## Topic outline

Lectures and seminars for this module from week 5 onward will take place here. This link also lets you view recordings of past lectures from this period.

Lectures and seminars in the first four weeks of this module took place in this MS Teams meeting, which is now no longer in use. Recordings of lectures from these weeks can be found in the weekly sections of the Module Content tab.

This forum is available for everyone to post messages to. If you have any questions about the module, please ask them here. I will be monitoring it to answer your questions.

You can add maths notation in your posts using the button with a calculator icon in the forum posting interface.

Full lecture notes for the module are given here. These notes will serve as a definitive record of what is examinable.

I may edit these notes as the semester progresses but only in minor ways, e.g. to correct typos or improve explanations. I will not add new content, and the topics and numbering of sections in the notes will not change.

Information about what is taught in each week can be seen in the "Module Content" tab below, in the sections for the individual weeks. After lectures I will scan the papers I wrote on during the lecture and upload those under the header for the week as well. Some weeks also have an appendix on a topic going beyond the notes, labelled as "not examinable", in case you're interested.

My intention is that you will not

*have*to take your own notes during the real-time lectures. But some students find it helps their learning to take notes anyway, or to download or print my notes and add their own annotations during the lecture. Think about whether this is you.### What is examinable?

The following items in the lecture notes are not examinable:

- Proposition 2.11 and Definition 2.12;
- Theorem 4.12 and its setup.

Everything else in the lecture notes is examinable.

### Online learning

### Assessment Information

*Introduction to Algebra*has two kinds of assessment:- Those not worth marks and provided to support your learning: extra problems, quizzes, etc.
- Those worth marks: 25% of your total mark for this module will be awarded for coursework, and 75% for the exam.

All of these are described below.

*Introduction to Algebra*follows the general policies of the School of Maths regarding extenuating circumstances claims and students who get special accommodations from DDS. Refer to the Student Handbook. The module does not use Turnitin.### QMplus Quizzes

The QMPlus quizzes linked in the sections for each week's content provide you immediate feedback on your answers and are meant for consolidation and/or revision after you have worked through each week's lectures and notes. They do not count towards your module mark and are provided to support your learning.

For a few computational topics for which it's harder to get a QMPlus quiz to generate random questions, I have also included links to simple webpages to generate more.

### Extra questions

### Coursework Assignments

### Final exam

Format of the final exam

The exact format of the final exam is not yet decided; it depends on how Covid-19 restrictions evolve. However, the most likely format is a QMPlus quiz, similar to those used for first-year modules in the January exam period.

In an ordinary year, the exam for this module has several questions like "write down the definition of X" or "write down the proof of Theorem Y". Because you will have access to your notes during the exam, it will not feature straight bookwork questions like these. Instead I will examine definitions and theorems in other ways, e.g. "which of the above is equivalent to X?" "which of the above would contradict Y?" Or I may give you two re-worded definitions, but one of them will be inaccurate, and I'll ask you to say which one, and why. Overall the exam will require more thought and the ability to use your knowledge.

Past papers

The 2020 exam was a QMPlus quiz, but the course of lectures was interrupted by industrial action so not all topics were examinable.

In 2019 and earlier, Introduction to Algebra was examined the traditional way, on paper, and the exam papers are collected here. In 2020, the exam was a randomised QMPlus quiz, and the PDF in this folder is one random variation.

Many are for earlier versions of the module syllabus, and as such their topic coverage and/or rubric might not match this year's exam. In particular, the following are

*not*examinable:- Extracting roots of complex numbers, i.e. solving
*z*=^{n}*a*in the complex numbers. - Pseudocomplex numbers, hypercomplex numbers, quaternions.
- Isomorphism.
- Cosets.

- Fermat's little theorem.
- Mathematical induction "for its own sake", like Q1 on the 2017 paper. You are expected to know mathematical induction; it is used in some of our proofs. But earlier versions of this module spent a few lectures at the beginning just revising
induction, which is no longer done.

- Extracting roots of complex numbers, i.e. solving

### Syllabus

### Learning outcomes

### Week 1

### Week 2

### Week 2 activities

- Read the sections of the notes featured in this week's lectures:
- Monday–Tuesday: Section 1.3.
- Wednesday: Section 2.1.
- Participate in the live lectures, in the online lecture room:
- Monday 11:30am: Partitions.
- Tuesday 4pm: Translating between relations and partitions.
- Wednesday 10am: Integer division.
- Friday noon: Review, questions, examples.
- After Wednesday's lecture, try this week's quiz.
- The submission question on the Week 3 coursework, below, is on Week 2 material, so I suggest starting to think about it this week.

- Not attempted

### Week 3

### Week 4

### Week 5

### Week 6

### Week 7 (Reading Week)

### Week 8

### Week 9

### Week 10

### Week 11

### Week 12

### Revision lecture

### Exam