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 18.310 Principles of Discrete Applied Mathematics as it was taught by Professor Michel Goemans, Dr. Lorenzo Orechhia, Dr. Richard Peng, and Susan Ruff in Fall 2013.

This course introduced students to topics such as probability, counting, linear programming, number-theoretic algorithms, sorting, data compression, and error-correcting codes. It was also a Communication-Intensive in the Major course.

Course Outcomes

Course Goals for Students

  • Gain a basic understanding of topics in discrete mathematics
  • Begin to communicate successfully as mathematicians

Possibilities for Further Study/Careers

This course prepared students to enroll in courses such as 18.312 Algebraic Combinatorics, 18.440 Probability and Random Variables, and 6.006 Introduction to Algorithms.

 

Instructor Insights

In the following pages, Michel Goemans, Peter Shor (a colleague in the Mathematics Department), Lorenzo Orecchia, and Susan Ruff describe various aspects of how 18.310 Principles of Discrete Applied Mathematics was developed and taught.

 

Curriculum Information

Prerequisites

18.02 Calculus II: Multivariable Calculus
GIR

Requirements Satisfied

Offered

Every fall

The Classroom

  • Classroom with sliding chalkboards, two narrow tables in front of the chalkboards, three rows of tiered seating with tablet desks, A/V equipment, and an overhead projector.

    Room 1 of 2 Click for next classroom.

    Lecture

    The lecture classroom featured sliding chalkboards, A/V equipment, and tiered seating for 81 students.

  • Classroom with three chalkboards and four long tables with 19 modern black chairs visible.

    Click for previous classroom. Room 2 of 2

    Recitation

    Recitations took place in classrooms that featured sliding chalkboards, tables, and seating for up to 30 students.

 

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 problem sets and writing assignments. 55% Problem sets and writing assignments
The color used on the preceding chart which represents the percentage of the total grade contributed by quiz 1. 15% Quiz 1
The color used on the preceding chart which represents the percentage of the total grade contributed by quiz 2. 15% Quiz 2
The color used on the preceding chart which represents the percentage of the total grade contributed by quiz 3. 15% Quiz 3
 

The instructors discuss their assessment insights here.

Student Information

66 students took this course when it was offered in Fall 2013.

Breakdown by Year

About 50% sophomores and 50% juniors.

Breakdown by Major

Almost exclusively Mathematics majors or students with a double major in Mathematics and another concentration.

Typical Student Background

Many students entered the class with limited experience writing mathematical proofs.

Enrollment Cap

Enrollment in the recitations was limited to about 20 students in order to enable instructors to provide students with adequate writing support; this cap largely determined the overall enrollment cap of 70-80 students in the course. 

 

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 3 times per week for 1 hour per session.
  • Instructors demonstrated technical aspects of discrete applied mathematics; at the end of some lectures, they conducted computer demonstrations of key concepts.
 

Recitation

1 hour per week
  • Met 1 time per week for 1 hour per session; mandatory attendance.
  • Instructors and students further discussed course content and how it related to professional writing and oral communication in the field of mathematics.
 

Out of Class

8 hours per week

    Students completed problem sets and writing assignments, including a term paper.

 

Semester Breakdown

WEEK M T W Th F
1 No classes throughout MIT. No classes throughout MIT. Lecture session. Recitation session. Lecture session.
2 Lecture session. No session scheduled. Lecture session; assignment due date. Recitation session. Lecture session.
3 Lecture session. No session scheduled. Lecture session; assignment due date. Recitation session. No classes throughout MIT.
4 Lecture session. No session scheduled. Lecture session. Recitation session. Lecture session; assignment due date.
5 Lecture session. No session scheduled. Lecture session; assignment due date. Recitation session. Lecture session; quiz held.
6 Lecture session. No session scheduled. Lecture session; assignment due date. Recitation session. Lecture session.
7 No classes throughout MIT. No classes throughout MIT. Lecture session. Recitation session. Lecture session.
8 Lecture session. No session scheduled. Lecture session. Recitation session. Lecture session.
9 Lecture session; assignment due date. No session scheduled. Lecture session; assignment due date. Recitation session. Lecture session; quiz held.
10 Lecture session. No session scheduled. Lecture session. Recitation session. Lecture session.
11 No classes throughout MIT. No session scheduled. Lecture session. Recitation session; assignment due date. Lecture session.
12 Lecture session. No session scheduled. Lecture session; assignment due date. Recitation session. Lecture session.
13 Lecture session. No session scheduled. Lecture session. No classes throughout MIT; assignment due date. No classes throughout MIT.
14 Lecture session. No session scheduled. Lecture session; assignment due date. Recitation session. Lecture session; quiz held.
15 Lecture session. No session scheduled. Lecture session. No classes throughout MIT; assignment due date. 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 assignments are due. Homework/Writing Assignment 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 recitation sessions are held. Recitation session
Displays the symbol used on the preceding table to indicate dates when quizzes are held. Quiz
 

Course Team Roles

Lead Instructor (Prof. Michel Goemans)

  • Delivered lectures
  • Met with teaching team to plan recitations
  • Co-facilitated norming meetings
  • Assessed students’ writing

Recitation Leader (Dr. Lorenzo Orecchia)

  • Met with team to plan recitations
  • Taught recitations first, providing a model for other recitation leaders
  • Participated in norming meetings
  • Assessed students’ writing

Recitation Leader (Dr. Richard Peng)

  • Met with team to plan recitations
  • Led recitations
  • Participated in norming meetings
  • Assessed students’ writing

Writing Across the Curriculum Lecturer (Susan Ruff)

  • Met with team to plan recitations
  • Co-facilitated norming meetings
  • Recorded recitations for research purposes
  • Assessed students’ writing
  • Coached undergraduate graders on assessing students’ writing

Undergraduate Graders

  • Participated in norming meetings
  • Assessed students’ writing