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Math 109b:Introduction to Geometry and Topology

Lectures: 10:00--10:55 a.m. on Monday, Wednesday, Friday at 159 Sloan
Instructor: Amin Gholampour
Email address: agholamp@caltech.edu
Office: Sloan 258
Office Hour: 11-12 a.m. on Friday

Course description:
The course will give an introduction to differential geometry of curves and surfaces in the 3-dimensional Euclidean space.
We will cover: local theory of curves and surfaces, first and second fundamental forms of surfaces, covariant differentiation, parallel translation, geodesics, Gauss-Bonnet's theorem and its applications.

Reference:
Differential Geometry of curves and surfaces by Manfredo Do Carmo.

Course Policy:
Grades will be based on assigned homework, a midterm, and a final (homework 30%, midterm 30% and final 40%.).

Midterm: To open the exam click on PDF

Remarks:

Office hour for assignments: Thursdays 4-5pm at Sloan 385.
Discussing assignment with your classmates is encouraged, but the solutions must be written independently.
Please put your assignment into the tray in the math department before 5pm on the due date.
Unless stated otherwise, all the problems assigned are from Do Carmo's book, e.g. 1-5-12-c means do part c of problem 12 in section 5 of chapter 1.
You can use the hints at the end of the book, but show all nontrivial details in your solution.

week	Assignments and suggested problems		Lecture notes
1st	1-3-2, 1-5-1, 1-5-4, 1-5-12-c, 1-5-13	Due 1/16	PDF
	Most of the problems in 1-5 are important and help mastering the subject.
2nd	2-2-3, 2-2-5, 2-2-11-a, 2-3-3, 2-4-2, 2-4-15	Due 1/23	PDF
	Suggested problems: 2-2: 1,2,4,9,10,11,12,13 2-3: 1,2,4,5,8,10,11 2-4: 1,3,4,5,6,7,8,9,10,11,12,14,16,17,18,19,20,22
3rd	2-5-1-d, 2-5-4, 2-5-6, 2-5-10, 2-5-12	Due 1/30	PDF
	Problems in section 2-5 are recommended.
4th	No assignment for this week due to midterm (see above).		PDF
	Suggested problems: 3-2: 2,3,4,5,6,8,9,13,14,15,16,17,18,19,20 3-3: 1,5(ignore part e),6,7,12,13,14,16
5th	4-2-16, 4-2-17, 4-2-18, 4-3-1, 4-3-6, 4-3-7	Due 2/13	PDF
	Suggested problems: All problems in 4-2, 4-3
6th	No assignment for this week.		PDF
	Suggested problems: Problems in 4-4 except 2, 5.b, 18, 20, 21
7th	Note: There will be no class on Friday 2/27.		PDF
	4-4-7, 4-4-10, 4-4-13, 4-4-20, 4-5-1, 4-5-3, 4-5-5	Due 2/27
	Suggested problems: Problems in 4-5 except 6,7,8,9
8th	4-6-1, 4-6-6, 4-6-7, 4-6-10, 4-6-14	Due 3/9	PDF
	Problems in 4-8
	Note: Material needed for some of assigned problems above will be taught in class on Monday 3/2.
9th &10th	Suggested problems: section: 5-3: 1 to 4; section: 5-10; 1 to 10 There may be questions from 5-3 and 5-10 in the final exam, but they won't be mandatory.		PDF PDF

Final: Here you can find the PDF file for the final exam and related instructions.

Due date: Wednesday March 18th, at 5pm.
No starred or tricky problem in the book (even if it has been suggested above) is necessary for this exam.
You can use your class book and class notes (of your own or the ones posted above). No other sources (other books, notes, internet, person...) are allowed to use.
The time for the exam is 3 hours (with no interruptions).
You are encouraged to go over time if needed but please write the time you will spend on the top of your exam page no matter it will be more than 3 hours or less.

Click here to open the exam: PDF