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).
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.
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.