18.101: Analysis and Manifolds

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 12
Hours/Week 10.4 (8 responses)
Instructors Richard Melrose
Overall Rating 5.0/7.0

Realistic Prerequisites

  • 18.100A/B is a hard prerequisite for the course. Topology (18.901) was also useful, though unnecessary.

Subject Matter

  • This topic is foundational and theoretical.
  • It made one student more comfortable with using foundational tools in analysis.

Course Staff

  • The course staff was very caring.
  • The TAs were generous with their time and helped improve understanding of the material.


  • Sometimes the lectures were hard to follow, and handwriting was sometimes difficult to read.
  • Many got lost during the fast-paced lectures.

Problem Sets

  • Fair.
  • The psets were generally fair and easier than material presented in lectures, though they were quickly paced.
  • Some found psets and office hours to be the most helpful in the class.


  • Only a final exam, with little feedback on how it went.


  • There was no specific textbook for the course, though students made use out of Analysis on Manifolds by Munkres, Guillemin’s notes, and Spivak’s Calculus on Manifolds.
  • Professor Melrose also typed notes for the class throughout the semester, which students took advantage of.


  • The grading cutoffs were unclear, though grading on the psets was fair.

Advice to Future Students

  1. “Keep good notes! Very notationally heavy.”