Chapter 1 Introduction

Welcome! It’s lovely to have you here!

1.1 About this course

This book accompanies the course “Reason and Argue Better: Logic in Proof and Argument,” which was written between 2018-2019 and has been taught every semester since.

This is the third semester that this course has been taught online or partly online. The course has been adapted for online teaching, with some elements simplified and others expanded. Completing this course online offers some challenges, but also opportunities for things not possible when offline.

1.2 About this book

This book contains the material we will study as well as exercises (see the next section) and links for further reading. Most weeks I will assign you a chapter to read, and you should complete both the reading and the exercises within the chapter before our next class.

This textbook may be updated during the course. Therefore you are advised to access the book at the link at https://ijcwebb.github.io/proof, rather than printing or downloading it. Also, even though you can read ahead of the set chapter, you are advised that later chapters might change as the course procedes.

If you notice any mistakes in the book, there is a thread on the Forum on our course’s e-Course page. Post the mistake you’ve noticed, along with the chapter and section number. I will check the mistake and update the book accordingly.

1.3 How to use this book

When completing the week’s reading, you will encounter some exercises. I will indicate which of these you should attempt.

Exercise 1.1 Regular exercises look like this…

…with subparts…
…like this.

Solution. Solutions might be included underneath exercises, in which case you should aim to complete the exercise before checking the solution. If the solution is not included, then we will probably discuss it in class.

Exercise 1.2 Extension exercises look like this. These are exercises that require a little more thought.

Solutions won’t be given in the book for these exercises, but we may discuss these in class. You can also book one-to-one consultations to discuss. See our syllabus for full details.

There are a couple of other coloured boxes used in this book:

Proof.
Proofs look like this.

Careful!

This is where I alert you to mistakes commonly made by students in this course. Read these warnings carefully to avoid these mistakes yourself.

1.4 Contents

PART I: Chapters 2-5 cover the terminology of mathematical proof.
PART II: Chapters 6-9 cover the basics of proof.
PART III: Chapters 10-19 cover methods of proof.
PART IV: Chapter 20 covers mathematical incompleteness.

That’s it. You’re ready to begin!

An Introduction to Mathematical Proof