MATH40630 - Ring Theory

School plagiarism policy.

The course will be delivered in a "flipped classroom" mode. Details:

(1) Notes and videos will be available in advance. You will be told how much to study each week. We will not meet on Friday in order to free some of your time for this.
(2) We will meet on Tuesday at 3pm (in 128-SCN) and Thursday at 11am (in H2.20-SCH) to discuss the content and so that you can ask your questions, and then for the tutorial. I plan to use (=if no technical problems occur) the brightspace virtual classroom, from within the actual UCD classroom (so that it should be possible for you to attend online if you cannot always make it, or to review the recording).

Writen solutions as well as videos will be provided. The tutorial hour will be used to discuss these and answer questions.

Information: We will use this correspondence between percentages and letter grades: Grading.

The course notes.

Exercise sheets:
Exercise sheet 1 Solution 1
Exercise sheet 2 Solution 2
Exercise sheet 3 Solution 3
Exercise sheet 4 Solution 4
2021 midterm Solution
Exercise sheet 5 Solution 5
Exercise sheet 6 Solution 6
Exercise sheet 7 Solution 7
Extra optional exercise sheet
Exercise sheet 8 Solution 8
Exercise sheet 9 Solution 9
Exercise sheet 10 Solution 10
Midterm Solution

How to work:
You should work on your own on the course notes with pen and paper, until you really understand it all. Simply knowing the results and proofs in a "mechanical" way is not enough, understanding is key. It can take quite a bit of time and effort, it is normal. Really understanding the proofs will provide you with the tools to solve the exercises: you will be able to reuse or adapt small parts of the arguments (it is not always enough, sometimes you will need to come up with new ones).

Similarly, you should work seriously on the exercise sheets. Again, it can take quite some time, it is normal.

You should make lists of your questions and problems and mention them when we meet. Don't be afraid to ask. Or if you are, at least do not hesitate to send me emails with your questions. I will answer and also mention them in class if they are of general interest. I really encourage you to do this, it is the best way to proceed with a course in flipped classroom mode (and it will probably save you some time and effort, while preventing possible mistakes).

I do not know of any undergraduate text covering the topics that we will see. The most readable reference that I know of is:
Grillet, Abstract Algebra
and is available for free from the UCD library website. Some of the content of Chapter IX is related to this course (and I used some bits from it). It is definitely a graduate textbook, so is not easy to read. I do not particularly recommend using it (it is an excellent book, just not at the right level), but if you want to have a look in some book, it is the best I can think of for you.

If you are looking for a basic, definitely undergraduate book, with some very introductory results on rings (covering what you saw in the "Groups, Rings and Fields" course), you can try Judson, Abstract Algebra (freely available online). However, we will not really do anything that is in this book.