Algebraic Structures, MST20010

School academic integrity protocal (plagiarism policy).

My office is 1.72 in Science South.

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:

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.
We will meet on Wednesday at 12 noon to discuss the content and so that you can ask your questions.

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

Assessment:

5 short in-tutorial exercise solving: It will be done in small groups, you will have about 15 minutes to work together on a question, then 5 minutes to write your answer. Any real attempt to do something / engage with the material will bring 1%, even if there are mistakes or if it is completely incorrect. The first one of these will be in week 3. It will give a total grade out of 5.
One in-person midterm, counting for 25%. Probably in week 8, but it could be moved by one week if needed. It could be in the Monday or the Wednesday slot. The precise date will be determined at least 2 weeks in advance.
One end of trimester exam (in person) during the December exam session, counting for 70% of the final grade.

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 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 and solutions: On Brightspace.

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. It takes times, possibly several hours. It is normal, no one expects you to know or to understand the material at the end of a lecture.

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.

Finally: You should ask your questions. All of them, even if you are afraid of it (don't be, it is normal to have very basic questions on a sujet that you are learning). We expect you to do this. You can ask them: to me (in person or by email), to the tutor, and at the maths support centre.