07-401/About This Class
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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 (Linear Algebra II), MAT235Y1/MAT237Y1 (Calculus II/Multivariable Calculus), MAT246H1/MAT257Y1 (Concepts in Abstract Mathematics/Analysis II).
- Exclusion: MAT347Y1 (Groups, Rings and Fields).
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 (in particular, many of you know some of the prerequisites for this class a lot better than me). 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)
- (Required) J. A. Gallian, "Contemporary Abstract Algebra", chapters 12-17, 20-23 and 31-33 (approx.).
- (Recommended) D. S. Dummit and R. M. Foote, "Abstract Algebra", chapters 7, 8, 9, 13, 14.
- (Suggested) T. Hungerford, "Abstract Algebra, an Introduction".
Plan
I will aim to cover the above-mentioned 13 chapters of Gallian's book at a bit faster than one per week, so as to leave us some time for extras at the end, but we may fall back to a rate of just one chapter a week or even less. If so, chapters 23 and 31 will be the first candidates for skipping.
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 February 28. 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 approximately on the weeks shown in the class timeline. Typically an "in preparation" version of any assignment will be posted a bit before class and the "in preparation" tag will be removed shortly after class, once our progress in class is precisely measured. Assignments will be due in class a week after they are assigned and they will be marked by the TA, usually within another week. All students (including those who join the course late) will receive a mark of 0 on each assignment not handed in; though to allow you some leeway, 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.
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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 identify yourself on the Class Photo page of this wiki.
