Math 109b
Introduction to Geometry and Topology, II
Winter 2014-2015
MWF 10:00 // 257 Sloan
Course Description | Policies | Textbook | Lecture Notes| Handouts | Homework

Instructor: Faramarz Vafaee, 272 Sloan, 395-4345,
Office hour: Monday 4-5 pm

Grader: Tian Nie
Office hour: Wednesday 5-6 pm, room 220 (#2-2) in SFL library

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Course Description
This is the second course in the 109 sequence, and is an introduction to differential geometry. The goal is to understand the differential geometry of curves and surfaces in three-dimensional space. This includes both local and global geometry. We will introduce basic geometric concepts as length, area, curvature and torsion. We will prove deep theorems like Gauss's Theorema Egregium and Gauss-Bonnet theorem.

Other important subjects we will cover include geodesics and minimal surfaces.

Prerequisites: Ma 2, Ma 109a


The homework will count 40% of the final grade, the midterm and final will each
count 30%. The due date for homework is Thursday, 2 pm.
One late homework will be accepted. You should inform the instructor in advance 
in this case and bring it in a week after a due date.
Collaboration is allowed for the homework but you have to write your own solution. 
Collaboration for midterm and final exams is not allowed.
You can use the textbook, lecture notes, graded homework sets and solutions 
posted online on the course webpage.


  • Differential Geometry of Curves and Surfaces, Manfredo Do Carmo, ISBN:

  • Elementary Differential Geometry, Second Edition, Barrett O'Neill

Lecture Notes

Date Description 


Date Description 


Due Assignment
Thursday 1/15 Homewrok set 1
Thursday 1/22 Homewrok set 2
Thursday 1/29 Homewrok set 3
Tuesday 2/10 Midterm Exam
Thursday 2/26 Homework Set 4
Thursday 3/5 Homework set 5
Thursday 3/12 Homework set 6
Wednesday 3/18 Final Exam

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