MATH 240
Discrete Mathematics


MWF 9:10am - 10:00am (A2)


MC Reynolds 115


Dr. Brent Yorgey
(501) 450-1377
Office Hours


An introduction to the discrete paradigm in mathematics and computer science. Topics include logic, set theory, number theory, induction, recursion, counting techniques, and graph theory.

Learning Goals

Upon completing this course, you will be able to:


Optional Resources


Assignment submission form

Date Topic Notes
  stream = video     pdf = PDF     disco = disco code  
W 1/18 Introduction to Disco stream pdf disco  
F 1/20 Syllabus and more Disco stream disco CSCI student info survey due
    Module 0 assigned
M 1/23 Propositional logic stream pdf Grading contract due
W 1/25 Implication & logical equivalences stream pdf  
F 1/27 Logical equivalences stream pdf Module 0 due, Module 1 assigned
M 1/30 Predicates & Quantifiers stream pdf disco  
W 2/1 No class (ice)  
F 2/3 Nested & restricted quantifiers stream pdf Module 1 due, Module 2 assigned
M 2/6 More quantifiers, intro to proofs stream pdf  
W 2/8 Proofs stream pdf How to Prove Things
F 2/10 Proof examples stream pdf Module 2 due, Module 3 assigned
M 2/13 Proof by contradiction stream pdf  
  Introduction to set theory stream pdf  
W 2/15 Sets in Disco, subsets, empty set stream pdf disco  
F 2/17 Set operations stream pdf Module 3 due, Module 4 assigned
M 2/20 No class (midwinter break)  
W 2/22 Functions stream pdf Grading contract evaluation due
F 2/24 1-1 and onto functions stream pdf disco Module 4 due, Exam 1 take-home problems posted
M 2/27 Bijections and countable sets stream pdf  
W 3/1 Countable and uncountable sets stream pdf  
F 3/3 Midterm exam 1 Module 5 assigned
M 3/6 LaTeX stream Writing project 1 assigned
W 3/8 Divisibility stream pdf disco  
F 3/10 Modular equivalence stream pdf Module 5 due, Module 6 assigned
M 3/13 More modular equivalence stream pdf  
W 3/15 Primes stream pdf  
F 3/17 GCD and the Euclidean Algorithm stream pdf Module 6 due
M 3/20 No class (spring break)  
W 3/22 No class (spring break)  
F 3/24 No class (spring break)  
M 3/27 Bézout’s Theorem and Modular Inverses stream pdf  
W 3/29 Fermat’s Little Theorem stream pdf disco  
F 3/31 RSA stream pdf disco Grading contract evaluation due
    Writing project 1 due
    Module 7 assigned
M 4/3 Sequences stream pdf  
T 4/4   Exam 2 take-home problems posted
W 4/5 Induction stream pdf  
  Additional induction examples: yt yt  
F 4/7 Strong induction stream pdf Module 7 due, Module 8 assigned
    Writing project 2 assigned
M 4/10 Midterm exam 2  
W 4/12 Intro to combinatorics, product rule yt  
  Product rule examples yt  
F 4/14 Addition and subtraction rules, PIE stream pdf  
M 4/17 Division rule and binomial coefficients stream pdf Module 8 due
W 4/19 Binomial coefficients stream pdf Module 9 assigned
F 4/21 No class Writing project 2 due
M 4/24 Introduction to graphs stream pdf  
W 4/26 Vertex degrees, Eulerian paths stream pdf  
F 4/28 Hierholzer’s Algorithm stream pdf Module 9 due
M 5/8 Final exam, 8:30-11:30am  
  Practice problems  


Grading contracts

In this course, you determine your own final grade: you will prepare and submit for my approval a grading contract explaining your chosen final grade and what you will do to achieve it. You will then earn your chosen final grade by fulfilling the agreed-upon contract.

