Course Description

In this course we generalize the concept of a surface to arbitrary dimensional manifolds. We will use differentiable (smooth) functions to study both local and global properties of manifolds and maps between them.

For a more detailed syllabus see the schedule of topics.

Prerequisites

  • Multi-Variable Calculus (Math 51 or equivalent).
  • 115 or 171
  • Derivative as a linear map.
  • Some basic topology: open, closed, compact sets.
  • Continuous maps.

Texts:

 We are going to mainly follow Milnor's book Topology from differentiable point view.
For many details and comments we will refer to Differential Topolog by Victor Guillemin and Alan Pollack.

Grades:    

 Grades will be based on the following components:
  • Class Participation: 4%
  • Homeworks: 20%
  • Midterm: 34%
  • In class final exam: 44%

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).