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Math 108 Topics in Mathematics | Section 1000 | James Baglama | **Chapter 1**

Reading Assignment |
Video |
Lecture Notes |

1.1 Euler Circuits pages 5 - 8 |
Section 1.1 Video |
Section 1.1 Lecture notes |

1.2 Finding Euler Circuits pages 9 - 13 |
Section 1.2 Video |
Section 1.2 Lecture notes |

1.3 Beyond Euler Circuits pages 13 - 19 |
Section 1.3 Video |
Section 1.3 Lecture notes |

- Determine by observation if a graph is connected.
- Identify vertices and edges of a given graph.
- Construct the graph of a given street network.
- Determine by observation the valence of each vertex of a graph.
- Define an Euler circuit.
- List the two conditions for the existence of an Euler circuit.
- Determine whether a graph contains an Euler circuit.
- If a graph contains an Euler circuit, list one such circuit by identifying the order of vertices in the circuitâ€™s path.
- If a graph does not contain an Euler circuit, add a minimum number of edges to eulerize the graph.
- Identify management science problems whose solutions involve Euler circuits.

- The quiz for Chapter 1 will be available from 12:00am May 18 - 11:55pm May 22.
- The quiz will consist of 10 multiple choice questions.
- You will have a maximum of two hours to complete the quiz.
- You will be allow two tries. The computer will accept the best score.
- Failure to take the quiz by 11:55pm May 22 will be given a zero. No exceptions!

- Chapter 1

pages 25-29 Problems 4, 8, 14abc, 30, 34, 40

Due by 11:55 pm Friday May 22. - Use the Assignments tool to submit homework.
- Homework help.
- Problems 4 and 8. Carefully read the definitions and examples in Section 1.1 before responding to these exercises.
- Problem 14. Understand the definition of valences (Section 1.2) before answering the parts of this exercise that refer to figures in Section 1.2.
- Problems 30 and 34. Carefully read Section 1.2 before responding to these exercises. Problem 34, redraw the figures and label the edges, similar to problem 30 labeling.
- Problem 40. Carefully read Section 1.3 before responding to this exercise. Redraw the graph and label the edges to show the Euler circuit. Count the valence of each vertex.

- I will NOT accept homework with answers only.

- Go to the companion website and navigate to the applet
exercises.
- Click on the Euler Circuit applet and follow the directions.
- Click on the Eulerizing a Graph applet and follow the directions.

- In the companion website navigate to Video Clips and click on Euler circuits

Each worksheet will have 10 questions (each worth 1 point). The worksheets are designed to help you understand material. The worksheets are downloadable from the Assignment tool within Sakai as a Microsoft Word (or OpenOffice) and also as a pdf file. You can write on the worksheets and upload your answers or (similar to homework submissions) take a digital picture of your handwritten assignment with a camera or smart phone. All worksheet answers must be submitted within Sakai. The due dates for the worksheets are two days before the due date for homework assignments, so that you can get feedback on problems before submitting your homework and doing your quizzes. DO NOT SUBMIT ASSIGNMENTS VIA EMAILS OR FAXES! I will not accept them! Do not ask to submit late worksheets.

- Due by 11:55 pm Wednesday May 20.
- Use the Assignments tool to submit worksheet.

- If you were making a recommendation to the mayor of Providence concerning proposed new street-sweeping routes, designed using the theory of this chapter, would you recommend that the changes be adopted or not? List a few pros and cons. Does a grid of two-way streets always have a Eulerian solution? What effect would one way streets have on the problem of street sweeping? What effect would multiple sweeper trucks used have on the problem? Suppose that each night, one sweeper followed a Eulerian circuit on the street grid. Would there always be an Eulerian circuit left to sweep every night until all the sweeping is done?

- Discussion for Chapter 1 will open at 12:00 am Monday May 18.
- You are required to participate in the discussion boards.
- Discussion topic will end at 11:55 pm Friday May 22.
- See the syllabus on the grading rubric for discussions.

__Texting Number:__
(401) 268-7160

__Email:__ jbaglama@math.uri.edu

__Office hours:__
by appointment

__Office:__
Lippitt Hall 200D

__Office Phone:__
(401) 874-4412

The required textbook,
"For All Practical Purposes", 9^{th} edition by COMAP,
Publisher W.H. Freeman. Do NOT use an older edition. All students
must have either a phyiscal copy of the textbook or an
ebook.Click
on the textbook above to go to the ebook.

The required textbook,
The textbook "For All Practical Purposes", 9^{th} edition by COMAP,Publisher W.H. Freeman
has a campanion website. The campanion website contains a lot helpful material,e.g. Java Applets, falshcards, practice quizzes.
The site can be accessed via the link
Campanion or click
on the picture above to go to the campanion website.

Math 108 Topics in Mathematics | James Baglama | jbaglama@math.uri.edu | University of Rhode Island.