Introduction to Geometry and Topology


Course Description and Grading Breakdown
In this course, we will study the differential geometry of surfaces. Geometric concepts such as orientation, metrics, connections and curvature will be introduced. Theorems that we will prove include the classification of surfaces, Gauss's Theorema Egregium and the Gauss-Bonnet theorem. 

Grades: HW 50%; Final 50%

Course Meeting Time and Location
Monday, Wednesday and Friday
10:00 - 10:55 am
B111 Downs Physics Laboratory (DWN)

Course Instructor Contact Information and Office Hours
Dr. Qiongling Li email: qli4@caltech.edu
125 Math Building (Building 15)
Office Hour: Thursday 11:30 am-12:30 pm.

TA Contact Information and Office Hours
TA:  Lingfei Yi;  email:  lyi@caltech.edu; Office: 210-C, Math Building(Building 15);
Office Hour: Wednesday 4-5 pm.

Course Schedule and Textbook
Textbook: 
Differential Geometry of Curves and Surfaces, Manfredo Do Carmo, ISBN: 978-0-1321-2589-7 

 DateTopic 
 1/3 W Section 1-2, 1-3, 1-4(half)
 1/5 F Section 1-4, 1-5(half)
 1/8 M Section 1-5, 1-6
 1/10 W Section 1-7 (Part A)
 1/12 F Section 2-2 (half)
 1/15 M
 Martin Luther King Day (Institute holiday)
 1/17 W Section 2-2
 1/19 F Section 2-3, 2-4(half)
 1/22 M Section 2-4, 2-5(half)
 1/24 W Section 2-6
 1/26 F Section 3-2(half)
 1/29 M Section 3-2
 1/31 W Section 3-3(half)
 2/2  F Section 3-3
 2/5 M Section 3-5(half)
 2/8 W Section 3-5
 2/10 F Section 4-2
 2/12 M Section 4-3
 2/14 W Section 4-4(half)
 2/16 F Section 4-4(half)
 2/19 M President’s Day (Institute holiday)
 2/21 W Section 4-4
 2/23 F Section 4-5
 2/26 M Section 4-5
 2/28 W Section 4-5
 3/2 F cancelled
 3/5 M           Section 5-3(half)
 3/7 W Section 5-3
 3/9 F Section 5-4



Course Policies
The due date for homework is Monday 10:00am (at the start of class). Collaboration is allowed for the homework but you have to write your own solution. 

You are allowed to turn in one late homework (without penalty) in the quarter. However, you must inform me about turning in your homework late BEFORE the due date, and you must turn in the late homework within a week of the due date. In general, if the homework is late within a week of the due date, it is still acceptable but will be graded based on 20% points off. 

Assignments

***In case you don't have the textbooks in your hand, I have included the scanned page of the problems appearing in the homework. 

 Date PostedAssignment Due Date 
 Jan 5 HW 1                    Jan 12
 Jan 12  HW 2 Reading     Jan 22
 Jan 22 HW 3                 Jan 29
 Jan 29    HW 4 Reading    Feb 5
 Feb 5 HW 5               Feb 12
 Feb 14    HW 6                  Feb 26
 Feb 28 HW 7                   Mar 6


Final Exam
   final (It covers the material we learned in class except
           the last class. Due at 5 pm on March 15 Thursday)


Collaboration Table
 HomeworkExams
You may consult:  
Course textbook (including answers in the back)YESYES
Other booksYESNO
Solution manualsNONO
InternetYESNO
Your notes (taken in class)YESYES
Class notes of othersYESNO
Your hand copies of class notes of othersYESYES
Photocopies of class notes of othersYESNO
Electronic copies of class notes of othersYESNO
Course handoutsYESYES
Your returned homework / examsYESYES
Solutions to homework / exams (posted on webpage)YESYES
Homework / exams of previous yearsNONO
Solutions to homework / exams of previous yearsNONO
Emails from TAsYESNO
You may:

Discuss problems with othersYESNO
Look at communal materials while writing up solutionsYESNO
Look at individual written work of othersNONO
Post about problems onlineNONO
For computational aids, you may use:

CalculatorsYES*NO
ComputersYES*NO

* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work.  For example, "by Mathematica" is not an acceptable justification for deriving one equation from another.  Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them.