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 Concepts of Math 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 Probability. 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 determine how to move beyond simple calculations by formulating axioms for the subject.

Class website: http://www.math.cmu.edu/~jmackey/summer/concepts.html

Class Meetings: Class meets Monday through Friday (except for July 4th) from 9-10:20am in Scaife Hall 125.

Instructor Office Hours: Monday and Thursday from 11-noon, and by appointment.

Office: Gates 4005        Phone:268-1204       Email:jmackey@andrew.cmu.edu

Course Staff Office Hours: The Course Staff will also hold many office hours: Course Staff Office Hours
https://calendar.google.com/calendar/embed?src=q3e4c11v528q4sm5dmtb0qa0v0%40group.calendar.google.com&ctz=America%2FNew_York

I strongly encourage you to attend these office hours as they are an integral part of the course and they will be devoted to the understanding and amplification of material presented in class.

Homework: Homework exercises are an essential part of the course. It is difficult to understand the material and do well on the exams without working through the homework problems in a thoughtful manner. Discussion of the homework with your peers is encouraged, but copying any part of another person's homework is not permitted. Please think about the problems posed, your strategies, and the validity of your logic and explanations.

Homework assignments are posted here: http://www.math.cmu.edu/~jmackey/summer/homework.html
Homework is to be submitted through Gradescope (you should have gotten an email, if not, see me) by the required due date and time. Homework that is submitted after the due date and time, but before the solutions are posted will receive half credit (with an asterisk to get full credit if the course grade is borderline). Typesetting homework solutions using LaTex is encouraged. If you choose to handwrite and then scan homeworks, then here is a helpful resource for scanning documents on campus: Scanning documents
https://www.library.cmu.edu/using/print/scanning

Homework and Exam regrade requests must be submitted within two days of the return date.

Book: An infinite descent into pure mathematics -> https://infinitedescent.xyz/
An infinite descent into pure mathematics , default, by Clive Newstead.
An infinite descent into pure mathematics , tablet, by Clive Newstead.
An infinite descent into pure mathematics , smartphone, by Clive Newstead.
An infinite descent into pure mathematics , print, by Clive Newstead.

Supplemental (optional) Book: Everything You Always Wanted To Know About Mathematics , by Brendan Sullivan
http://www.math.cmu.edu/~jmackey/summer/bws_book.pdf

Supplemental (optional) Book: Mathematical Thinking: Problem-Solving and Proofs (2nd Edition), by D'Angelo and West

Midterms: There will be three in-class midterms. The dates of the midterm exams are as follows:

Midterm 1: Tuesday, July 16

Midterm 2: Friday, July 26

Midterm 3: Thursday, August 8

Grading: Your course grade will be determined as follows:

Each of the two high midterm scores: 30%
The low midterm score: 15%
Homework: 25%
The highest possible grade cutoffs will be 90% for an A, 80% for a B, 70% for a C, and 60% for a D.
These cutoffs may be lowered slightly, and they will not be increased.

Calculators: Calculators and other technology will be of little use in this course. Calculators will not be allowed during the exams.

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