Instructor Interview
Below, Professor Yufei Zhao describes various aspects of how he taught 18.226 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.
Prof. 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.
OCW: How did you use the lecture time in class to ensure maximum benefit to your students?
Prof. 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
- 18.211 Combinatorial Analysis
- 18.600 Probability and Random Variables
- Real Analysis—either 18.100A, 18.100B, or 18.100C
or permission of instructor
Requirements Satisfied
18.226 can be applied toward a doctorate degree in Pure or Applied Mathematics, but is not required.
Offered
Every other fall semester.
Assessment
Grade Breakdown
Grading for 18.226 was primarily based on homework grades (no exams). A modifier up to 5 percentage points may be applied (in either direction) in calculating the final grade, based on factors such as participation.
Student Information
Enrollment
41 students
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
Met 2 times per week for 1.5 hours per session; 25 sessions total.
Out of Class
Outside of class, students spent most of their time solving problems from the six assigned problem sets.
