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.

Lectures

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.

Exams

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.

Resources

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.

Grading

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

“Only take this class if you are planning on studying algebra or something algebra-related.”

“General maturity with ideas in algebra and category theory goes a long way.”