Algebraic Structures, MST20010
School academic integrity protocal (plagiarism policy).
Extra information about the module descriptor:
The list of prerequisites is not displayed properly (apparently the computer system does not deal well with boolean operators). It should read:
(MST10030 or MATH10290 or MATH10340) AND (MST10010 or MATH10310 or MATH10350).
Or similar: You need at least one first year linear algebra course that covers at least matrices and determinants, and at least one other first year course (to get the extra familiarity with university mathematics), it is usually provided in UCD by one of the listed calculus courses. If you have a slightly different background and are unsure, contact me.
The course will be delivered in a "flipped classroom" mode.
Details:
Lectures:
(1) Notes and videos will be available in advance. You will be told how much to
study each week. We will not meet on Monday in order to free some of your time
for this.
(2) We will meet on Wednesday at 12 noon to discuss the content and so that you can
ask your questions. I plan to use (=if no technical problems occur) the
brightspace virtual classroom, from within a UCD classroom (so that it should be possible for you
to follow it online if you need to; there will also be a recording, accesible via Brightspace).
Tutorials:
Writen solutions as well as videos will be provided. The tutorial hour will be
used to discuss these and answer questions.
Assessment:
Two online in-trimester short exams, during the Monday slot (11am to 12 noon), counting altogether for 30% of the final grade.
One end of trimester exam (in person) during the December exam session, counting for 70% of the final grade.
I plan to have the two in-trimester exams on week 5 and week 10, but it could move by one week if needed for the organization (and the date will be confirmed at least 10 days in advance).
Lectures: Monday 11am (we will not meet, see above), Wednesday 12 noon in G-24 Ag
Tutorials: Tuesday 11am, Friday 1pm
Information: The method for calculating A's in this course (and usually in maths) is:
Grading.
Comparison with MST10030 + How to work.
Very short presentation.
Some basic facts about sets, functions,
mathematical notation and some proofs, in case you are not too sure about some
details. Ask me if you want more.
The course notes.
Ask me if you need to have them in a different format (html, different font, etc).
They may contain misprints and can very likely be improved, so I welcome any comment.
Videos: Go to Brighspace.
About proofs ``by rewriting''.
How to use the exercise sheets:
Attempt every question seriously (put some real effort into it if needed, it is not always easy). Do this BEFORE the tutorial, so that when you go there you know what you can do, where you difficulites are, and what questions you want to ask.
Exercise sheets:
Exercise sheet 0 Solution (optional and will not be covered in the tutorial, it is just there to try to introduce some ideas that led to the notion of group).
Exercise sheet 1 Solution
Exercise sheet 2 Solution
Exercise sheet 3 Solution
Exercise sheet 4 Solution
Exercise sheet 5 Solution
Some of the exercises mentioned in Chapter 4
Exercise sheet 6 Solution
Exercise sheet 7 Solution
Exercise sheet 8 Solution
Exercise sheet 9 Solution
Exercise sheet 10
Exercise sheet 11
How to work in general:
You should work on the material of each lecture with pen and paper,
your objective is not only to learn the content, but to understand
it (I cannot overstate how important this is),
to be able to explain it to yourself or someone else. Do not forget to
study and understand the proofs (at least most of them), they are at
least as important as the results.
The exercises are there as a starting point, and are the bare minimum
of what you should do. To be better prepared for the exam you should
do more. There are plenty of books containing an introduction to
permutations and groups in the library and you can look at their
exercises. There are also good free online books, for instance (there
are many others):
-Judson, Abstract Algebra: Theory and Applications
-Goodman, Algebra: Abstract and Concrete
-Pinter, A Book of Abstract Algebra.
You will need to be selective about what parts you read or what
exercises you attempt, since we may not see all topics in the same
order.