Syllabus

	OTTERBEIN COLLEGE MATHEMATICAL SCIENCES DEPARTMENT Math 165 Discrete Mathematics II Spring 2008
	Class	TR 11:00 - 12:15 p.m. in Towers 116
	Class Web Page	http://www.otterbein.edu/home/fac/dvdjstck/math165/LinkFrames.htm
	Instructor	David J. Stucki
	Office	Towers 133
	Office Hours	M 3:00 - 4:00, W 1 - 2, R 12:30 - 1:30, or by appointment
	Email	DStucki@otterbein.edu
	Phone	823-1722
	Home Phone	878-8002 (After 9 a.m. and before midnight, please)

Discrete structures is foundational material for computer science. By foundational we mean that relatively few computer scientists will be working primarily on discrete structures, but that many other areas of computer science require the ability to work with concepts from discrete structures. Discrete structures includes important material from such areas as set theory, logic, graph theory, and combinatorics.

The material in discrete structures is pervasive in the areas of data structures and algorithms but appears elsewhere in computer science as well. For example, an ability to create and understand a formal proof is essential in formal specification, in verification, and in cryptography. Graph theory concepts are used in networks, operating systems, and compilers. Set theory concepts are used in software engineering and in databases.

As the field of computer science matures, more and more sophisticated analysis techniques are being brought to bear on practical problems. To understand the computational techniques of the future, today's students will need a strong background in discrete structures.

-Computing Curricula 2001 Computer Science,
The Joint Task Force on Computing Curricula
IEEE Computer Society
Association for Computing Machinery

Description	Graph theory, including planarity, isomorphism, covering circuits, coloring, trees, searching, and network algorithms; combinatorics including counting, permutations combinations, binomial coefficients, recurrence relations, and binary sequences; cardinality & the pigeonhole principle.
Prerequisites	Math 155
Objectives	The student will become familiar with mathematical concepts and techniques that play a major role in computer science and engineering. This course will give students tools for utilizing precise vocabulary, powerful notation, useful abstractions, and rigorous thinking. In addition to developing skills through explanation, example, and much practice, the student will gain insight into the points of entrance that mathematics makes into computer science
Text	Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games , Ensley, Douglas E., and Crawley, J. Winston, Wiley, 2006. Amazon.com: $106.88 (new) $38.44 (used) BestBookBuys.com : $42.43 Otterbein Bookstore: $148.75 (new) $111.75 (used)
Work Load	"Students are expected to spend three hours per week (including class hours) in study for each quarter hour of credit attempted." (From p. 278 of the Course Catalog, Autumn, 2003 - Spring, 2005, Otterbein College Bulletin, Vol. XC.) Since Math 165 is 3 (Quarter) Credit Hours, 90 hours of study is expected: 24 hours in class (3 hours per week), and 66 hours beyond class hours (8.25 hours per week).
Homework	Homework assignments will be made on a daily basis. It is a basic assumption in this course that mathematics is learned by doing! It is also a cumulative endeavor. Missing key concepts or techniques in one section can handicap you for the remainder of the term. Practice, practice, and practice some more. In general, these assignments are given for you to learn. Homework will not be collected, but doing and understanding the homework will ensure that you are prepared for the quizzes and exams.
Quizzes	You should expect several quizzes to be given on an as needed basis (to be determined by me). These quizzes will be short, unannounced, and most will be very similar to homework problems.
Exams	There will be two tests and a final exam. These will all be closed-book. They will cover lecture material, readings, and homework exercises. The final will be a comprehensive exam covering the entire course. Make-ups will be scheduled only for documented emergencies. If you can document that you have three or more exams scheduled for the same day I will attempt to arrange for an alternate time only if given at least a week’s notice.
Participation	Each student is expected to participate in the class discussions and exercises throughout the semester. To this end, all assigned readings for each day should be completed before the class period in which they are discussed.
Academic Misconduct Policy	All members of the Otterbein College community of learners are expected to follow the rules and customs of proper academic conduct. Proper conduct includes avoiding academic misconduct as defined in the Student Life Handbook. Students are encouraged to help each other learn the course material. Unless specifically prohibited, you may discuss homework problems and lab exercises with one another. Participants in these discussions usually enjoy the benefit of deeper and greater learning. However, all work submitted for evaluation that is based on discussions with others must be your own work; created with your own hands and fingers while thinking it through. Any work submitted for evaluation that includes work done by another, copying of another's work, or the result of following another's step-by-step keystrokes and mouse clicks, is a case of academic misconduct. When academic misconduct is found in any assignment or examination you submit, you will receive a zero grade for that assignment or exam. The misconduct will also be reported to the Office of the Academic Dean. If a previous academic misconduct offense is on your record, you will receive a grade of F for this course and a referral to the judicial system.

Grading	Assignment	Weight	Range	Grade	Range	Grade
	Attendance & Participation	5%	93 - 100%	A	73 - 76.9%	C
	Quizzes	20%	90 - 92.9%	A-	70 - 72.9%	C-
	Midterm exams (2)	40%	87 - 89.9%	B+	65 - 69.9%	D+
	Final Exam	35%	83 - 86.9%	B	60 - 64.9%	D
			80 - 82.9%	B-	0 - 59.9%	F
			77 - 79.9%	C+

**Course Outline**
Week	Text	Topics
(1) 3/31 - 4/4	4.3 - 4.4	Properties of Functions & Relations; Set Cardinality

(2) 4/7 - 4/11	4.5 - 4.6	Equivalence Relations & Numerical Functions
(3) 4/14 - 4/18	5.1 - 5.2	Introduction to Combinatorics; Principles of Counting

		TEST I
(4) 4/21 - 4/25	5.3 - 5.4	Permutations & Combinations; Binomial Theorem
(5) 4/28 - 5/2	5.5 - 5.6	Recurrence Relations
(6) 5/5 - 5/9	7.1	Introduction to Graph Theory
(7) 5/12 - 5/16	7.2	Proofs about Graphs & Trees
		TEST II
(8) 5/19 - 5/23	7.3	Isomorphism & Planarity
(9) 5/26 - 5/30	7.4 - 7.5	Representation & Application
(10) 6/2 - 6/6	7.6 - 7.7	Binary Trees & Graph Problems
		FINAL EXAM: Tuesday, June 10, 1:30 - 3:30 p.m.

Note: This schedule is tentative and subject to change.

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