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Textbook |
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| Knot Theory by Charles Livingston (required) | |||||||||||||||
Other useful references in Knot Theory (not required) |
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| 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, more advanced than Livingston or Adams) | |||||||||||||||
Course Description |
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| 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. Here are some of the topics that we will discuss: 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. | |||||||||||||||
Prerequisite |
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| The prerequisite is a course in linear algebra or a course that discusses matrices and some of their properties: Math 221, Math 354, Math 355, CAAM 335, or equivalent. In particular, one should be familiar with the rank, nullity, determinant, and eigenvalues of a matrix. If you haven't taken the necessary prerequisite but would still like to take the course, please talk to me. | |||||||||||||||
Homework |
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| 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. 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 |
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| 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 |
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Your grade in the class will be based on the following weights:
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Disability Support |
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| 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 also need to contact the Disability Support Services Office in the Ley Student Center. | |||||||||||||||
