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:
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Translate natural language statements to and from formal
propositional logic.
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Apply the rules of propositional logic to derive correct mathematical
arguments.
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Recall and apply basic definitions, together with logical reasoning,
to solve problems involving naive set theory, number theory,
combinatorics, and graph theory.
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Solve problems using recursion and induction.
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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 |
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| 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 |
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due W 1/29 |
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| 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 |
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| 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 |
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due W 2/5 |
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| M 3 Feb |
More proofs (1.7, 1.8) |
(1.8) 4, 8, 26 |
(1.8) 3, 17, 19, 25, 35 |
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| W 5 Feb |
Sets (2.1) |
(2.1) 2, 42 |
(2.1) 7, 15, 17 |
(2.1) 46 |
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| 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 |
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due W 2/12 |
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| 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 |
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| W 12 Feb |
Set cardinality (2.5) |
(2.5) 2abce, 16, 18 |
(2.5) 1abcef, 19, 20 |
(2.5) 27, 29 |
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| F 14 Feb |
Uncountable sets (2.5) |
(2.5) 10, 40 |
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due W 2/19 |
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| M 17 Feb |
No class (Presidents’ Day) |
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| W 19 Feb |
Sequences (2.4) |
No HW |
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| F 21 Feb |
Summation (2.4) |
No HW |
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Midterm 1 out; A note on big operator notation |
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| M 24 Feb |
Divisibility and modular equivalence (4.1) |
(4.1) 3, 4, 10a-d |
(4.1) 9 |
(4.1) 35 |
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| 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 |
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| F 28 Feb |
Midterm exam 1 |
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Project 1 assigned |
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due W 3/4 |
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| 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 |
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| 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 |
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| 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 |
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due W 3/11 |
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| M 9 Mar |
Chinese Remainder Theorem and Fermat’s Little Theorem (4.4) |
(4.4) 24, 35, 38 |
(4.4) 23, 33, 39 |
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| W 11 Mar |
Public-key cryptography and RSA (4.6) |
(4.6) 24, 26 |
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(4.6) 23 |
You can use Wolfram Alpha for modular exponentiation. |
| F 13 Mar |
RSA and digital signatures |
No HW |
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Project 1 due |
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due W 4/1 |
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| M 16 Mar |
No class (COVID-19) |
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| W 18 Mar |
No class (COVID-19) |
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| F 20 Mar |
No class (COVID-19) |
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Spring break |
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| M 30 Mar |
Online learning trial (shared Google doc |
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Meeting video |
| W 1 Apr |
Induction (5.1): Intro, Example 1 (sum of odds), Example 2 |
(5.1) 10, 20, 32 |
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| F 3 Apr |
Strong induction (5.2), Example 1 (FTA), Example 2 (Fibonacci) |
(5.2) 4, 12, 26a-d |
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| M 6 Apr |
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| W 8 Apr |
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| F 10 Apr |
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Project 1 revisions due; Project 2 assigned |
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| M 13 Apr |
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| W 15 Apr |
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| F 17 Apr |
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| M 20 Apr |
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| W 22 Apr |
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| F 24 Apr |
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Project 2 due |
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| M 27 Apr |
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| W 29 Apr |
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| F 1 May |
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| M 4 May |
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| F 8 May 8:30-11:30 |
Project 2 revisions due |
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Coursework
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:
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Homework may be turned in on physical paper, either handwritten or
printed. There will be a folder available at the start of class for
HW submissions.
- Homework may be turned in electronically via this Google
form. Electronic submissions must be in PDF format (Word,
Pages, etc. can export a PDF, typically as an option under the
“File” menu). If you wish to type your homework you are also
strongly encouraged to typeset it using LaTeX (which you are
required to use for the projects anyway). You may also write your
HW on physical paper and scan it using an app such as Genius
Scan which can export your
document as a PDF.
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.
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:
- Project 1 will be assigned Friday, February
28 and due Friday, March 13.
- Project 2 will be assigned Friday, April 10 and due Friday, April
24.
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.
- Midterm 1: Friday, February 28
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Midterm 2: Friday, April 10
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Final exam: Friday, May 8, 8:30--11:30am
Your final grade in the course is based on:
- Homework
- Quizzes
- Projects
- Exams
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.