Math 38
Graph Theory
Last updated March 25, 2016 14:17:43 EDT

## General Information

Goals, Teaching Methods, and Expectations

Course Description

The subject of Math 38 is graph theory. These are not the graphs of calculus, but a different kind of graph, consisting of vertices (points) connected by edges (line segments or curves). Graphs are useful as models in many, many different areas. You can find some graphs here, here, and here.

Graph theory also features some very beautiful and fun mathematics, which is where our emphasis will be. We will learn about graphs, and we will learn how to prove things about graphs.

By the end of the course you will be able to solve problems, answer questions, and prove theorems about graphs. You will have improved your ability to write clear, elegant mathematical proofs.

Class Structure

During a typical class period, most of your time will be spent working in small groups, and perhaps sharing your work with each other. I will always be prepared to answer questions, but most of the time I will not give lectures, except to explain things that you did not understand from the reading.

I structure class this way because the most efficient use of me, as a resource, is not to have me lecture on things you can learn from the textbook, and because you learn best from active involvement with the material and with each other. Working in groups and working independently have different benefits for learning, and you should develop both skills. (Also, most jobs require both, with an emphasis on collaboration.) The more different ways you approach material, the more kinds of neural pathways you build, and the better you understand. Communicating your ideas, and your confusions, is particularly valuable.

For the first week, I will assign groups each class day. At the beginning of the second week, you will choose groups to work in for the remainder of the term. (These are in-class groups only. You can always work on your homework with whomever you choose.)

For at least the first couple of weeks of the course, we will use the x-hour as an optional problem session. Whether we continue this throughout the term depends on whether a significant number of you show up to take advantage of it.

General Expectations

Class participation is part of the course, which means you should attend all classes. You can miss up to three classes without it affecting your grade.

Reading is assigned each class day, and is to be done by the following class. These assignments are intended to help you to stay on top of the material.

Homework is also assigned each class day, but due weekly. Information about due dates and grading policies is in the Homework section below.

Please come to office hours. I am always happy to answer questions. You can come even if you don't have questions.

Textbook

The textbook for this course is Introduction to Graph Theory (second edition) by Douglas West. There will be regular assigned reading from the textbook.

Scheduled Lectures

 Groszek MWF 12:30 - 1:35 (x-hour) Tue 1 - 1:50 Kemeny 108

Instructor

 Professor M. Groszek Office: 330 Kemeny Office Hours: MTh 2:00-3:30, and by appointment Contact via email.

Exams

There will be two "midterm exams" and a takehome final exam. All exams will be cumulative.

The exams are tentatively scheduled as follows. See the Special Considerations section for information on schedule conflicts.

 Exam 1 Monday, 4/18, 4:00-6:00 pm Room 008 Kemeny Exam 2 Monday, 5/16, 4:00-6:00 pm Room 008 Kemeny Final Exam Due Thursday, 6/2, 6:00 pm Take-home

Homework Policy

• Homework assignments will be posted on the course web page, listed under the day they are assigned. It is your responsibility to find out what homework is due each day, and to complete it on time.

• Homework consists of written assignments and reading assignments, and is assigned daily.

• Reading assignments are due by the beginning of the next class meeting. These assignments are intended to help you to stay on top of the material.

• Written homework problems are due by the beginning of class on the Wednesday after they are assigned. The beginning of class is 12:30 sharp. If you will not be in class, be sure your homework reaches me before class starts. If you put it under my office door, please do so by noon to be sure I get it on time.

• Written homework must be legible, on standard size paper with no ragged edges (as from tearing paper out of a spiral notebook), and clearly labeled with your name and the due date.

• Late homework will be graded on a sliding scale. Homework turned in after the start of class but before the end gets 90 percent of the earned grade; before the beginning of the next class, 75 percent; before the beginning of the second following class, 50 percent; within a week of the due date and time, 25 percent. Homework more than a week late gets no credit.

Class participation each day will be graded either 0 or 1. To get a grade of 1 you must be present in class, your group must be working together and not leaving anyone behind, and you must (attempt to) answer questions when asked. You do not get more credit for volunteering a lot, or for getting the right answers.

