3 Credit Hours Semester: Fall 2007

MAT 251 Discrete Mathematics

Sec 001 MWF 1:35 to 2:30 pm

INSTRUCTOR: George Matthews

Phone and voice mail: x2381

email:

Office: M210G

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TEXT:

Discrete Mathematics, 5th edition, by Ross and Wright.

ATTENDANCE POLICY:

Regular attendance in class is expected. A daily record will be compiled but will

not be used as a factor in grading.

GRADING POLICY:

Homework: Students are expected to spend up to two hours of study per class hour, to keep a notebook of regularly assigned homework, and to show this work on request. Completion of regular homework will earn up to two “bonus points” for each of four units in the course, to be factored into the Final Exam score.

Quizzes: Informal quizzes and reviews will be given for each unit, but they will not be used as a factor in grading. [Option: Quizzes may be handed in for bonus points to be factored into final grade.]

Graded work: Each unit will have a “take-home exam” component consisting of selected graded-work problems, with variable (up to five) “bonus points” to be added to individual unit exam scores.

WORK NOT COMPLETED ON TIME OR NOT READABLE WILL REDUCE EXAM SCORES.

Exams: Four one-hour exams will be given on the following schedule: No make-up exams will be given. Sep 26; Oct 19; Nov 9; & Dec 7

Also, a comprehensive two-hour final exam will be given during the week of Dec 17, 2007.

Course grade: The three highest of the four unit exam grades and twice the grade on the final exam will determine the course grade. [This has the effect of counting the final in place of the lowest exam.]

Letter grades will be assigned according to the following intervals:

<60:F | 60-62:D- | 63-65:D | 66-67:D+ | 68-69:C- | 70-76:C | 77-79:C+ |

80-82:B- | 83-86:B | 87-89:B+ | 90-92:A- | >92:A

Exception: Students who achieve a total of 372 or more points on all four unit exams, with all work being completed on time, will be given an A for the course without taking the final.

STUDENTS WITH SPECIAL NEEDS:

The Disability Services Office (DSO) at OnondagaCommunity College is available to assist students who have a documented disability. If you require special accommodations for this class, visit the DSO in Room 130 in the GordonStudentCenter or call them at 498-2245. In addition, please see me to discuss your individual circumstances concerning this course.

CATALOG DESCRIPTION:

Study of theoretical bases of set theory, logic, techniques of proof, number systems, functions, relations, algorithms, graph theory, counting, permutations, combinations, binomial coefficients, recurrence relations, induction and recursion, and trees.

Prerequisite: MAT161 or permission of instructor.

COURSE OUTLINE:

MAT251 Discrete Mathematics – Topical outline – Fall 2007

Text: Ross & Wright, Discrete Mathematics, 5th edition.

Sets, Sequences, and Functions, selected portions of Chapter 1 [Objectives S and A]

1.1 Some warmup questions

*1.2 Factors and multiples

1.3 Some special sets

1.4 Set operations

1.5 Functions

1.6 Sequences

1.7 Properties of functions

Review for unit one Exam #1 Sep 26

Elementary Logic and Relations, selected portions of Chapters 2 and 3 [Objectives L and A]

2.1 Informal introduction (to elementary logic)

2.2 Propositional calculus

2.3 Getting started with proofs

2.4 Methods of proof

2.5 Logic in proofs

2.6 Analysis of arguments

3.1 Relations

3.2 Digraphs (and graphs)

Review for unit two Exam #2 Oct 19

Matrices, Induction and Recursion, selected portions of Chapters 3 and 4 [Objectives L and A]

3.3 Matrices

3.4 Equivalence relations and partitions

3.5 The Division Property and Integers (mod p)

4.1 Loop invariants

*4.2 Mathematical induction

4.4 Recursive definitions

Review for unit three Exam #3 Nov 9

Relations and Combinatorics, selected portions of Chapters 4 and 5 [Objectives C and A]

4.5 Recurrence relations

4.6 More induction

4.7 The Euclidean Algorithm

5.1 Basic counting techniques

5.2 Elementary probability

5.3 Inclusion-Exclusion Principle; Binomial methods

5.4 Counting and partitions

5.5 Pigeon-hole Principle

Review for unit four Exam #4 Dec 7

[Graphs, Trees, Algebraic structure] – as time permits, portions of Chapter 6, 12

Review of units one through four Final Exam