Discrete Mathematics is a survey of dozens of mathematical topics. Obviously, much of the material is deeply connected to your other math and computer science courses, and there are a few topics which explicitly use math that you have learned in other classes. However, discrete math is an incredibly rich subject area, and our class only scratches the surface of the true depth of this subject. Additionally, if you pay close enough attention, you will find several connections between the material covered in this course and your other non-Math/CS courses, as well as your other extracurricular activities and hobbies. Your paideia project will involve two parts:
Depth: You must explore an advanced topic that builds on one of the subjects that we discussed in the course. Here are some possible topics that you could pick:
Breadth: you must describe two ways in which the course material is connected to one of your other experiences at Southwestern (other than your Math/CS classes). This could be a non-Math/CS course, an extracurricular activity, a personal hobby, or some other part of your life that is not one of your Math/CS courses.
You will explore the depth and breadth of discrete math through both a presentation and a written report. You'll submit your work through the following checkpoints:
Project proposal (due 10/29/2026, 5 points): Tell me what advanced topic that you want to pursue for depth, and what to connection you want to explore for breadth. I will provide feedback on whether your depth topic is relevant and appropriately deep, and whether your proposed breadth connections are plausible and sufficiently far outside of math/CS. You can pivot later but your proposal needs to demonstrate that you've started thinking seriously about your paideia project.
First draft (due 11/17/2026, 15 points): You will submit a first draft of your writeup. Your writeup should have two sections for depth and breadth, respectively. In the depth section, you should describe what you learned about the advanced topic that you studied. Write this section as if you were trying to teach this advanced subject to one of your fellow discrete math students who knows the fundamental ideas but hasn't studied this particular topic as deeply as you have. Write to convince me that you've learned about a powerful and interesting discrete math result that we haven't covered in class. For the breadth section, You should thoroughly describe the two non-Math/CS connections that you found. Got each connection, recap the topic from the class that you found interesting, describe the outside activity, and describe the connection. Write it as if you were trying to explain two topics from this course to someone who has zero Math/CS background, and you decided that the best way to explain it would be to use a non-Math/CS analogy. I will provide feedback on whether your depth section explores the advanced topic with enough depth, clarity, and rigor; for the breadth section I will provided feedback on whether the connections are relevant, accurate, and well-explained. Your first draft should be at least one page in total length, and it will be graded strictly on whether you've demonstrated significant progress and effort. However, the more work you put into your first draft, the less work you will have to put into your final submission.
Depth presentation (30 points): During the final week of class you will give a short presentation (5-10 minutes, not including time for questions) about your chosen advanced topic. First, clearly introduce and motivate the topic at hand. Then teach the class about that topic. This could mean showing how to solve a new kind of problem using a new technique; it could mean replicating a famous proof; it could mean exploring some important breakthrough that helped make significant progress towards solving the problem. Your goal is to for your fellow discrete mathematicians to come away from your lecture having learned something new that builds on what they've already been learning about all semester. You may present your work using a slideshow, a blackboard/whiteboard presentation, or some other medium that you approve with me ahead of time. Your presentation will be graded as follows:
Written report (50 points): Your final written report should describe what you explored for depth and what connections you made for breadth. Your report should be at least two pages long (at least one page each for the depth and breadth sections, respectively), single-spaced, 11 point font, default margins for your document editor, and either Arial, Times New Roman, or Computer Modern font. Visual aids are highly encouraged but not required, and they do not count towards the length requirements. Your report will be graded on the following criteria:
Any use of AI tools to produce any portion of the paideia project could result in an F in the course.