Some evidence that your group is working together: Anyone in the group can tell me what problem your group is working on and what your ideas are. If someone raises a hand to ask a question, anyone in the group can ask it for them.

Each written homework problem will be given one of the following scores:

• 10 points: Flawless. A completely correct solution explained with crystal clarity. Or, possibly, an almost flawless solution distinguished by unusual brilliance or creativity.

• 9 points: Well done. A basically clear explanation of a solution with no significant errors. This is what I expect most of the time.

• 8 points: Good but partial. May have significant mathematical errors, require effort to understand the explanation, or provide a solution to only part of the problem.

• 7 points: Shows some progress toward a solution and an explanation.

• 6 points: Shows enough understanding of the problem to at least attempt a solution.

• 5 points: States the problem.

• 0 points: No credit.
Note that a clear solution must include a statement of the problem being solved. "Problem 2, page 35," is not sufficient. It is acceptable either to copy the statement from the textbook or assignment sheet, or to restate the problem in your own words.

Exams will be graded on both mathematical content and clarity of explanation. On the take-home final, in particular, your grade will reflect the clarity and completeness of your explanations as well as the correctness and completeness of your mathematics.

The numerical course grade will be computed as follows:

 Class Participation 10 percent Homework 10 percent Exam 1 20 percent Exam 2 25 percent Final Exam (cumulative) 35 percent Total 100 percent

Before computing the numerical course grades, I may scale (upward) scores on a particular exam, to prevent one unusually hard exam from having a disproportionately large effect on your grade.

The conversion of numerical grades to letter grades will be at least as generous as:

 90 or above A range 75 or above B range 60 or above C range 50 or above Passing

Letter grades may be somewhat higher than shown here, if higher grades better represent student achievement in the course.

The Honor Principle

Academic integrity is very important to me.

Homework: You are strongly encouraged to work together on homework problems. However, the solutions you submit must be written by yourself and in your own words. Any form of copying (electronic or otherwise) of another person's solutions, in whole or in part, is a violation of the Academic Honor Code. What you turn in as homework solutions has to show your own understanding. You must state what sources you have consulted, with whom you have collaborated, and from whom you have received help. Working with others will never lower your grade.

Midterms and Final Exam: You are not allowed to provide or receive help of any kind. Midterms are closed book examinations, and on the take-home final you may consult only our textbook and your own notes. However, you may always ask me for clarification of questions.

If you have any questions as to whether some action would be acceptable under the Academic Honor Code, please ask. It is NOT easier to get forgiveness than permission for violation of academic standards.

Special Considerations

Students with disabilities enrolled in this course who may need disability-related academic adjustments and services are encouraged to see me privately as early as possible in the term. Students requiring disability-related academic adjustments and services must consult the Student Accessibility Services office (301 Collis Student Center, 646-9900, Student.Accessibility.Services at Dartmouth.edu). Once SAS has authorized services, in order to get accommodations you may either show me the originally signed SAS Services and Consent Form and/or a letter on SAS letterhead, or authorize SAS to speak with me. As a first step, if you have questions about whether you qualify to receive academic adjustments and services, you should contact the SAS office. All inquiries and discussions will remain confidential.

Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, or any other conflict with one of the midterms, please meet with me before the end of the second week of the term - and in no case later than a week before the scheduled exam - to discuss appropriate accommodations.

For students with midterm exam schedule conflicts due to regularly scheduled lab periods or other regularly scheduled course activities, provided you notify me in time, I will schedule an alternate time period to take the exam. Students with other commitments, such as jobs, performances, or athletic competitions, should also be accommodated with sufficient notice, although this is not absolutely guaranteed.

The due date and time for the take-home final are firm and non-negotiable. The only exception is for serious illness or similar circumstance that warrants arranging a grade of incomplete with the Dean's Office.

If you are unable to attend class one day, it is your responsibility to submit your homework on time, and to make up the material you missed. It is polite to notify your instructor if you expect to miss class.

Marcia Groszek
Last updated March 25, 2016 14:17:43 EDT