### 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 *18.212 Algebraic Combinatorics*, *18.440 Probability and Random Variables*, and *6.006 Introduction to Algorithms*.

### Instructor Interview

*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*.

- Addressing Communication in Mathematics through Recitations
- Creating the Term Paper Assignment
- Assessing Students’ Writing

### Curriculum Information

#### Prerequisites

*18.02 Calculus II: Multivariable Calculus*

GIR

#### Requirements Satisfied

- CI-M in Mathematics
- 18.310 can be applied toward a Bachelor of Science in Mathematics.

#### Offered

Every fall

### Assessment

The students’ grades were based on the following activities:

- 55% Problem sets and writing assignments
- 15% Quiz 1
- 15% Quiz 2
- 15% Quiz 3

The instructors discuss their assessment insights here.

### Student Information

#### Enrollment

66 students

#### 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

- 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

- 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

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

### 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