MWF 10:20am  11:10am (A3)
Mills 304
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.
Note: all exercises are taken from the 7th edition of the textbook. If you have a different edition, that’s fine, but you are responsible for finding a way to doublecheck that you are doing the correct problems (sometimes the problems are renumbered between different editions). e.g. find a friend who has the 7th edition and do a quick comparison each week.
Date  Topic / Sections / Video  Problems  Practice  Notes 

Propositional logic and proof  
W 1/20  Intro, propositions  
F 1/22  Propositional logic (1.1, 1.2)  (1.1) 14, 32e  (1.1) 1, 3, 9, 15, 21, 22, 27, 33  
(1.2) 5, 7, 19, 21  
M 1/25  Propositional equivalences (1.3)  (1.3) 12b  (1.3) 5, 6, 7, 9, 11, 25, 26  
Exam problem: NAND  
W 1/27  Predicates and quantifiers (1.4, 1.5)  (1.4) 10, 24  (1.4) 5, 7, 9, 12, 13, 27, 45, 60, 61  
(1.5) 14ce, 31  (1.5) 7, 19, 27, 31, 37  
sample solution for (1.5) 14b  
F 1/29  Introduction to proofs (1.7,1.8)  
M 2/1  More proofs (1.7, 1.8) [unfortunately it seems video recording did not work] 
(1.7) 8, 16, 26  (1.7) 5, 7, 15, 27, 34  
W 2/3  Additional proof techniques and examples (1.7, 1.8)  (1.8) 26  (1.8) 3, 4, 8, 17, 18, 25, 35  
Exam problem: favorite books [LaTeX]  
Exam problem: irrationals [LaTeX]  
F 2/5  No class  
Set theory  
M 2/8  Introduction to sets (2.1)  (2.1) 42  (2.1) 2, 7, 15, 17  
W 2/10  Set operations (2.1, 2.2)  (2.2) 2, 26  (2.1) 26, 30 (2.2) 3, 4, 7, 9, 25, 51  
F 2/12  Functions (2.3)  (2.3) 12, 20, 40b  (2.3) 13, 14, 15, 17, 21, 23, 34  
Injections, surjections, and bijections (2.3)  sample solution for (2.3) 40a  
M 2/15  Set cardinality (2.5)  (2.5) 2  (2.5) 1, 16, 18, 19, 20, 27, 29  
W 2/17  Uncountable sets (2.5)  (2.5) 10  
Exam problem: Boolean functions [LaTeX]  
Exam problem: Composing bijections [LaTeX]  
F 2/19  Class discussion: homework  
Number theory  
M 2/22  Divisibility (4.1)  (4.1) 4, 10ad  (4.1) 3, 9  
W 2/24  No class  
F 2/26  Modular equivalence (4.1)  
F 2/26  Primes (4.3)  
M 3/1  GCD and the Euclidean Algorithm (4.3)  
W 3/3  Bézout’s Theorem and modular inverses (4.3, 4.4)  
F 3/5  CRT and Fermat’s Little Theorem (4.4)  
M 3/8  Publickey cryptography and RSA (4.6)  
Induction and recursion  
W 3/10  Sequences (2.4)  
F 3/12  Summation (2.4)  
M 3/15  Induction (5.1)  Project 1 due  
W 3/17  Strong induction (5.2)  
F 3/19  Recursively defined functions and sets  
M 3/22  Structural induction  
W 3/24  No class  
Combinatorics  
F 3/26  Introduction to combinatorics  
M 3/29  Product and sum rule  
W 3/31  Subtraction rule, division rule, and PIE  
F 4/2  Binomial coefficients  
M 4/5  More binomial coefficients  
W 4/7  Flex  
Relations  
F 4/9  Relations  
M 4/12  Equivalence relations  Project 2 due  
W 4/14  Partial orders  
F 4/16  Flex  
Graphs  
M 4/19  Introduction to graphs  
W 4/21  Paths and trees  
F 4/23  No class  
M 4/26  Eulerian paths  
W 4/28  Planar graphs  
F 4/30  Flex 
Problems from the textbook (and some I make up myself) will be assigned daily. There are three types of problems:
Regular problems are graded on a simple binary credit/no credit scale, based on whether you have demonstrated understanding of the required concepts.
Practice problems are not graded but recommended if you would like extra practice. If you turn them in I will provide feedback on them just like a regular problem.
Exam problems are like regular problems, but you must also submit a short video (via flipgrid) of yourself explaining the important ideas of your solution, as a further way of demonstrating your mastery of the relevant concepts.
Problems have no specific due date, though in order not to get behind, I recommend trying to have problems submitted by one week after they are assigned.
All problems may be submitted, revised, and resubmitted any number of times up until (and including) Friday, May 7. However, revised problems must also include a paragraph reflecting on your learning (for example, what did you misunderstand the first time you submitted the problem? What have you learned since then?)
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 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.
There will also be opportunity to revise and resubmit both projects based on feedback; details will be shared once the projects are posted.
Your final grade in the course is based on:
Regular and exam problems: 65%
Projects: 35%
Final letter grades will be determined according to the usual correspondence:
Score  Grade 

90%  A 
80%  B 
70%  C 
60%  D 
<60%  F 
You are guaranteed a letter grade no worse than the one corresponding to your final average in the table above, but I reserve the right to assign a higher letter grade in certain circumstances (e.g. if you have good attendance and participation and have shown improvement over the course of the semester).
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 


Although attendance in this class is not reflected formally in your grade, I expect you to attend. If you cannot attend class for some reason please let me know in advance (or as soon as possible).
If you have chosen to attend class in person, you are expected to do so consistently; you may not decide to attend remotely some days just because you feel like it. However, there are legitimate reasons for attending remotely, such as feeling ill or travelling unavoidably.
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 Dean Mike Leblanc at leblanc@hendrix.edu or 5014501222 or the Title IX Coordinator Allison Vetter at titleix@hendrix.eduor 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!