University of LaVerne – Athens Campus

Mathematics/Computer Science 327 – Fall 1999

DISRETE MATEHMATICS

Instructor: Nicholas Harkiolakis

E-mail: nick@beryl.kapatel.gr

Message phone: 6206-188/9

Pre-requisites: MATH 201

Course Description:

Development of mathematical tools necessary for algorithmic applications in computer science. Includes set theory and logic, various algebraic structures, graph theory, Boolean algebra, and computability theory. Emphasizes applications in computer science.

Teaching Goals:

· To present mathematical reasoning in order to read, comprehend, and construct mathematical arguments.

· To understand combinatorial analysis.

· To familiarize with discrete structures such as sets, permutations, relations, graphs, trees, and finite state machines.

· To analyze algorithmic thinking.

· To develop models for applications in computer science and various areas of study.

Learning Objectives:

The students will be able to:

· Understand mathematical reasoning and logic, which serves as the foundation for methods of proof such as mathematical induction.

· Develop problem-solving skills such as the ability to count or enumerate objects.

· Work with discrete structures to represent discrete objects and relationships between these objects.

· Specify algorithms for certain classes of problems. Than includes the specification of the algorithm, the verification that it works properly, and the analysis of the computer memory and time required to perform it.

· Appreciate the many application areas of discrete mathematics, from computer science and networking to chemistry, botany, zoology, linguistics, geography, business, and the Internet.

· Model with discrete mathematics.

Course Requirements:

· Class attendance and participation

· Weekly homework assignments

· In class assignments

· Special topic presentation

· 2-hour midterm exam

· 2-hour final exam

Syllabus/Course Topics:

· Logic, Sets, and Functions

· Algorithms, the Integers, and Matrices

· Mathematical Reasoning

· Counting

· Relations

· Graphs

· Trees

· Boolean Algebra

· Modeling Computation

Method of Evaluation

· Class Attendance and Participation: 10%

· Compulsory coursework: 40%

· Special Topic Presentation: 20%

· 2 hour midterm exam: 15%

· 2 hour final exam: 15%

Textbook

Rosen K.H., Discrete Mathematics and Its Applications fourth edition, McGraw-Hill, 1999.

Supplemental Readings

Johnsonbaugh R., Discrete Mathematics, fourth edition, Prentice Hall, 1997.

Lipschutz S., Lipson M.L., 2000 Solved Problems in Discrete Mathematics, SCHAUM series, McGraw Hill, 1992.