Course Outline: The ability to reason logically and clearly from a set of accepted principles is fundamental not only in Mathematics, but in Life in general. In this class we will learn how to provide complete explanations of why certain things are true. We will also determine how to detect false statements and provide conclusive evidence of their falsity.
We will begin with concrete objects like numbers, sets and functions and learn to prove things about them using elementary logic. After studying a proof technique known as induction, we will explore functions and use them to classify the size of infinite sets (yes, there are different sized infinite sets).
Next we will find out how to count the number of objects that can be obtained as the result of a certain process. For example, we can count the number of distinct poker hands which have three aces and two kings or the number of different three-topping pizzas that can be made if ten toppings are available. We then tackle elementary problems concerning integers, such as factorization, divisibility and their possible applications to cryptography.
Lastly, we will study some classic topics from Discrete Math. Elementary probability will be explored in order to ascertain, for example, just how likely are we to be dealt a poker hand containing three aces and two kings. We will see that probability is related to counting and will move on to study useful topics in counting known as the pigeonhole principle and inclusion/exclusion.
Classes and Recitation Sessions: 21-128 meets via Zoom MWF from 12 to 12:50. 15-151 meets via Zoom MWF from 2:40-3:30. Here is a Zoom link for the class sessions: Classes
Our wonderful Teaching Assistants will also hold two weekly recitation sessions. I strongly encourage you to attend the recitation sessions as they are an integral part of the course and may cover examinable material not covered in lecture.
TA Zoom (not Office) Hours: Click here for the calendar of Teaching Assistant Zoom (not Office) Hours.
We will be holding office hours online this semester. Students will go to the OHQ website
and upon logging in, find the 21-128/15-151 queue. When adding themselves to the queue, students must add a link in the
description box to their personal zoom meeting so that TAs can provide them (and any collaborators) with help. They can also include a
brief description as to their question(s). At the top of the hour, the TA will enter the zoom room linked in the
calendar to discuss general questions. This room will be open for the entire OH period for students to enter and leave freely.
Remote Classes and Recitations: Students have the option of attending lectures and recitations remotely. These will be scheduled and conducted through Zoom, and we will be solely using the remote instruction method for all lectures and recitations after Thanksgiving. Please make sure to have a computer with a good internet connection and a good web camera for remote instruction and exams. In particular, we will proctor remote exams through Zoom and it is a requirement that students taking remote exams use a webcam to clearly display their testing environment throughout the exam.
In the event of a poor internet connection (for either students or instructors), lectures and recitations will be recorded and made available to watch at a later time.
Instructor's Office: Gates 4005 Phone:268-1204 Email:firstname.lastname@example.org
Course Website: www.math.cmu.edu/~jmackey/151_128/welcome.html
Instructor Zoom (not Office) Hours: Tuesday from 1:00-2:00,
Wednesday from 10:15-11:15, and by appointment:
Mackey Zoom Hours
Help: In addition to class, recitation sessions, and zoom (not office) hours, the University operates Peer Tutoring Centers. Individualized tutoring and other help options are also available through Academic Development.
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