## Topic outline

Here are links to the Late-Summer alternative assessment 2020 (this year's resit exam as a QMPlus quiz) and a place for you to upload your working out for the exam. But please scroll down to the "Exam" section of this page for full descriptions.

### General Information

#### How the module will run online

Please carefully read my forum post for a description of how Introduction to Algebra will be run now that in-person lectures and tutorials are suspended.

#### Lecture notes

I will post two sets of notes for this module:

- a polished set of typeset lecture notes, below. These are the notes I am teaching from, although I usually give different examples in lecture than those that appear here, so that you have more examples to refer to.
- scans of the notes I write in lecture on the document camera, which I will upload after lectures. These I will put in the weekly sections of this QMPlus page.

I may edit the typeset notes as the course progresses, to correct errors or typos or to improve explanations etc. (I will not be adding all-new content.) You can check whether you have the latest version by comparing the dates on the first page.

#### OFFICE HOURS

I will hold office hours on Microsoft Teams regularly until the exam. Please join the Introduction to Algebra team.

Office hours are Mondays, Tuesdays, and Fridays from 11:00 to 12:00 British Summer Time. During those hours you can send me a message on Teams and I'll respond in real time as long as I'm not engaged with another student; if I am, I'll say so and get back to you after that. We can use text, voice or video chat as you prefer.

#### QReview recordings

This module's lectures are recorded on QReview. Here are the Q-Review Lecture Recordings.

#### Engagement

For this module, engagement monitoring will be carried out in line with the student engagement policies of the School of Maths.

#### Recommended texts

- D A R Wallace: Groups, Rings and Fields, Springer, London 1998; ISBN 3540761772
- A Chetwynd and P. Diggle: Discrete Mathematics, Butterworth-Heinemann, 1995

#### Quizzes

The weekly quizzes provide you immediate feedback on your answers and are meant for consolidation and/or revision after you have worked through each week's notes. They do not carry any marks, and are provided solely to support your learning.

### Week 1

### Week 2

### Week 3

### Week 4

### Week 5

Strike: no lectures.

### Week 6

### Week 7: Reading week and midterm test

The

**midterm test**takes place on*Tuesday, 3 March from 10:30 to 11:50*. (I don't expect you to need 80 minutes to complete it; I have arranged a longer time just to mitigate time pressure on you.)Please arrive ten minutes early so that you can take your seats. Check your timetable for which room you have been assigned to.

There are no lectures in the week of the midterm test. My office hours will run as usual on the following day.

The midterm test counts for

**10%**of your mark for this module.*At least half of the marks*on the midterm will be for questions taken from the coursework. The examinable coursework sheets are numbers 1 through 4. The examinable material from lecture is everything covered up to and including Friday, 28 February.As for format, the midterm will have one page of questions on definitions and/or theorem statements, and three pages with longer questions.

I have included some past mid-term test papers below. There are a few topics on the past papers which will not appear this year:

- Extracting roots of complex numbers, modulus-argument form for complex numbers, De Moivre's theorem
- Variations on the complex numbers: "pseudocomplex numbers", "hypercomplex numbers"

After I have marked the test, you will be able to collect your marked paper from the Maths office. I will announce in a forum post and email when they are ready for collection. Normally this takes me between one and two weeks, but in view of the strike it may take longer.

### Strike

The UCU strike continued until Thursday of week 9.

There will be no physical lectures from this point on due to coronavirus-related closures. Please refer to last year's Q-Review lecture recordings for all remaining lecture material.

### Week 10

### Week 11

### Week 12

### Revision Lectures

I gave a revision lecture on

*Tuesday, 28 April 2020, at 11:00*British Summer Time, via Zoom. The revision lecture discussed the format of the exam as a quiz and what kinds of questions might be expected on various topics, as well as revising relevant material from the course.A recording of the revision lecture is available below, as are the whiteboards from the revision lecture.

You may also wish to refer to last year's revision lecture, which is present among last year's QReview recordings. Note though that last year's exam was of a different format and covered more chapters of the notes.

### Exam

The final exam counts for

**90%**of your final mark for this course. It will be run as a QMPlus quiz, called "Alternative assessment 2020", which I will post below in this section of the QMPlus page. The exam will be open for 24 hours, starting on*Thursday 4 June at 11:00*British Summer Time (UTC+1). It is intended to take only two hours to complete. The timing is designed so that, if you have limited computer or internet access, you can open the exam, save or print or (carefully!) write down the questions, work on them offline, and then come back to enter your answers.

There will also be a QMPlus assignment, where you will be able to upload photos of your working out on paper. I will look at these to see if I can find part marks in it to help you pass the module, when you would not have passed otherwise. But aside from that circumstance I won't mark your working out.

#### What is examinable

Chapters 7 and 8 of the notes are not examinable. Any material in chapters 1 through 6 that has been lectured on is examinable. Please ask me if you have questions about whether particular subsections, theorems, etc. are covered.

No more than 20% of the marks will pertain to chapters 5 and 6.

#### Format of the exam

The exam will have 10 questions, each worth 10 marks. Eight questions will be on chapters 1 through 4 of the notes, and two on chapters 5 and 6.

The exam will have the following kinds of questions on:

- True or false
- Multiple choice
- Numerical answer
- Short answer, where the answer is e.g. a set or an equation
- Drag and drop

The drag and drop questions will be "put together a proof from the pieces below". Because this is a novel kind of question, I have made a sample drag and drop proof question which you can try below. There are examples of all the remaining kinds of questions in the weekly quizzes above.

Two of the questions will have two or three true-or-false or multiple-choice parts in one question. Some but not all of the ten questions will have part marks possible.

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, I have not been able to use these kinds of questions this year. Therefore, the exam will have comparatively more computation, but will also have questions that examine definitions and theorems in other ways, e.g. "which of the above is equivalent to X?" "which of the above would contradict Y?"