|Lecture||(2) MWF 2:10 - 3:15pm|
|x-Hour||Th 1:20 - 2:10|
|samantha.g.allen AT dartmouth.edu|
|Canvas||We will use Canvas for the gradebook.|
A mathematical knot is a closed loop in three-dimensional space. Many questions in knot theory are easy to state, but difficult to answer; we will set out to explore some of these questions. In this course, we will rigorously define knots and what it means for two knots to be equivalent. We will then discuss various mathematical techniques which arise in knot theory and apply these techniques to problems. The topics will include knot coloring, unknotting number, Alexander polynomials, surfaces whose boundary is a given knot, symmetries of knots, and higher dimensional knot theory, among others.
Along the way, we will touch on ideas and techniques from various areas of mathematics: topology, graph theory, linear algebra, abstract algebra, and number theory.
Prerequisites: MATH 8 or placement into Math 11
Knot Theory by Charles Livingston
The course grade will be based upon class participation and the scores on the midterm exam, homework, and the final project as follows:
Academic integrity is at the core of our mission as mathematicians and educators, and we take it very seriously. We also believe in working and learning together.
Collaboration on homework is permitted and encouraged, but obviously it is a violation of the honor code for someone to provide the answers for you.
On written homework, you are encouraged to work together, and you may get help from others, but you must write up the answers yourself. If you are part of a group of students that produces an answer to a problem, you cannot then copy that group answer. You must write up the answer individually, in your own words. A good practice is to discuss ideas on a blackboard, then erase the blackboard and try to reproduce the arguments later, on your own paper, and without assistance.
On the midterm exam, you may not give or receive help from anyone.
Students with disabilities who may need disability-related academic adjustments and services for this course are encouraged to see me privately as early in the term as possible. Students requiring disability-related academic adjustments and services must consult the Student Accessibility Services office (Carson Hall, Suite 125, 646-9900, Student.Accessibility.Services@Dartmouth.edu). Once SAS has authorized services, students must show the originally signed SAS Services and Consent Form and/or a letter on SAS letterhead to their instructor. As a first step, if you have questions about whether you qualify to receive academic adjustments and services, you should contact the SAS office. All inquiries and discussions will remain confidential.
The academic environment at Dartmouth is challenging, our terms are intensive, and classes are not the only demanding part of your life. There are a number of resources available to you on campus to support your wellness, including your undergraduate dean (http://www.dartmouth.edu/~upperde), Counseling and Human Development (http://www.dartmouth.edu/~chd/), and the Student Wellness Center (http://www.dartmouth.edu/~healthed/).
Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with your instructor before the end of the second week of the term to discuss appropriate accommodations.