Instructor Insights

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

Instructor Insights

Professor Yufei Zhao, who took 18.A34 Mathematical Problem Solving (Putnam Seminar) as an undergraduate at MIT and was a three-time Putnam Fellow, has gone on to a flourishing career in mathematics:

It is an incredibly satisfying feeling to struggle with an interesting problem and eventually solve it.

— Yufei Zhao

Yufei Zhao Wins Future of Science Award

Four from MIT Named 2019 Sloan Research Fellows

Under his coaching, MIT students have been remarkably successful in the Putnam Competition:

MIT Students Take Back Putnam Competition Honors

Below, Professor Zhao describes various aspects of how he teaches the Putnam Seminar.

OCW: How do you cultivate and sustain students’ interest in problem-solving?

Yufei Zhao: By exposing them to interesting problems that hook them. It is an incredibly satisfying feeling to struggle with an interesting problem and eventually solve it.

OCW: What strategies do you use to promote students’ perseverance during problem-solving?

Yufei Zhao: I try to show them how the problems we discuss are related to more advanced mathematics and help them see the big picture. (Of course, in research, the time horizon is much longer than in math competitions!)

OCW: In what ways does the Putnam Seminar create a sense of community among learners engaged in problem-solving?

Yufei Zhao: Each week one of the classes is a lecture (often guest lectures by upper-level undergraduates who have previously done well in the Putnam Competition) and the other class is for student presentations of homework problems. The student presentations really help in building the sense of community. During student presentations, the other students in the class often comment and point out flaws or gaps in the arguments presented. I also try to encourage good presentation skills.

 

Curriculum Information

Prerequisites

None

Requirements Satisfied

Unrestricted elective credits

Offered

Every fall semester

The Classroom

  • A classroom with rows of tables and chairs facing four large blackboards.

    Room 1 of 1

    Seminar

    Classes were held in a room equipped with long tables, about 30 chairs, blackboards on two walls, and an A/V system.

 

Assessment

Grade Breakdown

  • Grading was based on homework and in-class presentations.
  • All students registered in the class were required to participate in the Putnam Competition.

Student Information

18 students took this course when it was taught in Fall 2018.

Enrollment

In the Fall 2018 semester, enrollment was 18 students, an increase from 7–12 students in previous years

Breakdown by Year

First-year students

Breakdown by Major

Mostly prospective math majors, some prospective computer science majors

Typical Student Background

Most students have previous experience with math competitions and camps from high school

 

How Student Time Was Spent

During an average week, students were expected to spend 6 hours on the course, roughly divided as follows:

In Class

2 hours per week
  • Met 2 times per week for 1 hour per session; 26 sessions total; mandatory attendance
  • First session each week: usually a lecture, delivered by an upper-level undergraduate
  • Second session each week: student presentations of solutions to homework problems
  • Last five class sessions: student presentations of solutions to past Putnam Competition problems and to student-created Putnam-type problems
 

Out of Class

4 hours per week
  • Completion of at least 6 problems each week, drawing on the week’s topic-based problem sets and sets of supplementary problems
  • Preparation for in-class presentations
  • Preparation for Putnam Competition
 

Semester Breakdown

WEEK M T W Th F
1 No classes throughout MIT. No classes throughout MIT. No session scheduled. Lecture session scheduled. No session scheduled.
2 No session scheduled. Student presentations scheduled and problem set due. No session scheduled. Lecture session scheduled. No session scheduled.
3 No session scheduled. Student presentations scheduled and problem set due. No session scheduled. Lecture session scheduled. No session scheduled.
4 No session scheduled. Student presentations scheduled and problem set due. No session scheduled. Lecture session scheduled. No session scheduled.
5 No session scheduled. Student presentations scheduled and problem set due. No session scheduled. Lecture session scheduled. No session scheduled.
6 No classes throughout MIT. No classes throughout MIT. No session scheduled. Student presentations scheduled and problem set due. No session scheduled.
7 No session scheduled. Student presentations scheduled and problem set due. No session scheduled. Lecture session scheduled. No session scheduled.
8 No session scheduled. Student presentations scheduled and problem set due. No session scheduled. Lecture session scheduled. No session scheduled.
9 No session scheduled. Student presentations scheduled and problem set due. No session scheduled. Lecture session scheduled. No session scheduled.
10 No session scheduled. Student presentations scheduled and problem set due. No session scheduled. Lecture session scheduled. No session scheduled.
11 No classes throughout MIT. Student presentations scheduled and problem set due. No session scheduled. Lecture session scheduled. No session scheduled.
12 No session scheduled. Student presentations scheduled and problem set due. No session scheduled. No classes throughout MIT. No classes throughout MIT.
13 No session scheduled. Student presentations scheduled. No session scheduled. Student presentations scheduled. No session scheduled.
14 No session scheduled. Student presentations scheduled. No session scheduled. Student presentations scheduled. No session scheduled.
15 No session scheduled. Student presentations scheduled. No session scheduled. No classes throughout MIT. 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 symbol used on the preceding table to indicate dates when problem sets are due. Problem set due
Displays the color used on the preceding table to indicate dates when no class session is scheduled. No class session scheduled
Displays the color used on the preceding table to indicate dates when student presentations are scheduled. Student presentations