MWF 10:10am - 11:00am (A3)
MC Reynolds 317
Dr. Brent Yorgey
yorgey@hendrix.edu
(501) 450-1377
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 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 |
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:
Late homework problems can be accepted for half full credit up until the
last day of finals (May 13).
Graded homework will generally be handed back by the Monday after it is submitted.
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 |
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.
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.
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).
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.
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.
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.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.
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:
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.
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 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.