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, in-class activities, projects, and reflection.


Required Text:

Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd Edition.
Available for free at in both pdf and an interactive online version.

Additional resources may be provided in print or online

Class Web Site:

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:

(A preliminary schedule can be found on the course web page.)

Sets and Functions (Chapter 0)
Counting (Chapter 1)
Sequences (Chapter 2)
Symbolic Logic and Proofs (Chapter 3)
Graph Theory (Chapter 4)
Number Theory (Chapter 5)
Additional Topics as time allows

Grades will be based on:

Homework Assignments, In-class Activities 50%
Projects/Papers 15%
Reflective Responses, Quizzes, Tests 35%

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 will have many in-class exercises. If you are not in class, you are responsible for finding out what you can do to get credit for these exercises. 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, announcements, class notes, and other material will be made available on the course web site:
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 almost every 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 should be typed and saved into a pdf file or written neatly and scanned into a pdf file and then submitted on Kit by the beginning of class. Any handwritten assignment that cannot be clearly read is subject to a loss of points.

There will be one or more Projects and/or Papers and/or 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 several Quizzes throughout the quarter, and possibly a longer test if the need arises. Quizzes and tests are intended for you to demonstrate mastery of the material being covered in the course.

The course will also involve at least 2-3 Reflective Responses. These will be opportunities to describe key ideas that have been covered in class and to reflect on what you have learned so far. These will tentatively take place at the end of 2nd week, 6th week, and 9th week.

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.

Homework questions: You should feel free to work with others on the homework questions. As you work with others, keep in mind that the goal is not just getting a solution to the problem, but learning how to solve the problem yourself. The write-ups of these problems should be your own work. You should also state at the top of the write-ups who you discussed these problems with. You should also feel free to take advantage of the Math Physics Center (MPC) and/or the CS Collaboration Center for help on the homework questions.

Projects: You may work in pairs or individually on any of the projects that are assigned. You may not work with the same partner more than once. When you work with a partner, you should only submit one copy of the project, with both names on it. I may also ask both partners to submit separate statements accounting for who did what on the project.

You may discuss the requirements and strategies of a programming project with others in the class, but you should not look at code belonging to anyone outside your team or make your code available to anyone other than your teammate. If you have code-specific questions you should address them to a TA or faculty member only. Computer Science TAs are available in the CS Collaboration Center, Sunday through Thursday. Check the door of OU 312 for a schedule. You should acknowledge in your program documentation any help you receive.

Quizzes, Tests, and Reflective Responses should be entirely your own work unless otherwise specified.

Title IX Support and Responsibilities:

Kalamazoo College strives to provide an environment free of bias, discrimination, and harassment. If you have been the victim of sexual or gender-based harassment, discrimination, misconduct, or violence, I encourage you to report this so the College can provide you options for support or resolution though the Title IX process. If you share information of an incident with me, I am required to notify the Title IX Coordinator about the facts of the incident. For more information about your options and confidential resources, please visit the Title IX website.