 22M:150 Introduction to Discrete Mathematics  Fall :30A - 11:20A MWF 218 MLH  Instructor: Dr. Isabel Darcy Office:B1H MLH Phone: idarcy AT math.uiowa.edu THIS WEEK'S Office Hours: M 12:10-1:00pm, T 1:00 - 1:50pm, Th 2:30 - 3:20pm, F: 2:30 - 3pm, and by appointment. Course WWW site: SES/150/FALL09/150.htmlhttp:// SES/150/FALL09/150.html 1

2016/1/12 (c) , Michael P. Frank 2 So, what’s this class about? What are “discrete structures” anyway?  “Discrete” - Composed of distinct, separable parts. (Opposite of continuous.) discrete:continuous :: digital:analog  “Structures” - objects built up from simpler objects according to a definite pattern.  “Discrete Mathematics” - The study of discrete, mathematical objects and structures. From: MI112A & MI112B Discrete Mathematics, Jen-Liang Cheng Ph.D.

CS 1813 Discrete Mathematics, Univ Oklahoma Copyright © 2000 by Rex Page 3 Tiling with Dominos a mathematical proof – just for practice checkerboard with two missing corners Problem  cover board with dominos  no overlapping dominos  no dominos outside board Dominos – size matches board One domino covers how many red squares? How many squares on board? So, how many dominos will it take? 31 dominos cover how many red squares? How many red squares are there? TILT Yikes! What’s wrong here? Adapted from Singh, Fermat’s Enigma, Walker & Co,