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


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 Homework (turn in) Practice problems (optional) Challenge problems Notes
W 22 Jan Intro, propositions student info survey      
F 24 Jan Propositional logic (1.1, 1.2) (1.1) 8, 14, 32e (1.2) 8a-d, 20 (1.1) 1, 3, 9, 15, 21, 22, 27, 33 (1.2) 5, 7, 19, 21 (1.2) 38  
    due W 1/29      
M 27 Jan Propositional equivalences (1.3) (1.3) 6, 8, 10b, 12b, 26 (1.3) 5, 7, 9, 11, 25, 27, 31 (1.3) 42-45; prove the absorption equivalences using the core equivalences  
W 29 Jan Predicates and quantifiers (1.4, 1.5) (1.4) 10, 24, 60 (1.5) 6, 14b-e, 32 (1.4) 5, 7, 9, 12, 13, 27, 45 (1.5) 7, 19, 27, 31, 37 (1.4) 49, 61 Grade weight choices due
F 31 Jan Introduction to proofs (1.7, 1.8) (1.7) 8, 16, 26, 34 (1.7) 5, 7, 15, 27 (1.7) 38  
    due W 2/5      
M 3 Feb More proofs (1.7, 1.8) (1.8) 4, 8, 26 (1.8) 3, 17, 19, 25, 35    
W 5 Feb Sets (2.1) (2.1) 2, 42 (2.1) 7, 15, 17 (2.1) 46  
F 7 Feb Set operations (2.1, 2.2) (2.1) 26, 30 (2.2) 2, 12, 26, 50 (2.2) 3, 4, 7, 9, 25, 51 (2.2) 46  
    due W 2/12      
M 10 Feb Functions (2.3) (2.3) 12, 14, 22, 40 (be sure to explain/prove your answers!) 13, 15, 17, 21, 23 34, 35, 72  
W 12 Feb Set cardinality (2.5) (2.5) 2abce, 16, 18 (2.5) 1abcef, 19, 20 (2.5) 27, 29  
F 14 Feb Uncountable sets (2.5) (2.5) 10, 40      
    due W 2/19      
M 17 Feb No class (Presidents’ Day)        
W 19 Feb Sequences (2.4) No HW      
F 21 Feb Summation (2.4) No HW     Midterm 1 out; A note on big operator notation
           
M 24 Feb Divisibility and modular equivalence (4.1) (4.1) 3, 4, 10a-d (4.1) 9 (4.1) 35  
W 26 Feb Modular equivalence and arithmetic (4.1) (4.1) 14c-f, 22a-b, 34, 37 (4.1) 13, 23, 25, 29, 35 44-46  
F 28 Feb Midterm exam 1       Project 1 assigned
    due W 3/4      
M 2 Mar Primes (4.3) (4.3) 4, 12 (4.3) 1, 3, 5 (4.3) 6, 13; come up with divisibility rules for 11 and 19  
W 4 Mar GCD and the Euclidean Algorithm (4.3) (4.3) 18, 24a-f, 32 (4.3) 15, 17, 19 (4.3) 36, 37  
F 6 Mar Bézout’s Theorem and modular inverses (4.3, 4.4) (4.3) 42 (4.4) 12, 16 (4.3) 43, 44 (4.4) 11 (4.4) 7, 18  
    due W 3/11      
M 9 Mar Chinese Remainder Theorem and Fermat’s Little Theorem (4.4) (4.4) 24, 35, 38 (4.4) 23, 33, 39    
W 11 Mar Public-key cryptography and RSA (4.6) (4.6) 24, 26   (4.6) 23 You can use Wolfram Alpha for modular exponentiation.
F 13 Mar RSA and digital signatures No HW     Project 1 due
    due W 4/1      
M 16 Mar No class (COVID-19)        
W 18 Mar No class (COVID-19)        
F 20 Mar No class (COVID-19)        
           
  Spring break        
           
M 30 Mar Online learning trial (shared Google doc       Meeting video
W 1 Apr Induction (5.1): Intro, Example 1 (sum of odds), Example 2 (5.1) 10, 20, 32      
F 3 Apr Strong induction (5.2), Example 1 (FTA), Example 2 (Fibonacci) (5.2) 4, 12, 26a-d      
           
M 6 Apr          
W 8 Apr          
F 10 Apr         Project 1 revisions due; Project 2 assigned
           
M 13 Apr          
W 15 Apr          
F 17 Apr          
           
M 20 Apr          
W 22 Apr          
F 24 Apr         Project 2 due
           
M 27 Apr          
W 29 Apr          
F 1 May          
           
M 4 May          
           
F 8 May 8:30-11:30 Project 2 revisions due        

Coursework

Homework

Assignment submission form


Homework and practice problems will be assigned daily. Homework problems will be graded; practice problems are optional and carry no credit.

Unless otherwise noted, homework problems assigned in a given week are due by the beginning of class the following Wednesday. For example, the problems assigned Monday March 3, Wednesday March 5 and Friday March 7 are due Wednesday, March 12.

I encourage you to work together on homework problems, and I will not be checking for academic integrity violations on HW submissions. However, keep in mind that copying your HW solutions from your classmates or other sources, while it will not get you in trouble, is simply stupid and short-sighted: it will come back to bite you on quizzes and exams.

