An Introduction to Math Beyond Calculus: Knot Theory

Instructor | Samantha Allen |
---|---|

Lecture | (2) MWF 2:10 - 3:15pm |

x-Hour | Th 1:20 - 2:10 |

Classroom | TBA |

samantha.g.allen AT dartmouth.edu | |

Office Hours | TBD |

Office | Kemeny 311 |

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

- Written homework assignments will be assigned weekly. They are
**due each Wednesday at 11:59pm EST**. Homework assignments will typically cover the material up through the previous Friday. So the first written assignment (soon to be available on the Homework page) covers the first three classes worth of material and is due on Wednesday of week 2.

The course grade will be based upon class participation and the scores on the midterm exam, homework, and the final project as follows:

Class Participation | 10% |

Weekly homework | 30% |

Midterm Exam | 30% |

Final Project | 30% |

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.

**Accessibility Services
etc.**

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.

**Mental Health**

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/).

**Religious Observances**

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.