06-1350/About This Class

06-1350/Navigation Panel   # Week of... Links 1 Sep 11 About, Tue, Thu 2 Sep 18 Tue, Kurlin(P), Thu 3 Sep 25 Tue, Photo, Thu 4 Oct 2 HW1, Tue, Thu 5 Oct 9 Tue(P), Thu(P) 6 Oct 16 HW2, Tue(P), Thu(P) 7 Oct 23 Tue(P), Thu 8 Oct 30 HW3, Tue, Thu 9 Nov 6 Tue ($\nu$), Thu 10 Nov 13 Tue, Thu 11 Nov 20 HW4(P), Thu 12 Nov 27 Thu 13 Dec 4 Syzygies in Asymptote, Final Jan 8 Grades Note. (P) means "contains a problem that Dror cares about". Add your name / see who's in! On to 07-1352

Crucial Information

Agenda: Understand the promise and the difficulty of the not-yet-existant "Algebraic Knot Theory".

Instructor: Dror Bar-Natan, drorbn@math.toronto.edu, Bahen 6178, 416-946-5438. Office hours: by appointment.

Classes: Tuesdays 9-10 and Thursdays 10-12 at Bahen 6183.

SVN repository: http://katlas.math.toronto.edu/svn/06-1350/.

URL https://drorbn.net/drorbn/index.php?title=06-1350.

Good Deeds and The Final Grade

Your "bare" final grade will be a 50-50 average of your homework grade and your final exam grade.

In addition, you will be able to earn up to 60 "good deeds" points throughout the year for doing services to the class as a whole. There is no pre-set system for awarding these points, but the following will definitely count:

• Solving an open problem.
• Drawing a beautiful picture to illustrate a point discussed in class and posting it on this site.
• Taking classnotes in nice handwriting, scanning them and posting them here.
• Formatting somebody else's classnotes, correcting them or expanding them in any way.
• Writing an essay on expanding on anything mentioned in class and posting it here; correcting or expanding somebody else's article.
• Doing anything on our 06-1350/To do list.
• Any other service to the class as a whole.

Good deed points will count towards your final grade! If you got $n$ of those, they are solidly your and the formula for the final grade below will only be applied to the remaining $100-n$ points. So if you got 40 good deed points (say) and your final grade is 80, I will report your grade as $40+80(100-40)/100=88$. Yet you can get an overall 100 even without doing a single good deed.

Important. For your good deeds to count, you must do them under your own name. So you must set up an account for yourself on this wiki and you must use it whenever you edit something. I will periodically check Recent changes to assign good deeds credits.

Homework

There will be 4-5 problem sets. I encourage you to discuss the homeworks with other students or even browse the web, so long as you do at least some of the thinking on your own and you write up your own solutions.

Class Photo

To help me learn your names, I will take a class photo on Thursday of the third week of classes. I will post the picture on the class' web site and you will be required to send me an email and identify yourself in the picture or to identify yourself on the Class Photo page of this wiki.

Old Title and Abstract

Before my decision to go radical and risky, the title of this class was "The Jones Polynomial" and the abstract read:

The Jones polynomial is perhaps the simplest knot invariant to define; it can be defined (and will be defined in the first class) in about 5 minutes, invariance can be proven in about 15 minutes, it can be programmed in another 10 minutes, and then it can be evaluated for the first few hundred knots in some 10 minutes or so. In the rest of the semester we will see that the Jones polynomial has some knot theoretic implications, has lovely generalizations and fits within some nice pictures, and is a wonderful excuse and unifying centre for the study of several other deep subjects, including but not limited to combinatorics, homological algebra, Lie algebras, quantum algebra, category theory and even quantum field theory. Some of these subjects we will cover in great detail; others, for the lack of time, will only be briefly touched. The prerequisites are the graduate core classes in topology and in algebra, or anything equivalent to that.

These old title and abstract are not entirely lies. I do plan to start with the Jones polynomial (it is quick fun), and in some historical sense, the Jones polynomial is the start of much of what we will do.