COS 250 - Discrete Structures

Larry Latour
Fall, 2007
Course Description:
Introduction to discrete structures used in various areas of computer science. Topics include logic, sets, relations, functions, cardinality, enumeration, and computability. Prerequisites: COS225 and MAT126. Credits: 3.
Place and Time:
Tuesday/Thursday, 9:30am-10:45am, NV206, Neville Hall.
Instructor:
Larry Latour, Assoc. Prof., Dept. of Computer Science
Office: 222 Neville Hall
Dept. Tel: 581-3941
Office Tel: 581-3523
Email: Firstclass (Larry Latour) or larry_latour@umit.maine.edu
Office Hours: Tuesday/Wednesday/Thursday 1-2pm
Required Textbook:
Discrete Mathematics and Its Applications, Sixth Edition, Kenneth H. Rosen, McGraw Hill, 2007.
Supplementary Textbook:
Student's Solutions Guide To Accompany Discrete Mathematics and Its Applications, 6th Edition, Kenneth H Rosen, AT&T Laboratories, Softcover, ISBN 0073107794, Kenneth H. Rosen, McGraw Hill, 2007.

Course Goals:

This course provides the mathematical foundations needed for the study of Computer Science. Students should understand and apply the elements of proof as they apply to the analysis of classical Computer Science problems. Throughout the course the relevance and practicality of discrete mathematics to the study of Computer Science is demonstrated.

ADA Notice:

If you wish to request an accommodation for a disability, please contact Ann Smith, Director of Services for Students with Disabilities (East Annex, 581- 2319) as early as possible in the term.

Course Outline:

The course outline is closely aligned with the required text.
1. The Foundations: Logic, Chapter 1
Propositional logic, propositional equivalences, predicates and quantifiers, nested quantifiers, rules of inference
2. The Foundations: Proofs, Chapter 1
Introduction to proofs, proof methods and strategy.
3. Basic Structures: Sets, Functions, Sequences, and Sums, Chapter 2
Sets, Set operations, functions, sequences and summations.
4. The Fundamentals : Algorithms, Chapter 3
Algorithms, the Growth of Functions, and Complexity of Algorithms.
5. Induction, Chapter 4
Mathematical Induction, Strong Induction and Well-Ordering
6. Recursion, Chapter 4
Recursive Definitions and Structural Induction, Recursive Algorithms, Program Correctness.
7. Counting, Chapter 5
The Basics of Counting, The Pigeonhole Principle, Permutations and Combinations.
8. Advanced Counting Techniques, Chapter 7
Recurrence Relations, Solving Linear Recurrence Relations, Divide and Conquer Algorithms and Recurrence Relations.
9. Relations, Chapter 8
Relations and Their Properties, Representing Relations, Equivalence Relations.

Grading:

Grades will be using the (+/-) grade scale based on the following work: Incomplete Grades: The "I" grade (incomplete) indicates that the decision on a final course grade has been postponed because work ordinarily expected to be completed by the end of the semester has not been finished as the result of circumstances beyond the control of the student. The "I" grade is not a postponement for an "F" grade! An incomplete grade is not a guaranteed option selected by the student but must have the approval of the Instructor. The “I" grade will be considered only in very rare cases and only when there is a reasonable expectation that the incomplete work can be completed in a reasonable amount of time. Normally the work must be completed and the grade filed by the tenth week of the next full semester.

Students need to complete all exams, AND all 9 homework packages, to be eligible for a passing grade. No makeup exams are given unless the circumstances warrant. Work will only be accepted if reasonable care and effort on the part of the student is evident.

Class preparedness and participation: Students must come prepared to discuss the text readings, text examples, and homework solutions on the due date.

Class attendance is a very important ingredient for learning the material associated with this course. Much of the insight for understanding material included in the course occurs through questions and discussions within the classroom that may not be covered in the text or lecture notes. Hence, it is expected students will attend class regularly. You should notify me as soon as you anticipate or have an unavoidable absence.

Class attendance will also directly affect a student's grade in the course through class participation, homework, and exams. Each week consists of class attendence, class participation, and (possible) homework assignments for review. Therefore each week the student will recieve 1% of the final grade if and only if the requirements for that week are met.

The student is responsible for all material presented in lectures regardless of whether it is covered in the text or in class. It is the student's responsibility to determine the material covered in any class he/she is absent from and to make it up. NOTE: From previous classes it has been shown that there is a high correlation between a student’s final grade and class attendance!

Homework completeness and timeliness: All homework (1) must be complete, (2) must be NEATLY-written, (3) must have a cover page containing the student's name, class, homework number, and list of problems, and (4) must be stapled in the upper left-hand corner. Although I won't take points off for homework lateness, not having homework completed on time will adversely affect the student's class preparedness and participation grade, and will usually adversely affect their performance on exams. Also, students should not expect late homework to be graded and returned in a timely manner.

Last updated: 8/31/07