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 184
Hours/Week 9.3 (74 responses)
Instructors Scott Roger Sheffield (Lecturer), Elisabeth D. Bullock (UA), Pakawut Jiradilok (TA), Sergei Korotkikh (TA), Andrew Y. Lin (TA)
# of Responses to Course 18 Underground Questions 47/184

Realistic Prerequisites

  • 18.01 is a hard prereq.
  • Students also found 18.02 useful for taking double integrals.
  • Experience with combinatorics (e.g. 6.042, math competitions) was helpful.
  • No programming experience required.

Subject Matter

  • There was a mix of theoretical and applied content. Some students found the course very theoretical, while others found it very applied.
  • Extremely foundational for applied math.
  • “Felt like the class was good prep for more 18.6xx courses, or even courses in other majors like 8 or 6”
  • “The class gives a good sense for how probability and stats are useful - we have frequent “stories” in lecture and remarks in psets that give context for how something is applied in real life. We also cover a broad range of topics, though examples are more heavily financial applications.”

Course Staff

  • Students had universally positive experiences with the course staff.
  • “Yes! The course staff were all very helpful! Professor Sheffield cares about the students and his Office Hours are very helpful; he also is very kind and considerate about making sure students can all see the board during lecture. The TAs also spend a lot of time to help; for example, Andrew even held extra sessions to review a full practice exam before each exam.”
  • “This is the first time I’ve had teaching staff in a Messenger chat for the class! The TA’s being there provided the students direct access to voice their concerns, which were readily answered and improved upon. The grading is generous and the staff were really approachable and responsive. The professor and TAs were definitely willing to put in the time!”
  • “review sessions were great, but not required by course staff – was simply bc TA wanted to help out”
  • “Overall very understanding. They gave me extensions when I needed them without a problem. This staff also has AMAZING response time on piazza (even Prof. Sheffield)– I felt like it showed that they really care.”


  • Many students found the lectures helpful.
  • Some students found the lectures too slow or difficult to learn from. Those that did learned more from the psets and recitations.
  • “I don’t go to office hours very often but Andrew Lin’s problem solving session before exam has been very useful”
  • “During the lectures, Prof. Sheffield would spend most of the time teaching new content and deriving the equations, but he would also spend some time each lecture to show us an interesting real world application.”

Problem Sets

  • Students generally found problem sets challenging. They are not direct applications of lecture material, but extend the content to new, colorful examples. Many found problems illuminating, but some found them frustrating, since they felt lectures did not adequately prepare them for solving the problems.
  • Many found lectures useful for problem sets, and those who didn’t found recitations more helpful.
  • Problem sets are rather long compared to other Course 18 classes, with problems having many parts. However, problem sets may seem artifically lengthy because Prof. Sheffield includes long sections of context and remarks.
  • Prof. Sheffield uses creative examples and stories in the problems, which make them engaging to think about. A memorable one concerns the probability a baby sloth on the road gets hit by a bus and killed.
  • Problem sets are more difficult than exams.


  • Exam problems are more straightforward than problem sets.
  • Exams can be quite stressful because of the 50 minute time limit. Students experienced a high variance in their performance, because they felt rushed and under pressure.
  • The difficulty was generally fair. Multiple practice tests and past exams are provided, and student found that they accurately reflect the nature of the exams.


  • The two main resources were Prof. Sheffield’s lecture slides and A First Course in Probability (8th ed.) by Sheldon Ross.
  • The textbook is not used heavily in the class, except for some homework problems being borrowed from it.
  • Some found the lecture slides to be sufficient background for problem sets, but those who didn’t found the textbook and Wikipedia to be helpful in approaching difficult problems.


  • Fair!
  • Cutoffs fell around or slightly under 90 for an A, 80 for a B, etc.
  • Prof. Sheffield says around 60% of students receive an A, 30% receive a B, and 10% receive a C or below.

Advice to Future Students

  1. “The first two weeks and first pset might be tough for someone who has little or no high school math competition background, and some people dropped the class because of that. But it will get better as the semester goes, and I enjoy the class a lot.”
  2. “Read lecture slides/textbook before class as Prof Sheffield can go through slides a bit fast.”
  3. “do all the online practice for the midterms - they will save you”
  4. “Doing past exam problems really helps! (However it does feel like the past problems tend to be easier than the present ones…)”
  5. “Work on the practice exams early and read the textbook. The lecture is not that helpful for exams or content understanding unless you did math olympiads”
  6. “Definitely 100% go to recitation”