MATH 240
Discrete Mathematics

Time

MWF 10:10am - 11:00am (A3)

Location

MC Reynolds 317

Instructor

Dr. Brent Yorgey
yorgey@hendrix.edu
(501) 450-1377
Office Hours

Overview

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:

Resources

Optional Resources


Calendar

Assignment submission form


Date Topic Resources Due Notes
         
W 1/19 Introduction, propositions lecture notes    
F 1/21 Propositional logic lecture notes    
         
M 1/24 Logical equivalences      
W 1/26 Logical equivalences; predicates      
F 1/28 Predicates and quantifiers      
  predicates in Disco      
         
M 1/31 Introduction to proofs      
W 2/2 More proofs, examples lecture notes    
F 2/4 No class (snow)      
         
M 2/7 More proof techniques, examples lecture notes    
W 2/9 Sets lecture notes    
F 2/11 The empty set, Cartesian product, and power sets lecture notes    
         
M 2/14 Set operations lecture notes; Disco session    
W 2/16 Functions lecture notes; functions.disco    
F 2/18 1-1, onto, and invertible functions lecture notes; functions.disco    
         
W 2/23 Set cardinality lecture notes    
F 2/25 Countable and uncountable sets lecture notes    
         
M 2/28 Disco: loading, comments, subtraction, numeric types lecture notes; example.disco    
W 3/2 Disco: first-class functions first-class-functions.disco    
F 3/4 More proof examples lecture notes    
         
M 3/7 Intro to number theory: divisibility lecture notes    
W 3/9 Modular equivalence lecture notes    
F 3/11 Solving modular equivalences; prime numbers lecture notes    
         
M 3/14 Prime numbers lecture notes    
W 3/16 No class      
F 3/18 GCD lecture notes    
         
M 3/28 Euclidean algorithm lecture notes    
W 3/30 Bézout’s Theorem and modular inverses lecture notes    
F 4/1 Chinese Remainder Theorem lecture notes    
         
M 4/4 Induction lecture notes    
W 4/6 Strong induction lecture notes    
F 4/8 Recursive definitions induction.disco    
         
M 4/11 More recursive definitions and structural induction induction.disco    
W 4/13 Intro to combinatorics; product rule trees.disco / lecture notes    
F 4/15 Addition and subtraction rules lecture notes    
         
M 4/18 Division rule and binomial coefficients lecture notes    
W 4/20 Binomial coefficient patterns lecture notes    
F 4/22 Introduction to graphs lecture notes    
         
M 4/25 Paths, cycles, and trees lecture notes    
W 4/27 Eulerian paths lecture notes    
F 4/29 Eulerian circuits and Hierholzer’s Algorithm lecture notes    

Coursework and policies

Specifications grading

This course uses specifications grading. Briefly, this means that grading of individual assignments is on a credit/no-credit basis, with a specification that tells you what you must do in order to get credit. Your final letter grade in the course, in turn, is determined by the below specification that says what you must complete in order to get each letter grade.

Grade Specification
A Complete all modules to level 2
   
B Complete all but one modules, at least half to level 2
   
C Complete all but two modules to level 1
   
D Complete at least half of the modules to level 1

Due dates policy

Submission policies

Modules

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 readings. Each module can be completed to one of two levels:

Each individual module specifies what you need to do to get Level 1 or Level 2 credit. For example, there may be an extra challenge problem set and/or reading you must complete to get Level 2 credit.

# Module Resources Assigned Due
1 Propositional logic xor.disco F 21 Jan F 28 Jan
2 Quantifiers   F 28 Jan F 4 Feb
3 Proofs and sets sets.disco F 11 Feb F 18 Feb
4 Sets and functions module4.disco F 18 Feb F 25 Feb
5 Cardinality Survey F 25 Feb F 4 Mar
6 Disco   F 4 Mar F 11 Mar
7 Divisibility & primes module7.disco Th 24 Mar F 1 Apr
8 Modular arithmetic & induction   F 8 Apr F 15 Apr
9 Combinatorics   F 15 Apr F 22 Apr

Expectations

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
  • 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.
Preparation
  • 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 quiz and exam problems myself, to help ensure they are reasonable and don't hold any unintended surprises.
Engagement
  • 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

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).

Disabilities

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.

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 Dean Mike Leblanc at leblanc@hendrix.edu or 501-450-1222 or the Title IX Coordinator Allison Vetter at titleix@hendrix.eduor 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 hendrix.edu/nondiscrimination.

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 (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 well-being than I do about this class!