18.965: Geometry of Manifolds I

Table of contents

  1. Course Info
  2. Realistic Prerequisites
  3. Subject Matter
  4. Course Staff
  5. Lectures
  6. Problem Sets
  7. Exams
  8. Resources
  9. Grading
  10. Advice to Future Students

Course Info

Class Size 20
Hours/Week 9.3 (10 responses)
Instructors William Minicozzi
Overall Rating 6.4/7.0

Realistic Prerequisites

  • The content of 18.100A/B/P/Q was a necessary prerequisite, and experience with manifolds is a soft, but helpful, prerequisite.
  • There were some references to other areas of analysis such as functional analysis, topological concepts, and partial differential equations, but these were often blackboxed.
  • Experience with smooth manifolds is expected, though he does go over the foundational knowledge the first week.

Subject Matter

  • More on the theoretical side, but very applicable to any number of other classes/research.

Course Staff

  • Very friendly and approachable. Both the instructor and the TA were helpful in office hours to learn the material and ask questions.


  • Lectures were stimulating and interesting, though Professor Minicozzi was more than happy to slow down if anyone had questions or even just seemed confused!
  • Be sure to speak up if you don’t understand something because he wants to help you learn!
  • Textbooks helped clarify the lectures.

Problem Sets

  • Reasonable.
  • The problemsets were very reasonable, though occasionally required creativity/tricky solutions.
  • Sometimes the problemsets were seen as a “little light”, but efficiently helped students practice the concepts they had learned about in class.


  • There were no exams.


  • Used do Carmo’s “Riemannian Geometry” and his other book “Differential Geometry of Curves and Surfaces” was helpful for background/problemsets.
  • There were also course notes that were provided.


  • Students felt that grading was incredibly fair and reasonable.

Advice to Future Students

  1. ”Go to class and do the work and you’ll have a great time!
  2. “Enjoy this class – it’s a lot of fun.”