2016 Fall Course Syllabus - Mathematics 4096.001
Course: Mathematics 4096.001.
Course Title: Knot theory / Senior Problem-solving.
Time: Tuesday/Thursday 3:30-4:50.
Place: Wachman 010.
Instructor: David Futer.
Instructor Office: Wachman 1026.
Instructor Email: david.futer@temple.edu
Instructor Phone: 215-204-7854.
Course Web Page: http://math.temple.edu/~dfuter/teaching/math4096/
Office Hours: Tuesday/Thursday 1:30 - 3:00, or by appointment.
Prerequisites: Some experience with writing proofs.
Textbook: The knot book, by Colin Adams.
Course Goals: Learn some of the rudiments of knot theory. Develop proof-writing skills. Translate visual intuition into clear, written proofs. Learn how to write expository papers with serious mathematical content, and how to present mathematical material orally.
Topics Covered: We will cover most of chapters 1-6 of the textbook. We will begin by introducing the notion of mathematical knots and links. The main topic in the course is developing methods to determine when two knots are actually distinct. Our main technique will be to introduce various invariants of knots and links including tri-colorability, unknotting number, bridge number, crossing number, genus, and various knot polynomials. Along the way, we will have an opportunity to stop and look at surface topology, three- dimensional topology, and possibly hyperbolic geometry.
Course Grading: The homework counts for 30%. The in-class final exam counts for 30%. The writing project (including revisions and in-class presentation) counts for 40%.
Exam Dates: Final exam, December 15.
Attendance Policy: You are responsible for knowing all the material covered in class. The best way to learn about this material is to come to every class.
Any student who has a need for accommodation based on the impact of a disability should contact me privately to discuss the specific situation as soon as possible. Contact Disability Resources and Services at (215) 204-1280, 100 Ritter Annex, to coordinate reasonable accommodations for students with documented disabilities.
Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here.
Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar for exact dates.
During the first two weeks of the fall or spring semester, students may withdraw from a course with no record of the class appearing on the transcript. In weeks three through nine of the fall or spring semester, or during weeks three and four of summer sessions, the student may withdraw with the advisor's permission. The course will be recorded on the transcript with the instructor's notation of "W," indicating that the student withdrew. After week nine of the fall or spring semester, or week four of summer sessions, students may not withdraw from courses. No student may withdraw from more than five courses during the duration of his/her studies to earn a bachelor's degree. A student may not withdraw from the same course more than once. Students who miss the final exam and do not make alternative arrangements before the grades are turned in will be graded F.
The grade I (an "incomplete") is reserved for extreme circumstances. It is necessary to have completed almost all of the course with a passing average and to file an incomplete contract specifying what is left for you to do. To be eligible for an I grade you need a good reason and you should have missed not more than 25% of the first nine weeks of classes. If approved by the Mathematics Department chair and the CST Dean's office, the incomplete contract must include a default grade that will be used in case the I grade is not resolved within 12 months.