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TuTh 1:00 - 2:15 PM, LGRT 143

Course description and textbook

Introduction to the fascinating theory of knots, links, and surfaces in 3- and 4-dimensional spaces. This course will combine geometric, algebraic, and combinatorial methods, where the students will learn how to utilize visualization and make rigorous arguments.

Prerequisites: Math 235; Math 300 or CS 250. Math 411 is strongly recommended as a co-requisite.

Textbooks: "Knot Theory" by Charles Livingston and "The Knot Book" by Colin Adams.

Lecture format: 50% regular lecture + 50% guided group work and discussions. This will be a very interactive class.

Various resources for this class are available at the shared Dropbox folder (see the link in the welcome email).

Contact and office hours

The best way to contact me is via my umass email (inanc.baykur@). Always include "Math 481" in the subject line of your emails, and please do not expect me to see your messages or reply to them in the evenings or on the weekends.

Office hours: Tuesdays and Thursdays 2:30-3:15 PM ET at LGRT 1326. Or by appointment (contact me in advance) Tuesdays 3:15-4:00 PM ET.

Teaching assistant: Takuto Sato

TA office hours: Mondays 1-2 pm via Zoom (see class email / contact Takuto for the meeting link)

Grading and homework

70% Homework + 20% class participation + 30% final exam. (Yes, 20% extra points.) Then the total percentile typically goes into the standard letter scale:

Assignments: There will be 8-10 more or less weekly homework assignments. A good portion of the assignments will consist of questions raised during the lectures, some of which may amount to coming up with simple counter-examples on your own or finding out some answers in the literature. Since we will be discussing the answers to the problems after the assignment due date, no late homework will be accepted (partially or fully), no matter what the reasons are. Two homework assignments with lowest grades will be automatically dropped when calculating your grade at the end of the semester, so you can count a late homework as one of them.

I encourage you to discuss the homework problems with each other and to work in groups, let it be during the dedicated class meetings or outside of class. Please list the names of all people with whom you discussed each specific problem. You must write up your solutions completely independently. You should make sure that your proof is well-organized and all the steps are clearly explained.

Homework submission: All homework assignments will be submitted through Gradescope. Make sure that your username and student ID is entered correctly in Gradescope; they should match what you have in Spire. (This is essential for your grades to be transferred without any issues.) When submitting your homework, make sure you correctly indicate where your answer to each problem is in your PDF file. If you do not, or if you mark it incorrectly, the default assumption for the grader will be that you do not have the answer to that question.

The assignment problems will be split as "Homework" and "Additional"; only the former are the ones you are expected to submit your answers to. Please submit your answers to the additional problems only if you think you have a complete answer. Your work for them will be reflected on your class participation. You will be working on all these problems (and perhaps more) during the in-class group discussions.

How to use the textbook: The textbook by Livingston we are using is a lot of fun and very well written, but the content is certainly much denser than, say, that of a calculus textbook. You will probably need to read many parts slowly and work on the exercises before you really digest it.

If you read a sentence and you do not understand what it says or how it connects to what came before, you should stop and try to figure out what is going on. In many cases, there is a small argument or proof that the author expects you to supply, or there is a diagram you can draw that will make things clearer. Sometimes, even after spending some time on a point, you still may not understand it. At that point, you may want to try talking to other people in the class or asking me during office hours. We will discuss some of the really tricky or confusing points in class, but you will get a lot more out of those discussions if you have read the material and really thought about it.

Important notes

Please refrain from using laptops, iPads, smartphones, cell phones, etc. during our regular lectures, as they can distract not only yourself but also those around you. You will be allowed to use tablets, drawing pads, and similar devices during the problem sessions.

Make-up exams will not be given to accommodate travel plans.

UMass Accommodation Statement:  The University of Massachusetts Amherst is committed to making reasonable, effective, and appropriate accommodations to meet the needs of students with disabilities and help create a barrier-free campus. If you have a disability and require accommodations, please register with Disability Services (161 Whitmore Administration building; phone 413-545-0892) to have an accommodation letter sent to your faculty. Information on services and materials for registering are also available on their website www.umass.edu/disability.

UMass Academic Honesty Statement: Since the integrity of the academic enterprise of any institution of higher education requires honesty in scholarship and research, academic honesty is required of all students at the University of Massachusetts Amherst.  Academic dishonesty is prohibited in all programs of the University.  Academic dishonesty includes but is not limited to: cheating, fabrication, plagiarism, and facilitating dishonesty.  Appropriate sanctions may be imposed on any student who has committed an act of academic dishonesty.  Instructors should take reasonable steps to address academic misconduct.  Any person who has reason to believe that a student has committed academic dishonesty should bring such information to the attention of the appropriate course instructor as soon as possible.  Instances of academic dishonesty not related to a specific course should be brought to the attention of the appropriate department Head or Chair.  Since students are expected to be familiar with this policy and the commonly accepted standards of academic integrity, ignorance of such standards is not normally sufficient evidence of lack of intent.