MATH 250: Discrete Mathematics

Kalamazoo College

Spring 2009

Syllabus

This course is an introduction to formal structures and mathematial reasoning. Graphs, sets, logic, induction, structure of mathematical proof, counting, relations, and algebraic structures are presented. Hands-on work is a central component of the course, embodied in homework assignments and lectures that include hands-on exercises.

Instructor:   Pamela Cutter
Olds/Upton 203F, 337 - 7064

Pam's weekly schedule

Required Text:  

Gersting, Judith L., Mathematical Structures for Computer Science, 6th edition, W. H. Freeman and Company, 2007.

Class Web Site:   http://www.cs.kzoo.edu/math250/

Goals:   At the conclusion of this course, students should be familiar with the concepts and the language of logic, set theory, combinatorics, and other aspects of formal mathematics which arise in computer science. Skills in problem solving and analysis should be stronger, and students should feel more comfortable reading and writing mathematics.

Prerequisites: MATH 112 and one computer science course, or permission of the instructor.

Topics to be covered (and tentative course schedule):

Weeks 1 & 2:
 
Logic and Proofs (Chapters 1 and 2)
Weeks 3 & 4:
 
Sets and Relations (Chapters 3 and 4)
Weeks 5 & 6:
 
Functions (Chapter 4)
Midterm
Weeks 7 & 8:
 
Combinatorics and Probability (Chapter 3)
Weeks 9 & 10:
 
Graph Theory and Trees (Chapter 5)
Exam Week: Final Exam at time set by Registrar

Grades will be based on:

Attendance and Class Participation 5%
Homework 40%
Projects and Presentations 15%
Two Exams 40%

Attendance and Participation:

Regular attendance and fully engaged participation is expected of all students in this course. In the case of any absence, whether excused or not, you are responsible for all the material covered in class. We may occasionally do in-class projects. If you are not in class, you cannot get credit for these projects. Active participation in the class means being on time, being prepared, listening to others, contributing ideas of your own, and asking questions as they come up.

Assignments:

Assignments, announcements, class notes, and other material will be made available on the course web site:
http://www.cs.kzoo.edu/math250/
Students are responsible for checking this resource frequently.

Homework is an integral part of the course. Homework problems from the textbook, and possibly elsewhere, will be assigned each day, along with several pages of reading. You are expected to come to class having completed the reading. You should also bring questions you have from the reading and the exercises to class. There will always be at least one class day for questions and discussion between the assignment and its collection. Homework is due at the beginning of class. To allow for illness and excused absences, everyone will be allowed two late assignments over the entire quarter. After you have used both late assignments, I will not accept late assignments.

There will be several Projects and Presentations assigned throughout the quarter. These will be opportunities to apply the language and concepts learned in class, and to explore other related concepts.

There will be two Exams in this class, a Midterm during fifth week, and a Comprehensive Final Exam. The exams are meant to indicate how well you can apply what you have learned. They will encourage quick thinking and careful synthesis of ideas.

Collaboration and the Honor System

This course operates in accordance with the principles of the Kalamazoo College Honor System: responsibility for personal behavior, independent thought, respect for others, and environmental responsibility. In particular, academic integrity is a fundamental principle of scholarship. Representing someone else's work as your own, in any form, constitutes academic dishonesty. Unauthorized collaboration and receiving help from others outside the bounds permitted by the instructor are also violations of the College honor code. You are responsible for working within the permitted bounds, and acknowledging any help from others or contributions from other sources.

Any student with a disability who needs an accommodation or other assistance in this course should make an appointment to speak with me as soon as possible.