Instructor
Professor Shelly Harvey
Herman Brown 446
Phone: x3659
shelly at rice dot edu

Course Information
Class meets: MWF 10am -- 10:50am in HB 427
Office Hours: TBA
Recitation: TBA
Webpage: http://math.rice.edu/~shelly/304s12/
All homework and reading assignments can be found on OWL-Space
Teaching Assistant: Taylor Martin (taylor.martin at rice dot edu)

Textbook
Knot Theory by Charles Livingston (required)

Other useful references in Knot Theory (not required)
The Knot Book by Colin Adams (book, includes a lot of open problems)
Knot Knotes by Justin Roberts (notes found at http://math.ucsd.edu/~justin/Papers/knotes.pdf, slightly more advanced than Livingston or Adams)

Course Description
Knot theory is the study of smooth simple closed curves in 3-dimensional space. Knot theory is a large and active research area of mathematics that employs advanced techniques of abstract algebra and geometry. It is an essential tool in the study of 3 and 4-dimensional manifolds. The purpose of this course is to learn the basics of knot theory. We will learn how to formalize knots and learn techniques to distinguish them from one another. We will also discuss open problems in knot theory. Some topics we may discuss are Reidemeister moves, mod-p colorings, knot determinants, knot polynomials, Seifert surfaces, Euler characteristic, knot groups, and untying knots in 4-dimensions. The course will be mostly self-contained and will have an emphasis on careful proof writing.

Pre-requisites
The suggested prerequisite is a course in linear algebra or a course that discusses matrices and some of their properties: Math 221, Math 354, Math 355, or permission of instructor. In particular, one should be familiar the rank, nullity, determinant, and eigenvalues of a matrix. If you haven't taken necessary prerequisite but would still like to take the course, please talk to me.

Homework
Homeworks will be assigned every Wednesday and will be due the following Wednesday in class (or before class) unless otherwise stated; they will be posted on OWL-Space (use your netid to log in). Homework solutions must be legible. You must show all of your work for full credit. Late homework will receive at most 1/2 credit. Your homework grade will consist of two scores: one for correctness and one for exposition.

Exams
There will be one midterm (the date to be determined) and a final exam. Both exams will be take home exams. Good mathematical exposition will be counted on both exams.

Grades
Your grade in the class will be based on the following weights:
Homework:
Correctness35%
Exposition5%
Midterm:25%
Final Exam: 35%

Disability Support
Any student with a documented disability needing academic adjustments or accommodations is requested to speak with me during the first week of class. All discussions will remain confidential. Students with disabilities need to also contact Disability Support Services in the Ley Student Center.