Mathematics 55
Discrete Mathematics
Syllabus, Fall 1997

Professor: Ran (``RON'') Libeskind-Hadas
Office: Olin 245
Office Hours: Monday 1-3 PM, Tuesday 4:15 - 5 PM, Wednesday 3-5 PM, Friday 3 - 5 PM, and by appointment.

Phone: x18976
E-mail: hadas@cs.hmc.edu
Course Homepage: http://www.cs.hmc.edu/~hadas/courses/math55/index.html

Meeting Times: Tuesday and Thursday 2:45 - 4 PM
Meeting Place: Beckman Auditorium

Tutor: Alan Hatakeyama
Graders: Francis Carr and Marie Snipes

What Is This Course About?

This course is an introduction to a field of mathematics known as discrete mathematics. In contrast to continuous mathematics, discrete math deals with finite sets of objects and with small infinite sets. "Small infinite sets!?" I hear you cry. "Have you lost your mind?" Stick around and you'll see what this is all about.

Discrete math encompasses a number of different areas. In this course we concentrate on two important areas: combinatorics and graph theory. Both of these fields are interesting both from a purely theoretical perspective as well as for their many diverse applications in the sciences and engineering. This course will cover both the theoretical foundations as well as the practical applications. Combinatorics is the the mathematics of counting combinations of objects. Using combinatorial techniques, you'll learn how to win at certain 2-player strategy games, you'll learn how to distribute messages most efficiently in a computer network, and you'll learn how to compute the probability that a monkey could be hired as a librarian, to name just a few applications.

Graph theory is an area of discrete mathematics that deals with entities called graphs. These are not the kind of graphs that you may be used to drawing in calculus or in economics. A graph is a mathematical object that can be used to represent the important attributes of maps, computers, and even certain kinds of codes. Using graph theory, you'll be able to design efficient analog-to-digital converters, design optimal codes, and find out how a chicken can become be a king, to name just a few applications.

Books

There is no required textbook for this class. The lectures are entirely self-contained. However, three textbooks have been put on reserve at Sprague Library for your convenience. They are:

Assignments and Grades

There will be an assignment every week except for the weeks of the exams. Homeworks will be distributed on Tuesday and due the following Tuesday at the beginning of class. However, everyone is entitled to two extensions until Thursday at the beginning of class. You do not need to ask permission to use these extensions. No late homeworks will be accepted after these extensions have been used, except in the case of illness or emergency.

Their will be two exams during the term. Finally, there will be a comprehensive final exam at the end of the term. The relative weighting scheme will be as follows: 
 
	Homework: 40 %
	Exams: 25 %
	Class Participation: 10 %
	Final Exam: 25 %
"Class Participation" simply means being present and attentive in class. You are encouraged to speak up, ask questions, heckle, etc., but this is not required to receive full credit for class participation.

Collaboration Policy

Collaboration on homeworks is encouraged. This means that you may discuss approaches to solving a problem with anyone in the class. However, copying solutions from any source (person or book) is disallowed. All students are expected to conduct themselves in accordance with the Harvey Mudd Honor Code. If you have any questions about what is appropriate or inappropriate collaboration, please talk to Ran. No collaboration is allowed on the exams.

List of Topics

Foundations of Discrete Mathematics Combinatorics Graph Theory