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 course we will study finite sets and structures by reasoning logically about their properties.

We will begin with concrete objects like numbers, sequences and games and learn to conclude things about them using elementary logic. After studying a proof technique known as induction, we will explore sets, functions and modular arithmetic (think adding 4 hours to ten o'clock makes it two o'clock instead of sixteen o'clock) .

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.

We will then turn our attention to 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.

The study of relationships via Graph Theory will round out the course.

Office: Wean 6117        Phone:268-2545       Email:jmackey@andrew.cmu.edu

Office Hours: Monday, Tuesday and Thursday from 10-11am, and by appointment.

Homework: Homework exercises are an essential part of the course. It is difficult to understand the material at a worthwhile level 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 is due at the beginning of class each Thursday. The marked homework sets will be returned to you the following week by the TAs. Each problem on the set will receive comments and a score of 0, 1 or 2 indicating "not much correct", "basically correct with a detail or two missing" or "completely correct exemplary solution", respectively.

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