Selected Topics: Knot Theory

MATH 390- Spring 2007

Benedictine University

Contents:

Basic Information:

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Course Description:

This course will provide an introduction to knot theory. Topics include definitions of knots and links, composition of knots, Reidemeister moves, knot tabulation, basic invariants of knots, Seifert Surfaces and genus, special classes of knots, braids, and knot polynomials. Some emphasis will be placed on concepts related to the instructor's research in regular stick numbers. Students will be expect to give in class presentations and either begin work on research questions or read and report on research literature.

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Course Objectives:

We would like to develop proficient understanding of the course material . To serve these ends, we will emphasize critical thinking and effective communication skills, both verbal and written. Success in this course will be dependent upon your ability to communicate your technical understanding of course material to your peers as well as to the instructor. You will also be expected to successfully work collaboratively with others.

Specific Course Objectives are:

1. Learn basic concepts in knot theory.

2. Read a research paper in knot theory or in another scientific area in which knot theory is applied.

3. Present work based on library research or original research in both oral and written forms.

4. Communicate Mathematics Accurately and Effectively.

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Expectations:

This course is assumes some mathematical sophistication. Concepts and applications are flavors of mathematics that are quite different from the calculus course sequence. You should expect to spend significant amounts of time thinking about problems. You should expect to spend at least six hours of study to this class per week.  The instructor assumes that you will begin your homework and assignments in a timely fashion so that work is presented and submitted on time.  Ask questions!  If there is material with which you are not fully comfortable, you are expected to ask questions either during class, online, or during office hours. 

We are a community of learners working together to achieve our course goals. As such, it is incumbent upon all class members to show appropriate respect for each other. Each class member has something important to contribute to the class and should feel comfortable sharing with the class. Cell phones and pagers must be turned off. Inappropriate and disrespectful behavior including cell phone usage will result in dismissal from the class for the remainder of the class period.

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Technology Requirement:

Students are expected to use WebCT for all course communications, and course information. Final papers are expected to be prepared with proper typesetting using MS Word or mathematical typesetting software. Some coursework and research work may require the use of KnotPlot and/or Maple

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Evaluation:

The grading scale is 90% for A, 80% for B, 70% for C, and 60% for a D.  It is the student’s responsibility to seek clarification of the course requirements and evaluation policy.

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Participation:

You are expected to be in class, on time, for all class meetings. The participation grade will be decreased by the percentage of absence beyond 10% of the total number of course meetings. Coming to class on time and prepared will contribute positively toward the participation grade.

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Homework:

The will be 6-7 homework assignments throughout the term. There will be a minimum of a week's notice before an assignment will be due. Plan your study time wisely. Homework questions will not be answered on the due date, and no late papers will be accepted.

Studying mathematics is a social process. Much benefit can be gained by sharing insights and by struggling through problems with your peers.  You are strongly encouraged to study and work with other class members.  You are also strongly encouraged to consult Dr. Comar outside of the class periods either during office hours or via e-mail at tcomar@ben.edu.

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Class Lecture:

Each student will present one 50-minute class lecture. The topic will be determined in consultation with the instructor. Topics will come from our text, another text, research literature, or current original work.

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Oral Presentations:

You will make several oral presentations based on your independent course project. Your first oral presentation will take place during last week of March. The external presentation, based on your independent course project, will be presented at an external meeting, preferably at the Annual Meeting of the ISMAA at Western Illinois University on March 30-31. The final presentation will take place during the official final exam period: Friday, May 11, 8:00 a.m.-10:00 a.m.

These are due by to 7:00 a.m. prior to the next class meeting.  Questions not submitted in by this time will not receive credit and may not be addressed in the next day’s class. Your postings will be graded as a participation grade.  Credit is earned by submitting your questions and by seriously attempting to answer to the study questions--right or wrong.  Extra credit of one half a participation score may be earned (once each submission day) by correctly responding to a fellow’s student question before class discussion of the question.  The instructor reserves the right to post questions with responses to the class discussion board on WebCT. 

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Final Paper:

You will submit a formal, final paper based on your independent course project. This paper is expected to be at least 10 singled-spaced typed pages. This paper will be at the beginning of the final exam period of this course.

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Absence and Tardiness:

Absence due to documented illness, participation in Benedictine University athletic activities, religious observance, or other extenuating circumstances will be excused.  It is your responsibility to inform Dr. Comar in the event of such absences.  Class attendance is very important.  Others will depend on you to be to participate in group exercises. It is incumbent upon you to obtain class notes and updated assignments for missed classes. Tardiness will interfere with your time to complete homework quizzes and exams.  No student shall be admitted fifteen minutes after the scheduled classtime.

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Academic Honesty:

The search for truth and the dissemination of knowledge are the central missions of a university. Benedictine University pursues these missions in an environment guided by our Roman Catholic tradition and our Benedictine heritage. Integrity and honesty are therefore expected of all members of the University community, including students, faculty members, administration, and staff. Actions such as cheating, plagiarism, collusion, fabrication, forgery, falsification, destruction, multiple submission, solicitation, and misrepresentation, are violations of these expectations and constitute unacceptable behavior in the University community. The penalties for such actions can range from a private verbal warning, all the way to expulsion from the University. The University's Academic Honesty Policy is available at http://www.ben.edu/AHP , and students are expected to read it. Acts of any sort of academic dishonesty will not be tolerated.  All instances will be pursued.  The first case of any academic dishonesty will result in a grade of zero for the assignment.  A second case will result in failure of the course. Any incident of academic honesty on the final exam will result in failure of the course.

Your name should appear on all of your submissions of your work.  If collaboration is allowed, you must state with whom you have collaborated. You are responsible for understanding any authorized collaboriation policies on specific assignments. You must also properly reference any other print, electronic, or human resource that you consult.

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Academic Accommodations For Religious Obligations (AAFRO)

A student whose religious obligation conflicts with a course requirement may request an academic accommodation from the instructor. Students must make such requests in writing by the end of the first week of the class.

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Other Information:

If you have a documented learning, psychological, or physical disability, you may be eligible for reasonable academic accommodations or services.  To request accommodations or services, contact Tina Sonderby in the the Academic Resource Center, 249 Kindlon Hall, 630-829-6512. All students are expected to fulfill essential course requirements.  The University will not waive any essential skill or requirement of a course or degree program.

Final Drop Date: April 13, 2007

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This syllabus is subject to change. Any changes will be communicated to all class members electronically.

Contact Dr. Comar: tcomar@ben.edu

 Dr. Tim Comar's Homepage 

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