‘18.905: Algebraic Topology 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 24
Hours/Week 10.5 (15 responses)
Instructors Daniel Alvarez-Gavela
Overall Rating 6.4/7.0

Realistic Prerequisites

  • 18.901.
  • Some students mentioned that algebra at the level of 18.702/18.705 is very helpful.

Subject Matter

  • Course material was very theoretical and abstract.
  • Most students found the subject material to be very interesting.

Course Staff

  • Professor and course staff were helpful and approachable.


  • Several students had great things to say about the lectures, one even described them as the best vibes of any math class.
  • Students mentioned that the lectures were the best resource in learning for this class.

Problem Sets

  • Most students felt like problem sets were challenging but fun.
  • Reinforced what was being taught in lecture.


  • Both exams were take-home exams.
  • Several students mentioned that exams were long and challenging.


  • Textbook: Algebraic Topology by Hatcher.
  • Professor’s course notes were also a useful resource for many students.


  • Grading was described as fair.

Advice to Future Students

  1. “Take this course if you enjoyed 18.901 and have learned group theory/algebra.”
  2. ”Brush up on commutative algebra before you take this class, especially if you haven’t taken anything beyond 18.701.”
  3. “Definitely take this class if you have any interest in doing more advanced topology! It is extremely fun, interesting, and changes the way you think about topology. It is also the gateway to many topics in advanced math. I especially recommend taking the class with Prof. Gavela as he is excellent.”