‘18.705: Commutative Algebra’

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 19
Hours/Week 8.6 (10 responses)
Instructors Wei Zhang (Lecturer)
Overall Rating 5.1/7.0

Realistic Prerequisites

  • The content of 18.701 and 18.702 were very necessary prerequisites. Other than that, students found that exposure to category theory, algebraic geometry, or algebraic number theory helps a lot.
  • The class demands a high level of mathematical maturity.
  • Previous experience with grad classes is recommended.

Subject Matter

  • Students found the subject to be very theoretical, broad and foundational.
  • Part of the class seemed unmotivated without background knowledge of number theory, algebraic geometry, or algebraic topology.

Course Staff

  • Students found the course staff approachable.


  • Some students felt that the lectures were somewhat disorganized and confusing.
  • Lecture content mostly followed the textbook, which students found incredibly helpful to read.

Problem Sets

  • Difficult yet fun.
  • Many problems are taken directly from Atiyah-MacDonald, and the book often gives (extensive) hints.
  • After reviewing lecture notes and reviewing definitions, students found that problems were a matter of unraveling definitions.


  • Students found the exams reasonable and tested content from the problem sets.
  • A practice exam was provided, which students felt was similar to the content of the real exam.
  • Some students felt time-pressure on the exams.


  • The main resource was Atiyah-MacDonald’s Introduction to Commutative Algebra, which students found to be incredibly helpful.
  • Some students found Altman-Kleiman’s A Term of Commutative Algebra to be useful as well.


  • Students found grading to be fair and lenient.
  • Problem sets had more than 100 points assigned, with grades capped at 100.

Advice to Future Students

  1. “Only take this class if you are planning on studying algebra or something algebra-related.”
  2. “General maturity with ideas in algebra and category theory goes a long way.”