IMPORTANT:

THIS COURSE WILL BE ENTIRELY ONLINE FOR THE SECOND TRIMESTER OF 2020-2021.

Monday 4pm to 5:50pm

Wednesday 1pm to 1:50pm

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

This web page will contain the course notes, the exercise sheets with
solutions, and some advice. It will be kept up to date.

There will be videos supporting both the lecture notes and the exercises, and
these will only be available from Brighspace.

The course notes. Updated 18-3 (List of changes).

An example of elements that are left zero divisors but not right zero divisors, and right zero divisors but not left zero divisors: Here.

Exercise sheets:

Exercise sheet 1 Solution

Exercise sheet 2 Solution

Exercise sheet 3 Solution

Exercise sheet 4 (for Wednesday 17-2) Solution

Exercise sheet 5 (for Wednesday 24-2) Solution

Exercise sheet 6 (for Monday 01-03) Solution

Exercise sheet 7 (for Wednesday 24-03) Solution

Exercise sheet 8 (for Wednesday 31-03) Solution

Exercise sheet 9 (for Wednesday 7-04) Solution

Exercise sheet 10 (for Wednesday 14-04)

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 bring them to
the weekly sessions in the virtual classroom. Don't be afraid to ask.
Or if you are, at least do not hesitate to send me emails with your
questions, I really encourage you to do this.
With everything online, there is no other way I can find out where
your difficulties are.

Books:

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.

I mentioned another book in class, but I checked it again, and it would
not be a good idea.

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.