Instructor Insights

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

Course Overview

This page focuses on the course 18.304 Undergraduate Seminar in Discrete Mathematics as it was taught by Dr. Omer Tamuz in Spring 2015.

This course is a student-led seminar on combinatorics, graph theory, and discrete mathematics, in general. Instruction and practice in written and oral communication are emphasized, with participants reading and presenting papers from recent mathematics literature and writing final papers on related topics.

Course Outcomes

Course Goals for Students

  • Develop an understanding of topics in discrete mathematics
  • Teach others about these topics through lectures (or math talks)
  • Develop and refine a personal style of lecturing
  • Provide colleagues with feedback about their lectures
  • Communicate understanding of discrete mathematics through writing
 

Instructor Insights

Lectures were first given to me in my office before being given to the class. [...] These practice sessions often turned into joint efforts to understand the material and to improve the lectures.

—Dr. Omer Tamuz

Below, Dr. Omer Tamuz describes aspects of how he provides students with instructor and peer feedback in 18.304 Undergraduate Seminar in Discrete Mathematics.

In 18.304 Undergraduate Seminar in Discrete Mathematics, students gave 35-minute math talks during our class sessions. Almost all of these lectures were first given to me in my office before being given to the class. I didn't grade these practice sessions. Rather, they often turned into joint efforts to understand the material and to improve the lectures. 

There was a quiz at the end of each lecture during our class sessions. The quiz helped the lecturer and me assess whether or not students understood the concepts presented in the lecture. After completing the quiz, students provided the lecturer with written feedback. The students and I also provided the lecturer with oral comments. 

The students had to write a two-page paper in the beginning of the semester. For some of them, it was their first experience in writing formal math, and they needed to practice in order to understand what would be expected of them in the final paper. At the suggestion of our department communication specialist, I divided students into groups of three, had each group member read the first drafts of the others, and then had them give both written and oral feedback to each other. 

 

Curriculum Information

Prerequisites

Requirements Satisfied

CI-M

Offered

Every fall and spring semester

The Classroom

  • A classroom with four long tables spanning the classroom, chairs behind each table, and two sliding chalkboards at the front.

    Room 1 of 1

    Lecture

    18.304 is taught in a typical classroom with rows of seats and sliding chalkboards

 

Assessment

The students' grades were based on the following activities:

The color used on the preceding chart which represents the percentage of the total grade contributed by student math talks. 45% Student Math Talks (3 papers worth 15% each)
The color used on the preceding chart which represents the percentage of the total grade contributed by the short paper. 7% Short Paper
The color used on the preceding chart which represents the percentage of the total grade contributed by the very short paper. 3% Very Short Paper
The color used on the preceding chart which represents the percentage of the total grade contributed by the final paper. 25% Final Paper
The color used on the preceding chart which represents the percentage of the total grade contributed by class participation. 20% Class Participation

Instructor Insights on Assessment

Please see Instructor Insights for ways in which Dr. Tamuz provides students instructor and peer feedback.

Student Information

45 students took the class in spring 2015.

Breakdown by Year

Primarily juniors and seniors.

Breakdown by Major

All of the students were math majors, with many also majoring in business and some in computer science.

Typical Student Background

Students came to the class with varied levels of preparation. Some needed quite a bit of support, while others were already very knowledgeable. Almost all the students were motivated, curious, and eager to learn

 

How Student Time Was Spent

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

In Class

3 hours per week
  • Met twice per week for 1.5 hours per session; 25 sessions total; mandatory attendance.
  • Students gave 35-minute math talks during class sessions.
 

Out of Class

9 hours per week
  • Lecture Preparation
  • Writing Assignments
 

Semester Breakdown

WEEK M T W Th F
1 No classes throughout MIT. A lecture was scheduled for this session. No session scheduled. A lecture was scheduled for this session. No session scheduled.
2 No session scheduled. Student Presentations were scheduled for this session. No session scheduled. Student Presentations were scheduled for this session. No session scheduled.
3 No classes throughout MIT. Student Presentations were scheduled for this session. No session scheduled. Student Presentations were scheduled for this session. No session scheduled.
4 No session scheduled. Student Presentations where scheduled and an assignment was due. No session scheduled. Student Presentations were scheduled for this session. No session scheduled.
5 No session scheduled. Student Presentations were scheduled for this session. No session scheduled. Student Presentations were scheduled for this session. No session scheduled.
6 No session scheduled. Student Presentations were scheduled for this session. No session scheduled. Student Presentations were scheduled for this session. No session scheduled.
7 No session scheduled. Student Presentations were scheduled for this session. No session scheduled. Student Presentations where scheduled and an assignment was due. 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. Student Presentations were scheduled for this session. No session scheduled. Student Presentations where scheduled and an assignment was due. No session scheduled.
10 No session scheduled. Student Presentations were scheduled for this session. No session scheduled. Student Presentations were scheduled for this session. No session scheduled.
11 No session scheduled. Student Presentations were scheduled for this session. No session scheduled. Student Presentations where scheduled and an assignment was due. No session scheduled.
12 No classes throughout MIT. No classes throughout MIT. No session scheduled. Student Presentations were scheduled for this session. No session scheduled.
13 No session scheduled. Student Presentations were scheduled for this session. No session scheduled. Student Presentations where scheduled and an assignment was due. No session scheduled.
14 No session scheduled. Student Presentations where scheduled and an assignment was due. No session scheduled. Student Presentations were scheduled for this session. No session scheduled.
15 No session scheduled. Student Presentations were scheduled for this session. No session scheduled. Student Presentations were scheduled for this session. 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 students presentations are held. Student Presentations
Displays the symbol used on the preceding table to indicate dates when assignments are due. Assignment due date
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 lecture sessions are held. Lecture session