Senior Seminar - Knot Theory

Inga Johnson
Assistant Professor
Department of Mathematics
Willamette University
302 Collins Bldg.
ijohnson(at)willamette(dot)edu
503.370.6551

Math 499 Syllabus - Knot Theory
Class Meetings: Tu-Thr 9:40AM-11:10AM, Collins 306.

Course Goals: To create mathematics by finding examples, counterexamples, making conjectures, proving conjectures, and proving lemmas, propositions, theorems and exercises. The content of the course will be Knot Theory.

Text: The text hasn't been written yet. You will be given a set of notes that will serve as the basis for the course. The notes consist almost entirely of definitions, examples and the statements of theorems. Almost none of the usual details are supplied. Your job is to supply those details.

Homework: As you will see, the missing parts of the text are in boxes or labeled exercises. At each class meeting I will assign certain missing parts and exercises as homework. You will keep a Senior Seminar journal in which your thoughts, ideas and problem solutions will be kept. All journal entries will be dated and problem numbers clearly indicated in the margins. Your journal will be turned in and graded several times throughout the semester. You should bring your journal to every class meeting. Sometimes journal collection will not be announced in advance. After a homework assignment has been made, students will come to the next class period with 3''x5'' note card with their name at the top and a list of the assigned homework problems. For each problem students can indicate one of four possible options.

A circle around the problem number indicates you have completed the problem and have a solution you are willing to present at the board.
A square around the problem number indicates you have made significant progress on a problem that you are willing to share with the class, but your solution is not complete.
A triangle around a problem number indicates that you have thought deeply about the problem, but not made significant progress; however, you'd be interested in facilitating at the board a group discussion of the problem by writing out your ideas and the ideas of your classmates.
The last option is to put no shape around the problem number. This option indicates that you have yet to give the problem much thought.

From among those students that put a circle or square about a particular problem number, one student will be chosen to present his or her solution/ideas to the rest of the class. If a particular problem is not circled or "squared" by anyone, then a student that "triangled" that problem will be selected to facilitate a discussion about the problem.

Recorders: Each week of class will have two designated recorders that will be responsible for LaTeXing the problems presented that week and any relevant class discussion. The recording responsibilities will rotate through the students in the class. All students in the class are responsible for proofreading the document LaTeXed by their peers. As we finish each chapter we will take some time to edit the first draft of the document to produce a nearly final version of that material.

Quizzes: There will be a quiz given as we finish each chapter (approx every two to three weeks). The quiz problems will be on the content of the document thus far. Quizzes are designed to encourage you to review the text document often and to encourage you to understand all the problems including those that you didn't get initially.

Grading: Your grade will be calculated based on your homework, in-class homework presentations, and journal entries (75%), and quizzes (25%).

Circled problems will earn 4 points, squared problems will earn 2 points, and triangled problems will earn 1 point. Presentations will earn a score of 4-0 depending on the correctness of the solution, the difficulty of the problem, the clarity of presentation, and the ability of the presenter to answer questions from the class. There are varying degrees of difficulty in the homework problems. Some problems are example calculations and others are proofs. All students must complete solutions for a majority of the proofs assigned and present 3-5 proofs over the course of the semester. Not doing so will result in a lower course grade. Journal entries will be graded for correctness, completeness and should reflect that a significant amount of time outside of class has been spent thinking about the assigned problems. Journals that are lacking in these areas will result in a lower course grade.

The highest course grade given will be based on the accuracy and clarity of the document created from the course presentations. All other grades will be curved down from this highest course grade according to the standard rubric.

Honor Code: You may talk in general terms with each other about the homework, but the work you turn in is to be your own. No outside resources should be used unless it is a source that I direct you to.

LaTeX: An introduction to LaTeX and information about how to download it can be found here. I will give a brief intro to Xfig and Adobe Illustrator in class. These will be what is used to draw the knots and links you will be producing for the text. Both are mouse driven drawing programs that output eps files (encapsulated postscript) which can be easily included in the text document.

Math Colloquium: You are encouraged to go to many of the Math Department Colloquia this semester, and as part of the course you are required to go to four. Attendance will be taken in Colloquium and you should turn in your notes from each talk you attend. If your schedule conflicts with all the Colloquia scheduled, it is your responsibility to see me as soon as possible for an alternate reading and writing assignment.

Special Note: If you have a documented disability and anticipate needing accommodations in this course, please make arrangements to meet with me within the first two weeks of the semester. Please request that a Disability Services staff send me the appropriate forms verifying your disability and specifying the accommodation you will need.