MAT180 Special Topics: Knot Theory


Free extension for final project

If you need an extra day to complete the final project, you may submit your project by Saturday, June 3rd at 11:59 pm without any penalty.

Video by Brian Kinsley: Recovering the Figure 8 knot from its Seifert surface

Brian made this cool video!

Return to usual participation slips Week 6

Consistent with the University's evening class policy, we are returning back to the usual class attendance policy starting Monday, May 8. Note also that the P/NP deadline has been moved to 5/19. This will be reflected on the class calendar soon.

No particpation grade Week 5

I have just sent out the following Canvas announcement:

Dear MAT180 students,

In light of the current safety concerns, I'm suspending the participation/attendance/in-class work requirement for this class, at least for this week. That is, for Week 5, everyone will get 100% in participation. I will reevaluate my policy for Week 6 based on any changes to the situation.

Subject to University-wide changes to instruction, I will still be giving lectures as usual. I will also continue to post my notes on the class website, which I strongly encourage you to go through if you are unable to come to class.

If you or a friend are struggling emotionally (for any reason, not just the recent events), I want to remind you that you have resources:
Student Health and Counseling Services: 530-752-2300
Office of Student Support: 530-752-1128
Text "RELATE" to 741741
For emergencies: 911

College is a stressful time; I myself started on the path to mental well-being during college. It's very hard to learn when you don't feel ok. So, take care of yourself, your mental and physical health, and your personal safety. And remember to get enough sleep!

Take care,
Dr. Zhang

HW05 now up!

Thanks to Ignacio for pointing out that HW05 wasn't actually posted! To make up for the shorter time frame on this homework, I will go over Exercise 1 in class on Wednesday.
Update: Even better! Here's a video for Exercise 1 that was shared with me today.

HW04 sign issue

A couple of you pointed out that you're getting the negative of the Jones polynomials for the positively and negatively linked Hopf links! I just checked my computations, and indeed, I also have this extra minus sign. There's no error in the mathematics; there is just a convention difference. So, if you get the Jones polynomial up to a sign, I'm happy. (We are using this weird other version of the bracket polynomial because these are the standard conventions for Khovanov homology, which we will study later in the quarter.)

Coffee with a Prof, with me, May 18

advertisement for coffee with a prof See the flyer image below / to the right (click to enlarge). Here's the sign-up link.

HW03 is now due Monday, 4/24 at 11:59 pm on Gradescope

We will talk about knot polynomials on Wednesday; you should be able to do the first two problems in HW03 now.

HW03 is up!

Sorry for the delay. This HW is a tad shorter to account for this.

Bookshelf now added to Canvas

For those of you using the UC Davis Bookstore's Equitable Access program: I've just added Bookshelf to our Canvas page!

Course information

Lectures: Giedt Hall 1006, 1:10 pm — 2:00 pm

[MAT180 Course Syllabus]

[MAT180 Class Calendar]

Course instructor: Dr. Melissa Zhang, MSB 2145

Instructor office hours: MSB 2145, Tuesdays 3 pm — 4 pm

Teaching assistant (TA): Yuze Luan, MSB 2137

TA office hours: MSB 2137, Thursdays 9 am — 12 noon

Final Project

Here is PDF containing all the information about the final project, which is due 6/2/23 at 11:59 pm on both Canvas and Gradescope. [Final Project V1]
("V1" stands for Version 1; the time table for presentations hasn't been filled in yet.)

My notes for Lecture 22 are in the form of an expository article. Here are all the related files:



[HW08.tex] [HW08.pdf]


[HW07.tex] [HW07.pdf]


[HW06.tex] [HW06.pdf] [HW06solns.pdf]


[HW05.tex] [HW05.pdf]
YouTube video for Exercise 1


[HW04.tex] [HW04.pdf] [HW04solns.pdf]
(It appears I hadn't posted these solutions yet!)

HW03: Now due Monday, 4/24 at 11:59 pm

[HW03.tex] [HW03.pdf] [HW03solns.pdf]


[HW02.tex] [HW02.pdf] [HW02solns.pdf]


Here are my solutions for HW01, along with the .tex file, for your reference. In the future, I'll just post the PDF of the (sometimes abridged) solutions. [HW01solns.pdf] [HW01solns.tex]

The purpose of this homework is just to get you set up to TeX your future homework solutions, and to make sure you can upload your homeworks to Gradescope.

You'll find a version of the following instructions at the top of the HW01 PDF:

Instructions. Create a free Overleaf account, and create a new project (e.g. "MAT180-hw"). Upload the provided "HW01.tex" file for HW01, and click on it on the sidebar. Then, press the big green "compile" or "recompile" button at the top of the right half of your screen. You should then see the HW01 PDF show up on the right half of your screen.
There are two exercises in this HW. Type your solutions directly into the code, compiling every once in a while to admire your work. When you are done, press the download icon next to the recompile button to download your solutions as a PDF. Submit this PDF to Gradescope.

Reminder. Your homework submission must be typed up in full sentences, with proper mathematical formatting. The following resources may be useful as you learn to use TeX and Overleaf:


[Lecture 26 slides]

[Lecture 25 notes]

[Lecture 24 notes]

[Lecture 23 notes]

For the current unit on grid diagrams and grid homology (knot Floer homology), I am using the following reference: [Grid Homology Book]

[Lecture 22 notes]

[Lecture 21 notes]

[Lecture 20 notes]

[Lecture 19 notes]

[Lecture 18 notes]

Today we talked about the knot concordance group. Last time, I also talked about the basic idea behind Morse theory, and that wasn't exactly in the notes; I mentioned that we can also compute the Euler characteristic of a surface today based on its Morse decomposition. This topics are covered in the Lecture 18 notes.

[Lecture 17 notes]

We didn't cover everything in these notes yet. In particular, I'll talk more carefully about cobordisms next time, and also about "4-ball genus", which is on the last page of these notes.

[Lecture 16 notes]

[Lecture 15 notes]

[Lecture 14 notes]

[Lecture 13 notes]

[Lecture 12 notes]

[Lecture 11 notes]

[Lecture 10 notes]

This contains some of my notes for Lecture 11; see Chapter 4 for more details on the topics.

[Lecture 9 notes]

There's a typo! In the skein relation (Rule 2) in our convention for the Kauffman bracket, I drew the 0 resolution twice; the second instance should be a 1 resolution.

[Lecture 8 notes]

Updated 4/19 at 7 pm! The Jones polynomial of the two component unlink (which really only has one orientation up to isotopy) is -(q + q^-1), by the calculation shown in red on the first page.

[Lecture 7 notes]

Lecture 6: no lecture notes; Prof. Wein covered Section 7.4: a relationship between knot theory and statistical mechanics

[Lecture 5 notes]

[Lecture 4 notes]

[Lecture 3 notes]

[Lecture 2 notes]

[Lecture 1 notes]