Topic Name Description
Useful Information (old lecture notes, example sheets) File Lecture notes 2022-2023 (by Alex Fink)

To give you some idea of what this module is about. This is NOT the lecture notes for 2023-2024! 
File Example Sheet 1
File Example Sheet 2
File Example Sheet 3
File Example Sheet 4
File Example Sheet 5
File Example Sheet 6 (if you are gripped by the strong desire to do extra questions)
File Example Sheet 1 Solutions
File Example Sheet 2 Solutions
File Example Sheet 3 Solutions

As pointed out by my TA, James Kiln (he is also my PhD  student!), my model solution in A10-b 

deg(f+g)=max(deg(f), deg(g)) 

does not always hold. 

If deg(f) is distinct from deg(g), then deg(f+g)=max(deg(f), deg(g)) as advertised. However if deg(f)=deg(g), then it is possible that the leading coefficients of f and g cancel out and the deg(f+g) might be strictly smaller than max(deg(f), deg(g)).  So in the case deg(f)=deg(g), we cannot say anything definitive. 

This has been fixed in the pdf above.
File Example Sheet 4 Solutions
File Example Sheet 5 Solutions
Introduction File Hand-written lecture notes for Week 1, 22/01
File Hand-written lecture notes for Week 1, 26/01
File Typed-up notes for Week 1 (updated on 26/01)
Equivalence relations and partitions File Hand-written lecture notes for Week 2, 29/01
File Hand-written notes for Week 2, 02/02
File Typed-up notes for Week 2 *and* Week 3 (last updated 13/02)

Maxim Karasev pointed out a typo: [a]_R is the set of all elements b in S which are `in relation' to a (not to be as I originally wrote)! Thank you, Maxim, for pointing this out!
Week 3: Modular arithmetic File Hand-written notes for Week 3, 05/02
File Hand-written notes for Week 3, 09/02
Week 4: Modular arithmetic 2 File Hand-written notes for Week 4, 12/02
For the typed-up notes (for the lecture 12/02), please see the Typed-up notes for Week 2*and* Week 3 in the Week 2 tab.
File Week 2-Week 3 revision notes (as seen in the lecture 12/02)
File Hand-written notes for Week 4, 16/02

For the typed-up notes (for the lecture 16/02), please see the Typed-up notes for Week 5, Week 6 and Week 7 in the Week 5 tab.
Week 5: Algebraic structures (groups) File Assessed Coursework 1
When to submit: by 11am, the 4th of March. 

Where to submit: the Maths Office (1st floor of the SMS building).

What to submit: your solutions, with your name and ID number on the front page. 

You have at least two weekends to work through the problem set. You can discuss problems with others, but please do not waste your time copying each other.   

Marks you get directly add up to your overall grade (max 10 marks up for grabs). 
File Solutions for Assessed Coursework 1
File Hand written notes for Week 5, 19/02
File Hand-written notes for Week 5, 23/02
File Typed-up notes for Wee 5, Week 6 and Week 7 (last updated 08/03)

These contain what I covered on 16/02 (the second lecture in Week 4).
Week 6: Algebraic structures 2 (rings) File Hand-written lecture notes for Week 6, 26/02
File Hand-written lecture notes for Week 6, 01/03
File Typed-up notes for the exercise at the end of Section 4.5
Week 7: Algebraic structures 3 (fields) File Hand-written notes for Week 7, 04/03
File Hand-written notes for Week 7, 08/03
Week 8: Polynomials File Typed-up notes for Week 8 and Week 9 (last updated 21/03)

The notes contain what I covered on 08/03 (Week 7, Friday)
File Hand-written notes for Week 8, 11/03
File Hand-written notes for Week 8, 15/03
Week 9: Matrices File Hand-written notes for Week 9, 18/03
File Hand-written notes for Week 9, 22/03
Week 10: Revision File Week 4-Week 9 revision notes (extending the Week 2-Week 3 notes)
Week 11: Permutations File A complete set of typed-up notes (last updated 05/04)

This document includes `Typed-up notes for Week 11 and Week 12' in which I go through `Permutations' and `Group theory revisited'.

As I mentioned on the first day, *everything* in the notes, unless otherwise stated, is examinable. 

Having said that, I will definitely tinker as we go along, and make minor changes.  Read at your own risk. 
File Hand written lecture notes for Week 11, 05/04
File Solutions for Assessed coursework 2
Exam papers File 2014
File 2015
File 2016
File 2017
File 2018
File 2019
File 2020
File 2021
File 2022
File 2023
File Solutions 2014
File Solutions 2015
File Solutions 2016
File Solutions 2017
File Solutions 2018
File Solutions 2019
File Solutions 2021
File Solutions 2022
File Solutions 2023
Week 12: Groups revisited File Hand-written lecture notes for Week 12, 08/04
File Hand-written notes for Week 12, 12/04

The final set of notes! 

``Stand firm in your refusal to remain conscious during algebra. In real life, I assure you, there is no such thing as algebra.''-- Fran Lebowitz
Mock Paper 2024 File Mock Paper
File Mock Paper Solutions
File On a question of Francesca

Francesca asked me how one could find the multiplicative inverse of [22]_{44}X+[25]_{44} in Z_{44}[X] (presumably, this is one of the questions found in a past exam paper) and, though I made a passable attempt at answering her question after the mock session, I did not do a great job. Here's a copy of the email I sent to Francesca shortly after. She has kindly agreed to share it with you all.

Thank you, Francesca, for always asking me great questions!


  
Abridged notes (`cheat sheet') 2024 File A cheat sheet
This document might come in useful when you are revising for the exam.