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

Below, Professor Yufei Zhao describes various aspects of how he taught *18.217 Graph Theory and Additive Combinatorics*.

**OCW:** How did you approach designing and teaching this course?

**Yufei Zhao:** This is the second iteration of a course I first taught two years ago. My goal was to put together a cohesive introduction to an area of modern combinatorics that I actively work in. I wanted to showcase some of the most attractive mathematics that I have learned starting as a beginning graduate student. In particular, I wanted to explain a beautiful and extensive connection that bridges graph theory and additive combinatorics, two seemingly different areas of mathematics.

I am very happy to see that several of the students who took the first iteration of this course have gone on to produce excellent research in this area. One common theme in the feedback that I received from students in the class is that they appreciated how the subject touches upon a broad range of mathematics, including graph theory, combinatorics, number theory, analysis, geometry, group theory, topology, linear algebra, etc.

I wanted to explain a beautiful and extensive connection that bridges graph theory and additive combinatorics, two seemingly different areas of mathematics.

— Prof. Yufei Zhao

**OCW:** In this course, students wrote course notes, and you met with them to go over their writing. In what ways is this assignment important for students’ development as mathematicians, future lecturers, and/or math communicators?

**Yufei Zhao:** Some of the materials that I taught in this course were discovered only fairly recently, so they can be hard to find outside of research papers. I wanted to create a set of notes, eventually turning into a new textbook, that would cover the material in an inviting way and be accessible to non-specialists.

I built on a popular practice of asking students to “scribe” notes for individual lectures. Making good notes takes a lot of work and requires feedback from the lecturer.

To streamline this process, I created a single document on Overleaf, an online collaborative LaTeX editor. I asked students to sign up to cover lectures. The document was carefully set up on Overleaf so that students could add their lectures as new sections into the larger document. Other students in the class could then edit and correct these notes as the semester goes on.

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## Curriculum Information

### Prerequisites

There are no formal prerequisites for 18.217, but the course presupposes mathematical maturity at the level of a first-year math graduate student.

### Requirements Satisfied

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

### Offered

18.217 is taught every fall semester, but with a different topic each year.

## Assessment

### Grade Breakdown

The final grade was determined by the *minimum* of the student’s performance in two categories:

- 6 problem sets
- Writing assignments, consisting of (1) course notes and (2) Wikipedia contributions.

## Student Information

### Breakdown by Year

Mostly graduate students and advanced undergraduates

### Breakdown by Major

Primarily Mathematics and Electrical Engineering / Computer Science majors

### Typical Student Background

The subject tends to appeal to students who enjoy mathematical problem solving.

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

## In Class

Met 2 times per week for 1.5 hours per session; 26 sessions total; mandatory attendance.

## Out of Class

Outside of class, students spent their time solving problems from the five assigned problem sets and completing the two writing assignments.

## Semester Breakdown

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