07-401/About This Class

07-401/Navigation Panel   # Week of... Links 1 Jan 10 About, Notes, HW1 2 Jan 17 HW2, Notes 3 Jan 24 HW3, Photo, Notes 4 Jan 31 HW4, Notes 5 Feb 7 HW5, Notes 6 Feb 14 On TT, Notes R Feb 21 Reading week 7 Feb 28 Term Test 8 Mar 7 HW6, Notes 9 Mar 14 HW7, Notes 10 Mar 21 HW8, E8, Notes 11 Mar 28 HW9, Notes 12 Apr 4 HW10, Notes 13 Apr 11 Notes, PM S Apr 16-20 Study Period F Apr 24 Final Add your name / see who's in! Register of Good Deeds

In Preparation

The information below is preliminary and cannot be trusted! (v)

Crucial Information

Agenda: (Groups,) Rings, fields, groups and some of the most famed no-go theorems of algebra and geometry.

Classes: Wednesdays 6-9PM (OMG) at Sidney Smith 1086.

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

Teaching Assistant: Chao Li, chaoli@math.toronto.edu. Office hours: Tuesdays 12:00-2:00 at the Math Aid Centre, Sidney Smith 1071.

URL: https://drorbn.net/drorbn/index.php?title=07-401.

Abstract

Taken from the Faculty of Arts and Science Calendar:

Commutative rings; quotient rings. Construction of the rationals. Polynomial algebra. Fields and Galois theory: Field extensions, adjunction of roots of a polynomial. Constructibility, trisection of angles, construction of regular polygons. Galois groups of polynomials, in particular cubics, quartics. Insolvability of quintics by radicals.

• Prerequisite: MAT224H1, MAT235Y1/MAT237Y1, MAT246H1/MAT257Y1.
• Exclusion: MAT347Y1.

Public Disclosure Statement

I (Dror) have not studied some of the material for this class since I was an undergraduate student in the first half of the 80s, and my knowledge of some of the topics is definitely rusty and/or lacking. But I come from the trenches of honest mathematical research that uses a significant amount of algebra. How well will this play is yet to be seen.

Text Book(s)

• DF:= D. S. Dummit and R. M. Foote, "Abstract Algebra", chapters 7, 8, 9, 13, 14.
• G:= J. A. Gallian, "Contemporary Abstract Algebra", chapters 12-17, 20-22 and 31-33 (approx.).
• H:= T. Hungerford, "Abstract Algebra, an Introduction".

By-The-Week Optimistic Agenda

1. Rings, subrings, polynomial rings, matrix rings, group rings (DF 7.1, 7.2).
2. Ring homomorphisms and quotient rings, isomorphism theorems (DF 7.3).
3. Ideals, maximal ideal, prime ideals, rings of fractions (DF 7.4, 7.5).
4. The Chinese remainder theorem (DF 7.6).
5. A quick summary of PIDs and UFDs (DF 8).
6. Polynomial rings over fields (DF 9.1, 9.2).

Wiki

The class web site is a wiki, as in Wikipedia - meaning that anyone can and is welcome to edit almost anything and in particular, students can post notes, comments, pictures, whatever. Some rules, though -

• This wiki is a part of my (Dror's) academic web page. All postings on it must be class-related (or related to one of the other projects I'm involved with).
• If there's no specific reason for your edit to be anonymous, please log in and don't have it anonymous.
• Criticism is fine, but no insults or foul language, please.
• I (Dror) will allow myself to exercise editorial control, when necessary.
• The titles of all pages related to this class should begin with "07-401/" or with "07-401-", just like the title of this page.

Some further editing help is available at Help:Contents.

Marking Scheme

There will be one term test (25% of the total grade) and a final exam (50%), as well as about 10 homework assignments (25%).

The Term Test

The term test will take place in class on TBA. A student who misses the term test without providing a valid reason (for example, a doctor’s note) within one week of the test will receive a mark of 0 on the term test. There will be no make-up term test. If a student misses the term test for a valid reason, the weight of the problem sets will increase to 35% and the weight of the final exam to 65%.

Homework

Assignments will be posted on the course web page and distributed in class on the weeks shown in the class timeline. They will be due a week later at the tutorials and they will be (at least partially) marked by the TA. All students (including those who join the course late) will receive a mark of 0 on each assignment not handed in; though in computing the homework grade, your worst two assignments will not count. I encourage you to discuss the assignments 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. Remember that cheating is always possible and may increase your homework grade a bit. But it will hurt your exam grades a lot more.

Good Deeds

Students will be able to earn up to 25 "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:

• Drawing a beautiful picture to illustrate a point discussed in class and posting it on this site.
• Taking class notes in nice handwriting, scanning them and posting them here.
• Typing up or formatting somebody else's class notes, correcting them or expanding them in any way.
• Writing an essay expanding on anything mentioned in class and posting it here; correcting or expanding somebody else's article.
• Doing anything on our 07-401/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 25 good deed points (say) and your final grade is 80, I will report your grade as $25+80(100-25)/100=85$. 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.

Class Photo

To help me learn your names, I will take a class photo on 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.