); §2.4 # 3,9,11,15,18(extra credit) (pp. 88-90); §2.5 # 1,5,11(extra credit) (pp. 99-101). EXTRA: §2.5 # 14, 15(both extra credit).
• Assignment 3: (due date November 27) §3.2, # 1,5,6,8, 16(extra credit+done in class),19(extra credit),20(extra credit) (pp. 151-153). §3.3, #1,3, 5,7(extra credit),16(extra credit),19,20,24(extra credit) (pp. 168-174). §3.5, #1(extra credit),2(extra credit),6(extra credit), 11ab,11c(extra credit),14(extra credit).
• Assignment 3 will be returned on Monday, Dec. 8 by Joseph Malkoun in his office (Burnside 1036) between 12noon-2pm (time to be confirmed).
• Assignment 4: (due date Dec. 2) §4.2 #2,3(both extra credit), §4.3 #6,7(both extra credit).
• 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
• Vector product: a short blurb and another one, as well as a Java tutorial
• Professor Gilbert Strang's Linear Algebra course on the web (taught at MIT).
• Trigonometry at SOS Math