Math 2001 Fall 20

MATH 2001: Introduction to Discrete Mathematics (Fall 2020)

Peter Mayr
Schedule and assignments
Section 1, MWF 9:10-10:00 am, UMC 210 (Glenn Miller Ballroom)
Section 3, MWF 12:40-13:30 pm, MAIN 150 (Old Main Chapel)

Course description

Do you know a formula for adding up the first n positive integers, 1+2+...+n? How can you find such a formula and convince yourself and others that it is actually correct? The goal of this course is to enable you to

read and write mathematical texts on your own,
find arguments why a mathematical statement is true/examples why not,
write proofs as logically structured sequence of arguments using given definitions and theorems,
communicate mathematical ideas in speaking and writing in a logically structured sequence of sentences that others can understand.

We will learn and practice these skills in the area of discrete mathematics (as opposed to ``continuous'' mathematics like calculus or analysis). In particular we will cover the following topics:

sets - the basic building blocks to formulate Math
logic - how to reason about facts
combinatorics - counting
methods of proof - how to organize arguments
relations and functions - interactions between elements of sets

Specific learning goals

In addition to the general learning goals given above, the topic specific goals for this class are

Use the constructions of Zermelo-Fraenkel set theory to specify sets.
Check the equivalence of statements in propositional logic using truthtables.
Negate and prove statements with universal and existential quantifiers.
Distinguish and use direct proof, contrapositive proof, proof by contradiction, and induction in appropriate settings.
Recognize and count basic combinatorial objects like (un)ordered lists with(out) repetition using powers, factorials, binomial coefficients.
Investigate properties of relations (partial orders, equivalences and their partitions) and functions (injective, surjective, invertible).
Define and compute in the integers modulo n.
Establishing the cardinality of infinite sets using bijections, Schroder-Bernstein Theorem.

Texts

Richard Hammack. The Book of Proof. Creative Commons, 3rd edition, 2018. Available for free
Additional reading:

Paul Halmos. Naive Set Theory. Springer, 1974. Available via CU library link

Details on requirements for COVID-19, accomodations, etc

According to campus policy students who have tested positive for COVID-19, have symptoms of COVID-19, or have had close contact with someone who have tested positive for COVID-19, have symptoms of COVID-19 must stay home. If you must stay home, notify me as soon as possible to set up a plan to obtain lecture notes and take quizzes remotely.

Schedule

Classes are generally in-person. After Fall break all classes and the final exam are fully remote.

Office hours

W 10:00-11:00 am, 13:30-14:30 pm on Zoom (see address on Canvas) or by appointment
One necessary requirement for a passing grade is to pose at least one question in an office hour during the semester.

Assignments

There are 2 kind of assignments:

Homework problems are posted every Friday on the course website. Please submit your solutions as pdf on Canvas before class on the following Friday. I expect clearly organized and worded solutions (if you are able to type even better). Anything not legible will be marked as wrong.
Writing projects are posted 4-5 times during the semester. For these you will have about 1 week time to type a first draft in LaTeX and submit it on Canvas. This will then be marked, and you have another week to revise your solution accordingly and improve your grade on it.

Since communicating about mathematics is one goal of this course, you are allowed and encouraged to discuss your assignments with others. However I ask you to follow this approach: First try to solve your problem on your own. If you get seriously stuck, discuss it with your colleagues, me, etc. In any case write up the solutions that you hand in alone.

Exams

Quizzes every Monday in class. For distancing reasons answers will be submitted directly in Canvas. Please bring a laptop, tablet,... for this.
Midterms on Wednesday, September 30 and November 4, in class.
Final exam is take-home on a date TBA in December.

Grading

Your final grade will be determined by the scores of your assignments, quizzes, midterms, and final exam. To combine these items the following weights will be used:

Homework: 35%
Writing projects: 15%
Quizzes: 10 %
Midterms: 20%
Final exam: 20%

A further necessary requirement for a passing grade is to pose at least one question in an office hour during the semester.
Late homework will not be accepted. There is no make-up for missed quizzes. However the 2 lowest homework scores and the 2 lowest quiz scores will not count towards the final grade.

Scientific writing

There is a variety of word-processing software for writing Mathematics. LaTeX is the most widespread. You can use it with many text editors or via some cloud-based service, like OverLeaf.

How to succeed in this class

Go to class! It seems obvious, but learning the material in small portions 3 times a week is easier than reading up on it in some book by yourself. Always keep up with the topics. You also get nerdy Math jokes.
Ask questions early and often! If you are not sure about something, ask about it immediately -- no matter whether in class, in office hours, or by mail. Do not assume that you can skip or figure out things later that you do not understand now. If you are missing the basics, you may fall behind and struggle with more complicated concepts later in class.
Do the work! The only way to learn stuff is to try it yourself. Strive to do all the homework assignments. Some will be more challenging than others. If you are stuck on the hard ones, discuss them with colleagues or ask for possible hints in office hours or by mail.
Learn from mistakes! Look at all feedback you get on graded homework, quizzes, exams, etc. Make sure you understand where you went wrong and how to get the correct solution. In particular revise all relevant graded work before exams.
Organize in study groups! Meet with classmates a couple of times a week to discuss lectures and homework. Still write up your solutions to assignments when you are alone, never in a group.
Take advantage of office hours! If you cannot make it to the official hours, ask to meet at some other time. Office hours are an additional resource for you to discuss stuff for which there is no time during class. Come prepared! Try to solve homework problems alone before you ask for help and be ready to explain your thoughts and where you are stuck.