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
  11. Syllabus

Course Info

Class Size 52
Hours/Week 8.9 (31 responses)
Instructors Tobias Colding (Lecturer), Katie Gravel (UA), Andrew Y. Lin (UA)
# of Responses to Course 18 Underground Questions 12/52

Realistic Prerequisites

  • Mathematical maturity: some prior proof-writing experience (perhaps via the IAP proofs workshop or another course with a focus on proof-writing) is highly recommended, as the learning curve is quite steep.
  • Knowledge of calculus in a single variable is essential (perhaps also calculus in several variables, but this is more of a soft prereq).

Subject Matter

  • Theoretical, broad and deep, abstract. Could have been even more abstract, though – tended to focus mainly on the real line rather than higher-dimensional reals or a more general metric space.
  • The skills gained (i.e. formulating proofs with a high level of rigor) might be more important than much of the subject matter itself.

Course Staff

  • Approachable, very open to questions, and accommodating of extenuating circumstances.
  • Both the professor and the TAs were caring and helpful.


  • Many students learned the most from the problem sets and from the TA’s office hours, rather than from lectures.
  • Students tended to use the textbook as a secondary resource when confused about parts of lectures.
  • Lectures were engaging and had good examples; the professor addressed all student questions.

Problem Sets

  • Challenging, but generally doable.
  • Problems tended to be straightforward rather than requiring creativity.
  • Lectures generally prepared students well for the psets.


  • Many students found timing to be an issue.
  • The problems were on par with the psets difficulty-wise.
  • Solving psets and knowing critical facts from lecture was helpful.
  • Many students found the exams stressful and discouraging, primarily due to a mismatch of difficulty level with time allotted.


  • Two textbooks (Rudin and TBB); it was nice to have two perspectives on the material.
  • Some students found Rudin to be much more useful than class.
  • It would’ve been nice to have lecture notes posted.


  • Grade cutoffs were not publicized.
  • Students generally felt that grading was fair and consistent.
  • “The professor seems to expect most people to get Bs and As.”

Advice to Future Students

  1. “I think it’s better for them to practice proof-writing before taking this class, or at least have an idea of how to write rigorous proofs. Also, they should ask themselves, ‘Do I really want to learn how real numbers are constructed, and calculus is formed?’’ If yes, then they should take the class.”
  2. It is very rigorous! It can be a bit annoying, but it is a necessary challenge.”


Click here for a PDF of this course’s syllabus.