**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.