MAT 347: Groups, Rings, and Fields

This is the official website of the course MAT347 at the University of Toronto in the academic year 2018-2019.

Shortcuts:


ANNOUNCEMENTS


First term test

The first midterm will be held on Wednesday, November 21, 3:10-5:00pm at EX300. It will cover all the material up to and including semidirect products. You are responsible for all material from lectures, textbook chapters 1-5 (except 5.2, 5.3). You are also responsible for homework assignments 1-8.

I suggest that you study by reviewing your notes, reading the textbook, and going over the homework assignments. You might also find it helpful to practice non-assigned questions from the textbook.

No materials (textbook, notes,...) will be allowed.

You do not need to memorise proofs from class, in other words I would not ask you to prove one of the difficult theorems from class (such as Sylow theorems or simplicity of A_n).

Second term test

The second midterm will be held on Wednesday, February 13, 3:10-5:00pm. It will cover all the material that we have covered that was not on the first term test. You are responsible for all material from lectures, textbook chapters 5.2 (finite abelian groups), 6.3 (free groups), 7-9 (ring theory; except 9.6), and Alfonso's notes on UFDs. You are also responsible for homework assignments 9-14.

I suggest that you study by reviewing your notes, reading the textbook, and going over the homework assignments. You might also find it helpful to practice non-assigned questions from the textbook.

No materials (textbook, notes,...) will be allowed.

You do not need to memorise proofs from class, in other words I would not ask you to prove one of the difficult theorems from class.

HOMEWORK ASSIGNMENTS AND CALENDAR

I encourage you to attempt the reading assignments before the lectures on that topic start.

I will post every homework assignment here at least one week before it is due. I will not update them without warning less than a week before they are due.

I expect you to do all the problems in the homework set, but only the ones in bold and brackets are to be turned in on the day the homework set is due. Sometimes the not-to-be-handed-in problems will help you solve the to-be-handed-in problems.

You can certainly discuss homework problems with other students, but you need to write your solutions in your own words. If you find the solutions in e.g. books or the internet you must quote your sources.

I will not accept late assignments.

Most of these worksheets (and this webpage design) were graciously donated by Alfonso Gracia-Saz.

PART 1: Group theory.

PART 2: Ring theory.

PART 3: Fields and Galois theory.