# Syllabus - Introduction to Graph Theory  MTH548 - Spring 20000  Mon. Wed. 5:00 - 6:15

## Course Content

We will study basic concepts in combinatorial graph theory and see how graphs serve as models for many standard problems which have applications in science, business and industry. We will use the text, Graphs and Digraphs by G. Chartrand and L. Lesniak and cover much of Chapters 1 through 7.

## Goals and Expectations

I expect you to learn the standard uses of graphs as models and the fundamental theory about graphs. This includes definitions, basic theorems, and being able to reproduce proofs of theorems. Also, as with any math course, you will improve your problem solving skills and both oral and written communication skills.

## Methods

I don't want class time to be spent just reproducing what is given in the book. I would like to enhance what you find in the book. Often it is hard to follow proofs from text books, because they are written in a terse way. I will strive to make the proofs easy to follow and interactive. Then, if you take careful notes, you will have two sources to consult when you need to study. There is much more material given in the book than we can possibly learn in one semester. I will point out in class which topics you should learn.

In order to learn the material and attain the goals mentioned above, you should do the following work. Read each section of the book before we cover it in class, omitting proofs. Go to class and take notes on the material presented. Then, read the book again, including the proofs this time. Do the assigned homework on the section covered, and learn from my comments. You will be given an opportunity to present some of the solutions to homework problems in class. When it is time for a test, I will give you a list of the theorems that I expect you to be able to reproduce. Studying for this type of test increases your knowledge and ability to retain knowledge. Also, you will be given opportunities to present material from the book to the class.

## Tests

There will be two exams and a final. These tests will concentrate on the basic theorems from the topics which we have covered. You should learn the proofs of theorems that are presented in class. A list of theorems to be covered will be given before each test. The two exams will be given on: March 8 and April 17. The final will be given on Wed, May 10 3-6, and will be comprehensive.

## Homework and Presentations

Homework Point System

There will be homework problems assigned from the sections that we cover in class. You should begin working on them as soon as the section is covered. I will collect the homework periodically. You will get comments from me on your homework and a grade of either 0, 1 or 2 for each problem. You will have an opportunity to hand in problems more than once, for a higher score. Also, I will regularly ask class members to present their solutions on the board.

You will be asked toward the end of the semester to pick a section and present it to the class.