Syllabus

This page serves as the syllabus for math215-a-a22, Discrete Mathematics, taught by Chris Eppolito in the Advent 2022 semester. I may change any portion of this document at any time. In the event this is necessary, I will contact enrolled students by email.

Read this document carefully. This is a contract between us concerning how our course will run.

I suggest that you also see the study tips on the home page (and let me know if you have any further suggestions).

Mathematics is the language of certainty. We strive to build up our knowledge of the world from a few basic principles. Assuming these principles are correct, we can be absolutely certain of our conclusions; indeed, they come with proof!

This class is all about proof and certainty in mathematics. Our main goal in this class is to construct a standard tome of proof techniques and practice them. At the same time, we will study the fundamental mathematical structures necessary for doing computer science.

Even though the objects of focus are mathematical structures, the skills you develop in this course are generally applicable. We will spend a lot of time learning to read and write logical, rigorous arguments. Learning to do so helps us to be critical thinkers, to analyze the reasoning we have for our own positions, and to understand when someone else has position meriting review.

The official description of this course from the course catalogue is…

This course is required for most courses in mathematics or computer science numbered 300 or above. Topics normally include the following: logic, sets, functions, relations, graphs and trees, mathematical induction, combinatorics, recursion, and algebraic structures. The subject matter is to be of current interest to both mathematics and computer science students.

At the end of this course, you should…

1. have working knowledge of basic mathematical structures (sets, functions, relations, graphs, etc.).
2. have knowledge of the mathematics underpinning elementary computer science.
3. be able to translate mathematical statements into propositional/predicate logic.
4. have working knowledge of fundamental proof techniques.
5. be able to clearly communicate good mathematical proofs through your writing.
6. have strengthened critical thinking skills and the tools to analyze arguments (mathematical and otherwise) for logical rigour.

Here is what I expect from you at a minimum.

• Submit your own work, and adhere to the Honor Code (more below).
• Be mindful and courteous during ALL interactions with me and your peers (including emails).
• Communicate with me if you have any concerns—I can help you, but I need to know that I should!
• Know when assignments are due and planning accordingly so that they are submitted in a timely fashion.
• READ YOUR EMAILS.

• Solutions to exercises must clearly demonstrate the logic you used, and may only use methods and notations discussed in my lectures or OK'd by me in advance. Everything you turn in must be legible AND well-organized, with clear logic describing your solution.

  A few thoughts on how I do this:

  1. Write a first draft, solving the problems.
  2. REWRITE that draft, now including the necessary English to make full sentences so other people can understand what you've done.
  3. Take some time to do other things (e.g., get a coffee or have a nap).
  4. Return to your work, and check that it still makes sense.
  5. Repeat as necessary 2–4 until you attain work that makes us both proud.

  Remember: if your work would be too messy for an English class, it's too messy for my class.

• You must check the website for updates daily. I will not remind you of deadlines.

You agreed to follow the Honor Code when you matriculated. All forms of academic dishonesty, including plagiarism, are violations of the Honor Code and will be treated as such. If you ever have a question about an assignment or need additional help, please ask for assistance rather than jeopardize your academic career.

The University of the South is committed to fostering respect for the diversity of the University community and the individual rights of each member of that community. In this spirit, and in accordance with the provisions of Section 504 of the Rehabilitation Act of 1973 and the Americans with Disabilities Act (ADA), the University seeks to provide students with disabilities with the reasonable accommodations needed to ensure equal access to the programs and activities of the University.

Any student with a documented disability needing academic adjustments is requested to speak with Student Accessibility Services (SAS) as early in the semester as possible. If approved for accommodations, the student has the responsibility to present their instructors with a copy of the official letter of academic accommodations. Please note: Accommodation letters should be dated for the current term; accommodations will not be provided without a current accommodation letter; and accommodations cannot be applied retroactively.

SAS is located in the Office of the Dean of Students (931.598.1229). Additional information about accommodations can be found on the Student Accessibility Services website.

Students who have questions about physical accessibility should inform their instructors so that we can ensure an accessible, safe, and effective environment.

This syllabus operates under the assumption that our course meets in person for the whole semester. I will make a major update to this syllabus if COVID-19 interferes.