Algebraic Structures, MST20010

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IMPORTANT:
THIS COURSE WILL BE ENTIRELY ONLINE FOR THE FIRST SEMESTER OF 2020-2021.

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.

Lectures: Monday 11am, Wednesday 12 noon
Tutorials: Tuesday 11am, Friday 1pm



Information: The method for calculating A's in this course (and usually in maths) is: Grading.

Very general information about the contents this course: Information.

Practical organisation and advice:
Lectures.
Tutorials.
Assessment and advice.
Support.


The course notes. Updated 28-10 (List of changes).
They may contain misprints and can very likely be improved, so I welcome any comment.
Some extra information on symmetries
Some extra information on equivalence relations and equivalence classes
More explanations and examples on computations with permutations

Videos: Go to Brighspace.

Transcripts of video sessions:
-Monday 21-9
-Monday 21-9
-Wednesday 7-10
-Wednesday 14-10


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 sheet 1 Solution 1
Exercise sheet 2 Solution 2
Exercise sheet 3 Solution 3
Exercise sheet 4 Solution 4
Exercise sheet 5 Solution 5
Exercise sheet 6 Solution 6
Exercise sheet 7 Solution 7
Exercise sheet 8 Solution 8
Exercise sheet 9 Solution 9
Exercise sheet 10 Solution 10
Exercise sheet 11 Solution 11


2019 December exam Solution
2018 December exam> Solution

Exam week 4 Solution
Exam week 8 Solution
Exam week 10 Solution


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, to be able to explain it to yourself or someone else.

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.