This may be different than what you are used to. Professor Cathy Davidson of CUNY perfectly sums up the reasons for doing things this way:

The advantage of contract grading is that you, the student, decide how much work you wish to do this semester; if you complete that work on time and satisfactorily, you will receive the grade for which you contracted. This means planning ahead, thinking about all of your obligations and responsibilities this semester and also determining what grade you want or need in this course. The advantage of contract grading to the professor is no whining, no special pleading, on the student’s part. If you complete the work you contracted for, you get the grade. Done. I respect the student who only needs a C, who has other obligations that preclude doing all of the requirements to earn an A in the course, and who contracts for the C and carries out the contract perfectly.

Required components of a grading contract

There is no specific format required for a grading contract, but it must have the following components:

Example grading contract

For example, a grading contract might look like this:

My desired course grade in Discrete Math is a C. To achieve this grade, I will complete the following:

Grading contract submission

You must turn in an initial proposed grading contract by the start of class on Monday, January 23rd. After the initial submission, I may require some revisions before I approve your contract.

Contract evaluation and adjustment

Two times during the semester (Wednesday, February 22 and Friday, March 31) you are required to reflect on your progress in the course and complete an evaluation of your work, comparing it against what you agreed to in your grading contract. Your evaluation should:

  1. Contain a copy of your original grading contract, with items you have completed checked off.

  2. Revise your grading contract with more specific details as appropriate, for example, regarding which modules and writing projects you intend to complete.

  3. Include a 1-2 paragraph reflection, which answers questions such as the following:

    • What have you done well?
    • What have you learned?
    • What could you do to improve your learning?
    • What could I (the instructor) do to improve your learning?
    • Are there ways in which you have not lived up to the requirements of your contract, and if so, what steps are you taking, or will you take, to rectify that?

Your evaluation is also an opportunity to request an adjustment to your contract in either direction. If you find that you will be unable to meet the obligations of your contract, you may request to move to the next lowest grade and its requirements. Contrariwise, if you find that you’ve been performing above the obligations of your contract, you may request to fulfill the requirements for the next higher grade.

Note, however, that you don’t have to wait for an evaluation to adjust your contract. If your life has really gone off the rails (or if, say, you are finding the class easier and more enjoyable than you thought!) just come and talk to me about adjusting your contract.

A, B, and C grades

D and F grades

[Adapted from Cathy Davidson.] You cannot intentionally contract for a grade of D (and certainly not for an F). However, I reserve the right to award a grade of D or F to anyone who fails to meet their contractual obligations in a systematic way. A “D” grade denotes some minimal fulfilling of the contract; an “F” denotes absence of enough satisfactory work, as contracted, to warrant passing of the course. Both a “D” and “F” denote a breakdown of the contractual relationship.


Assignment submission form

There will be a number of modules corresponding to topics in the course. Each module consists of things like problems to solve, programming assignments to complete, and/or readings. Each item on a module will be graded on a 0-4 scale:

To get credit for a module, the average score on the items must be at least 3.25.

If you do not get credit for a module, you may revise it; see the resubmission policy below.

# Module Resources Assigned Due
0 Introduction to Disco   F 20 Jan F 27 Jan
1 Propositional logic disco F 27 Jan F 3 Feb
2 Quantifiers   F 3 Feb F 10 Feb
3 Proofs How to Prove Things F 10 Feb F 17 Feb
4 Sets   F 17 Feb F 24 Feb
5 Functions   F 3 Mar F 10 Mar
6 Divisibility   F 10 Mar F 17 Mar
7 Number theory   F 31 Mar F 7 Apr
8 Sequences & Induction   F 7 Apr M 17 Apr
9 Combinatorics   W 19 Apr F 28 Apr

Module submission policy

Writing projects

Assignment submission form

You will complete two writing projects during the semester, either individually or in groups of two. The projects will give you an opportunity to tackle some bigger problems, and focus on putting details together into a coherent written exposition. You are required to write up your projects using the LaTeX typesetting system.

You will have two weeks to complete each project:

More details about each project will be made available when it is assigned.


There will be three in-class exams in the course, two midterm exams and a cumulative final exam. Exams will typically have two types of questions:

Exam grading

Exam problems will be graded in the same manner as homework problems. To receive credit for an exam, you must score an average of 3.0 or better on the exam problems.

