Course Description

This course focuses on geometry of curves and surfaces in three dimensional space. We cover parallel transport, covariant derivative, curvature, geodesics, Gauss-Bonnet theorem and minimal surfaces. Some material - as it will be pointed out in the course - prepares for studying abstract surfaces.

For a more detailed syllabus see the schedule of topics.

Prerequisites

  • Multi Variable Calculus (Math 51, 52, or equivalent).
  • Linear maps and their matrices.
  • Quadratic forms.
  • Some exposure to mathematical reasoning is recommended.

Text:

 The text for the course is Differential Geometry of Curves and Surfaces, by Manfredo Do Carmo.
The text is required and is available at the bookstore.

Grades:    

 Grades will be based on the following components:
  • Class Participation: 10%
  • Homeworks: 20%
  • Midterm: 30%
  • Final Exam: 40%

Students with Documented Disabilities    

 Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Office of Accessible Education (OAE). Professional staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty dated in the current quarter in which the request is made. Students should contact the OAE as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (phone: 723-1066, URL: studentaffairs.stanford.edu).