Instructor Insights

Instructor Insights pages are part of the OCW Educator initiative, which seeks to enhance the value of OCW for educators.

Instructor Insights

Below, Professor Yufei Zhao describes various aspects of how he taught 18.218 Probabilistic Method in Combinatorics.

OCW: You structured problem sets a little differently in this course, providing students with a single file with many problems but only requiring a subset of these problems to be turned in for assessment. Tell us about your decision to structure problem sets this way.

Yufei Zhao: I wanted to give the students lots of opportunities to practice the techniques taught in lectures. The single-file format made it easier to add new problems to the list as the semester progressed, and in a way that was synchronized with the pace of the lectures. I only required the students to turn in a subset of the problems in order to ease the workload burden.

The lectures that work best are ones filled with small and neat examples and applications illustrating the method being discussed.

— Yufei Zhao

OCW: How did you use the lecture time in class to ensure maximum benefit to your students?

Yufei Zhao: The goal of the course was to introduce students to the probabilistic method, which has many applications that are quite nice and short. The students appreciated seeing a lot of examples in class. Longer proofs tend to be less well suited to the lecture format as they’re harder to follow. I’ve found that the lectures that work best are ones filled with small and neat examples and applications illustrating the method being discussed.

 

Curriculum Information

Prerequisites

No specific classes are required, but the course presupposes mathematical maturity at the level of a first-year math graduate student, with basic knowledge of combinatorics, graph theory, and probability.

Requirements Satisfied

18.218 can be applied toward a doctorate degree in Pure or Applied Mathematics, but is not required.

Offered

A course covering a different topic in combinatorics is offered every spring semester; this iteration of 18.218 was such a course, but in the future it will be offered regularly under its own course number every other fall semester. 

The Classroom

  • A view over several tiers of desks toward the classroom’s lectern area and blackboards.

    Room 1 of 1

    Lecture

    Classes were held in a small lecture hall with about 60 tiered seats at shared desks, multiple blackboards, and an A/V system.

 

Assessment

Grade Breakdown

Grading for 18.218 was entirely based on problem sets. There are no exams.

Student Information

68 students took this course when it was taught in Spring 2019.

Breakdown by Year

The class included a mixture of graduate students and undergraduates.

Breakdown by Major

Students in the course came primarily from mathematics and computer science.

Typical Student Background

Most students in the course had strong mathematical problem solving backgrounds; many of the undergraduates had experience participating in math competitions.

 

How Student Time Was Spent

During an average week, students were expected to spend 12 hours on the course, roughly divided as follows:

Lecture

3 hours per week

Met 2 times per week for 1.5 hours per session; 25 sessions total.

 

Out of Class

9 hours per week

Outside of class, students spent most of their time solving problems from the five assigned problem sets.

 

Semester Breakdown

WEEK M T W Th F
1 No classes throughout MIT. Lecture session scheduled. No session scheduled. Lecture session scheduled. No session scheduled.
2 No session scheduled. Lecture session scheduled. No session scheduled. Lecture session scheduled. No session scheduled.
3 No classes throughout MIT. No session scheduled. No session scheduled. Lecture session scheduled. No session scheduled, but a problem set due.
4 No session scheduled. Lecture session scheduled. No session scheduled. Lecture session scheduled. No session scheduled.
5 No session scheduled. Lecture session scheduled. No session scheduled. Lecture session scheduled. No session scheduled.
6 No session scheduled. Lecture session scheduled. No session scheduled. Lecture session scheduled. No session scheduled, but a problem set due.
7 No session scheduled. Lecture session scheduled. No session scheduled. Lecture session scheduled. No session scheduled.
8 No classes throughout MIT. No classes throughout MIT. No classes throughout MIT. No classes throughout MIT. No classes throughout MIT.
9 No session scheduled. Lecture session scheduled. No session scheduled. Lecture session scheduled. No session scheduled, but a problem set due.
10 No session scheduled. Lecture session scheduled. No session scheduled. Lecture session scheduled. No session scheduled.
11 No classes throughout MIT. No classes throughout MIT. No session scheduled. No session scheduled. No session scheduled.
12 No session scheduled. Lecture session scheduled. No session scheduled. Lecture session scheduled. No session scheduled, but a problem set due.
13 No session scheduled. Lecture session scheduled. No session scheduled. Lecture session scheduled. No session scheduled.
14 No session scheduled. Lecture session scheduled. No session scheduled. Lecture session scheduled. No session scheduled.
15 No session scheduled. Lecture session scheduled. No session scheduled. Lecture session scheduled and problem set due. No classes throughout MIT.
16 No classes throughout MIT. No classes throughout MIT. No classes throughout MIT. No classes throughout MIT. No classes throughout MIT.
Displays the color and pattern used on the preceding table to indicate dates when classes are not held at MIT. No classes throughout MIT
Displays the color used on the preceding table to indicate dates when lecture sessions are held. Lecture session
Displays the color used on the preceding table to indicate dates when no class session is scheduled. No class session scheduled
Displays the symbol used on the preceding table to indicate dates when problem set is due. Problem set due