Exam revision

If you do not receive credit for an exam, you may revise it; see the resubmission policy below.

However, if you score 2 or lower on an exam problem, Dr. Yorgey may also require you to complete an additional, similar problem. This additional problem must be completed under similar conditions as the original exam (that is, you may prepare a solution ahead of time using any resources you wish, but then you must write out your solution without referring to any resources, at an agreed-upon time). To receive credit for the exam you must score an average of 3.0 or better on all the exam problems, including any newly assigned problems.

Tokens, late submissions, and resubmissions

Each student starts the semester with three virtual tokens which they can spend however they wish. Tokens are non-transferable.

Conversely, additional tokens may be earned in the following ways:


Although you and I play different roles in the course, we both have your learning as a common goal. There are things I expect from you as a student in the course, but there are also things you can expect of me as the course instructor and facilitator.

If I am not fulfilling my responsibilities outlined below, you are welcome (and encouraged!) to call me out, perhaps via the anonymous feedback form. I will also initiate a conversation if you are not fulfilling yours. However, none of us will meet all of the expectations perfectly—me included!—so it’s also important that we have grace and patience with one another.

What I expect from you What you can expect from me
  • Check your email and Teams for occasional course announcements.
  • Let me know via email or Teams message if you will need to miss class for some reason.
  • Let me know as soon as possible if you feel you are struggling, would like extra help, or have something going on that will affect your engagement in the course or your ability to fulfill your responsibilities.
  • Clearly communicate expectations, assignment details and dates, and grading standards.
  • Return grades and feedback on submitted work within two business days of submission.
  • Respond to emails within 24 hours.
  • Come prepared to fully engage in class meetings, with distractions minimized, to the best of your ability.
  • Spend time outside of class actively practicing unfamiliar or shaky concepts or skills (not just reading over notes).
  • Have a concrete plan for how we will spend each class meeting, prepared to lead you through the plan.
  • Complete all modules and projects myself, to help ensure they are reasonable and don't hold any unintended surprises.
  • Make myself available to meet outside of class, and give you my full attention during a meeting.
  • Be committed to your learning, open to feedback and willing to respond in substantive ways to your suggestions or concerns.


Attendance in this class is expected, though not required as part of your grade. I appreciate you letting me know when you will need to miss class.

Academic integrity

Hendrix College is committed to high standards of honesty and fairness in academic pursuits. Such standards are central to the process of intellectual inquiry, the development of character, and the preservation of the integrity of the community. Please familiarize yourself with the statement of Academic Integrity.

You should also familiarize yourself with the Computer Science-specific Academic Integrity Policy.


If you have a documented disability or some other reason that you cannot meet the above expectations, and/or your learning would be best served by a modification to the usual course policies, I would be happy to work with you—please get in touch (via Teams or email)! The course policies are just a means to an end; I don’t care about the policies per se but I do care about you and your learning.

It is the policy of Hendrix College to accommodate students with disabilities, pursuant to federal and state law. Students should contact Julie Brown in the Office of Academic Success (505.2954; to begin the accommodation process. Any student seeking accommodation in relation to a recognized disability should inform the instructor at the beginning of the course.

Diversity and Inclusion

Hendrix College values a diverse learning environment as outlined in the College’s Statement on Diversity. All members of this community are expected to contribute to a respectful, welcoming, and inclusive environment for every other member of the community. If you believe you have been the subject of discrimination please contact the Dean of Students Office (Mike Leblanc,, 501-450-1222) or the Title IX Coordinator (Jennifer Fulbright,, 501-505-2901). If you have ideas for improving the inclusivity of the classroom experience please feel free to contact me. For more information on Hendrix non-discrimination policies, visit

Mental and Physical Health

Hendrix recognizes that many students face mental and/or physical health challenges. If your health status will impact attendance or assignments, please communicate with me as soon as possible. If you would like to implement academic accommodations, contact Julie Brown in the office of Academic Success ( To maintain optimal health, please make use of free campus resources like the Hendrix Medical Clinic or Counseling Services (501.450.1448). Your health is important, and I care more about your health and well-being than I do about this class!