MATH 240
Discrete Mathematics

Time

MWF 10:20am - 11:10am (A3)

Location

Mills 304

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


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 double-check 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) 14c-e, 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, 10a-d (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 Public-key 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      

Coursework

Problems

Assignment submission form


Problems from the textbook (and some I make up myself) will be assigned daily. There are three types of problems:

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).

Projects

Assignment submission form


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.

Grading

Your final grade in the course is based on:

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).


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).

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.

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!