MWF 9:10am  10:00am (A2)
MC Reynolds 115
Dr. Brent Yorgey
yorgey@hendrix.edu
(501) 4501377
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.
Upon completing this course, you will be able to:
Translate natural language statements to and from formal propositional logic.
Apply the rules of propositional logic to derive correct mathematical arguments.
Recall and apply basic definitions, together with logical reasoning, to solve problems involving naive set theory, number theory, combinatorics, and graph theory.
Solve problems using recursion and induction.
Write coherent mathematical proofs using proper mathematical notation and reasoning.
Date  Topic  Notes 

= video = PDF = disco code  
W 1/18  Introduction to Disco  
F 1/20  Syllabus and more Disco  CSCI student info survey due 
Module 0 assigned  
M 1/23  Propositional logic  Grading contract due 
W 1/25  Implication & logical equivalences  
F 1/27  Logical equivalences  Module 0 due, Module 1 assigned 
M 1/30  Predicates & Quantifiers  
W 2/1  No class (ice)  
F 2/3  Nested & restricted quantifiers  Module 1 due, Module 2 assigned 
M 2/6  More quantifiers, intro to proofs  
W 2/8  Proofs  How to Prove Things 
F 2/10  Proof examples  Module 2 due, Module 3 assigned 
M 2/13  Proof by contradiction  
Introduction to set theory  
W 2/15  Sets in Disco, subsets, empty set  
F 2/17  Set operations  Module 3 due, Module 4 assigned 
M 2/20  No class (midwinter break)  
W 2/22  Functions  Grading contract evaluation due 
F 2/24  11 and onto functions  Module 4 due, Exam 1 takehome problems posted 
M 2/27  Bijections and countable sets  
W 3/1  Countable and uncountable sets  
F 3/3  Midterm exam 1  Module 5 assigned 
M 3/6  LaTeX  Writing project 1 assigned 
W 3/8  Divisibility  
F 3/10  Modular equivalence  Module 5 due, Module 6 assigned 
M 3/13  More modular equivalence  
W 3/15  Primes  
F 3/17  GCD and the Euclidean Algorithm  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  
W 3/29  Fermat’s Little Theorem  
F 3/31  RSA  Grading contract evaluation due 
Writing project 1 due  
Module 7 assigned  
M 4/3  Sequences  
T 4/4  Exam 2 takehome problems posted  
W 4/5  Induction  
Additional induction examples:  
F 4/7  Strong induction  Module 7 due, Module 8 assigned 
Writing project 2 assigned  
M 4/10  Midterm exam 2  
W 4/12  Intro to combinatorics, product rule  
Product rule examples  
F 4/14  Addition and subtraction rules, PIE  
M 4/17  Division rule and binomial coefficients  Module 8 due 
W 4/19  Binomial coefficients  Module 9 assigned 
F 4/21  No class  Writing project 2 due 
M 4/24  Introduction to graphs  
W 4/26  Vertex degrees, Eulerian paths  
F 4/28  Hierholzer’s Algorithm  Module 9 due 
M 5/8  Final exam, 8:3011:30am  
Practice problems 
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 agreedupon 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.
There is no specific format required for a grading contract, but it must have the following components:
Your desired course grade. You may choose to contract for an A, B, or C (if you’re wondering about D’s and F’s, see below). Note that your grading contract should not explain the reasons for your choice. I will not judge you because of your choice, and you do not need to justify it: there are as many different valid reasons for choosing to work toward a particular final grade as there are students. If you do wish to explain to me the reasons for your choice—which you are in no way required to do—you may do so in an email, a personal conversation, etc., but it should not go in your contract.
A description of the work and requirements you will complete, in checklist format. It doesn’t have to be super detailed, but you do have to explicitly include everything. For example, you can’t just say “I will complete all the assignments listed in the syllabus”; you must actually list them. This is so that you and I both know that you are explicitly aware of the requirements, and to help you keep track of what you have completed and what you have yet to complete. You also have some choice in terms of which assignments you complete, so you must record your choice in the contract.
Note that at the beginning of the semester you may not have a very good idea about this. For example, if you need to complete eight modules, it’s not reasonable to insist that you know which specific modules you plan to complete. However, you can refine your contract over the course of the semester. You just have to put something to start; for example, a reasonable default would be to plan to complete the first eight modules assigned.
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:
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.
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:
Contain a copy of your original grading contract, with items you have completed checked off.
Revise your grading contract with more specific details as appropriate, for example, regarding which modules and writing projects you intend to complete.
Include a 12 paragraph reflection, which answers questions such as the following:
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.
[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.
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 04 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  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 
I encourage you to work together on problems; however, problem solutions must be your own work, and academic integrity will be taken seriously.
Problem solutions should be written or typed neatly, and turned in electronically via this Google form. Submissions must be in PDF format (Word, Pages, etc. can export a PDF, typically as an option under the “File” menu).
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 inclass exams in the course, two midterm exams and a cumulative final exam. Exams will typically have two types of questions:
Longanswer questions, such as proofs. You will be told these questions at least one week in advance and will be able to prepare your solution; however, you will not be able to bring any notes with you into the exam.
Shortanswer questions. You will not be given these questions ahead of time. However, Dr. Yorgey will provide resources such as information about what type of questions to expect and/or practice problems.
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.
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 agreedupon 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.
Each student starts the semester with three virtual tokens which they can spend however they wish. Tokens are nontransferable.
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  

Communication 


Preparation 


Engagement 


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.
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 Sciencespecific 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; brownj@hendrix.edu) 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.
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, leblanc@hendrix.edu, 5014501222) or the Title IX Coordinator (Jennifer Fulbright, fulbright@hendrix.edu, 5015052901). If you have ideas for improving the inclusivity of the classroom experience please feel free to contact me. For more information on Hendrix nondiscrimination policies, visit hendrix.edu/nondiscrimination.
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 (brownj@hendrix.edu). 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 wellbeing than I do about this class!