Course Policies Math 211 Discrete Mathematics, Spring 2023

Overview

Discrete Math is an important transition course in your mathematical development that builds on the mathematical maturity that you've begun developing in your previous math classes. We'll talk about some really interesting mathematics from several different areas, but the common theme is that all of the mathematical structures will have separate, discrete parts. This is in contrast to the framework of continuous functions that you have studied in a calculus course.

A major focus of this course will be helping you develop your abilities to form rigorous mathematical arguments and to write complete mathematical proofs. This is one of the reasons why Discrete is a pre-requisite for all of the proof-based 300-level math courses.

The course will stretch you to think in new ways, which may be a little disconcerting at times, but it will be really rewarding. Plus, the mathematics is beautiful.

This is going to be a really fun semester!

Goals for a 200-level Mathematics Course

By the end of this semester you should:

• Be able to formulate a concise, precise mathematical arguments and proofs, including recognizing when it is complete or when further justification is needed
• Be able to read and communicate advanced technical concepts
• Be willing to approach a problem even if you do not know whether or not your approach will be successful. If it doesn't work out, try something else!
• Appreciate the necessity of rigorous mathematical arguments
• Continue in your development from being a consumer of mathematics to being a producer of mathematics

Goals Specific to Discrete Math

You should develop:

• A deep understanding of discrete mathematical structures from topics in number theory, set theory, combinatorics, and graph theory
• The ability to communicate clear, concise, correct mathematical proofs using mathematical language and notation that any other student in the class could understand
• A fluency with different proof techniques, including direct proofs, proof by contradiction, and induction
• An embrace of productive confusion when you are approaching a problem that is not exactly like one you have seen in the past
• An appreciation that there can be many valid ways to prove the same mathematical result

Expectations

One of the features that makes your Wheaton education so special is that we have time in small classes to explore material together. It is important that you are present and engaged during the class meetings, but a significant part of your learning will occur outside of class during office hours or when working on problem sets.

You should expect to put in approximately 3 hours outside of class for each scheduled hour of class. In other words, expect to spend a roughly 9 hours per week on Discrete outside of the scheduled class meetings. There will be some weeks where you spend more time, and there may be some weeks where you spend slightly less.

The Honor Code

We operate under the Wheaton Honor Code for all of your academic work at Wheaton. This carries certain freedoms and responsibilities for both you as a student and me as a professor. I take this quite seriously.

Most likely, no Honor Code issues will arise this semester. If you are uncertain about whether a particular situation falls under the Honor Code, then please consult with me. However, if an Honor Code issue does come up, I will assume that you are prepared for the full consequences. Remember that you should write out, and sign, the following statement on all course work:

"I have abided by the Wheaton College Honor Code in this work."

Evaluation

Your final grade will be determined by

Class Engagement/Participation	15%
Problem Sets & Pre-Class Check-Ins	40%
Three Take-home Exams	45%

Class Engagement/Participation

A significant part of the class meetings will be devoted to working in small groups on problems that delve more deeply into the content introduced in the weekly Big Ideas notes and discussed at the beginning of class. A substantial amount of your learning will happen during these collaborative sessions by bouncing ideas off of other students and seeing how other groups approach the problems. I will also determine your Engagement/Participation grade for each class meeting using a binary scale: You were present and engaged with your peers or you weren't.

However, I also know that there may be times when you have a valid reason for missing class. I'll be really flexible, so if you need to miss class, please let me know. Let's just keep the lines of communication open.

Problem Sets & Pre-Class Check-Ins

Pre-Class Check-Ins

The purpose of the Pre-Class Check-Ins is to give you motivation to engage with the major ideas for the week before class. Mathematical understanding is built in stages, and you will understand the concepts more quickly if the class meetings are your second exposure to the fundamental ideas. The Pre-Class Check-Ins consist of three questions: Have you read the Big Ideas notes for this week? How is this week in Discrete going for you? Is there anything else you'd like me to know?

You will submit your Pre-Class Check-Ins through Canvas, and I will grade them on a binary scale: You submitted a response or you didn't. Notice that these are due at 9:00 am on Monday! This will give me enough time to review your responses before our class on Monday. You will be allowed to drop one Pre-Class Check-In at the end of the semester.

Problem Sets

You will have a Problem Set due most weeks of the semester that you will submit through Canvas. These will be posted to the webpage approximately a week before they are due.

Take-home Exams

The purpose of the exams is for you to demonstrate your understanding of the course material and, just as importantly, to give you feedback on where your understanding is strong and where you may need more work. The exams will be open-note take-home exams where you will have several days to work on them. See the Tentative Weekly Syllabus for dates of the exams. I will provide more details about the structure of the exams as the time gets closer.

I know that exams can be stressful, especially with the other academic, extracurricular, and family commitments that you may have. To try to reduce some of this stress concerning your grade, I will weight your exam scores by differing amounts: Your lowest exam score will count 20% of your exam grade, the second lowest will count 30%, and the highest will count 50% of your exam grade. For example, if your three exam scores are 71, 82, and 93, then your overall exam average will be 85.3.

Optional Textbooks

There is no required textbook for our course, but there are several texts that you may choose to use as a reference:

• Ernst: Introduction to Proof via Inquiry-Based Learning
• Epp: Discrete Mathematics with Applications, 4th edition, on reserve in the library
• Levin: Discrete Mathematics, An Open Introduction, 3rd edition
• Sundstrom: Mathematical Reasoning, Writing and Proof, Version 3 and accompanying screencasts

Getting Help with Discrete

Please come see me during my drop-in office hours! No appointment necessary! If you have a conflict and cannot make my office hours, please email me and we can set up an appointment for another time.

Remember that the goal of the course is to help you learn discrete math and develop your mathematical thinking! If there's any point where you feel that the structure of the class isn't working for you, please come by and we can figure out some possible strategies.