Homework problems should be written or typed neatly, and turned in via one of two methods:

If you are ill or absent for some reason, it is still your responsibility to turn in homework on time, except by prior arrangement.

Late homework problems can be accepted for half full credit up until the

day of the final exam

last day of finals (May 13).

Graded homework will generally be handed back by the Monday after it is submitted.

Quizzes

There will be weekly short quizzes, typically on Fridays, covering material from the homework turned in on Wednesday.

Quizzes can be retaken as many times as you want; each time you retake a quiz the new grade replaces the previous grade. To retake a quiz, just schedule a 15-minute meeting slot, being sure to clearly indicate which quiz or quizzes you intend to retake.

# Date Topic
1 Fri, 31 Jan Propositional logic
2 Fri, 6 Feb Predicate logic
3 Fri, 14 Feb Sets
4 Fri, 21 Feb Functions
5 Fri, 6 Mar Divisibility and modular arithmetic
6 Fri, 3 Apr GCD and stuff
7 Fri, 3 Apr CRT and FLT

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.

You will have two weeks to complete each project:

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

Exams

There will be two one midterm exam (worth 25% of your exam grade) and a cumulative final exam (worth 50% of your exam grade). For each exam, you will be given the exam questions one week in advance (at least a week and a half or two weeks for the final exam). You may use any resources in preparing your solutions to the exam—including your notes, textbook, online resources, and each other—with the only exception that I will not answer specific questions about the exam. On the day of the in-class exam, you must come with no notes and write out your solutions on a clean copy of the exam.

Grading

Your final grade in the course is based on:

By default, each category is worth 20% of your grade. The remaining 20% is yours to assign as you wish. For example, if you feel confident in your ability to do well on exams, you could assign all 20% to your exam grade, making exams worth 40% of your grade in the course. Or, if you feel better about doing well on quizzes and projects, you could make them each 30% of your grade, leaving homework and exams worth 20% each; or you could simply add 5% to each category to keep everything weighted equally.

You must inform me of your choice no later than Wednesday, January 29. Simply send me an email with the subject “MATH 240 grade distribution” letting me know how you would like to distribute the 20%. If you do not make a choice, by default all the categories will be weighted equally.

In any case, 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).


Commitments

It is my ultimate goal for this course, and my teaching, to develop your academic skills, advance your learning of math and computer science concepts, and support the liberal arts in general. To do so will require commitments from myself and from you toward meeting this goal.

Active Participation

I will be prepared and on time for class each day, ready to use class time to help you understand the course material. I will respectfully listen to, understand, and answer questions asked in class.

You are expected to attend class and actively participate in discussions every day, answering questions, asking questions, presenting material, etc. Your participation will be respectful of your classmates, both of their opinions and of their current point in their educational journey, as we each approach the material with different backgrounds and contexts.

Communication

I will clearly communicate expectations, assignment details and dates, and grading standards. I will respond to emails within 24 hours (including weekends).

You are expected to check your email for occasional course announcements, and to let me know via email if you will need to miss class for some reason.

You should 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.

Constructive Feedback

I will provide graded feedback on assignments (homework, quizzes, projects, and exams) within one week. I will be available for appointments outside of class and will give you my full attention during meetings. I will be open to feedback and willing to respond in substantive ways to your suggestions or concerns.

You are encouraged to provide constructive comments for improving this course for furthering your learning throughout the semester. You are welcome to submit anonymous feedback at any time. There will also be an opportunity for anonymous course feedback at the end of the term, in which I hope you all participate. Through your feedback I can improve this course and others for future students.

Academic Integrity

I will abide by the above syllabus and grade your work fairly.

As stated in the Hendrix Academic Integrity Policy, all students have agreed to adhere to the following principles:

  • All students have an equal right to their opinions and to receive constructive criticism.
  • Students should positively engage the course material and encourage their classmates to do the same.
  • No students should gain an unfair advantage or violate their peers' commitment to honest work and genuine effort. It follows that any work that a student submits for class will be that student's own work. The amount of cooperation undertaken with other students, the consistency and accuracy of work, and the test-taking procedure should adhere to those guidelines that the instructor provides.
  • Members of the Hendrix community value and uphold academic integrity because we recognize that scholarly pursuits are aimed at increasing the shared body of knowledge and that the full disclosure of sources is the most effective way to ensure accountability to both ourselves and our colleagues.

Learning Accomodation

I will make this classroom an open and inclusive environment, accommodating many different learning styles and perspectives.

Any student seeking accommodation in relation to a recognized disability should inform me at the beginning of the course. 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.

Physical and Mental Health

I am willing to work with you individually when life goes off the rails.

Coursework and college in general can become stressful and overwhelming, and your wellness can be impacted when you least expect it. You should participate in self-care and preventative measures, and be willing to find support when you need it.

  • The Office of Counseling Services welcomes all students to see a counselor in a private and safe environment regardless of their reasons for making an appointment. Counseling services are available to all Hendrix students at no cost.
  • Student Health Services provides free healthcare to Hendrix students. Services are provided by an Advanced Practice Registered Nurse (APRN) in collaboration with a local physician.

The Offices of Counseling Services and Student Health Services are located in the white house behind the Mills Center for Social Sciences at 1541 Washington Avenue.