This is the course text for the Spring 2021 version of MATH0007, an introductory algebra module for UCL first year joint honours students. These notes are split into three parts: Chapter 1 on sets, functions, and permutations, Chapters 2 and 3 on linear algebra, and Chapter 4 on group theory.

UCL students can find an exact syllabus, along with problem sheets, suggested reading, lecture videos, and online quiz questions on the module Moodle page. There is also a YouTube playlist for the lecture videos.

Take a moment to experiment with the controls in the toolbar at the top of the page. You can search these notes for a word or phrase (for example, to look up a definition). You can adjust the typeface, the font size, and the background colour to make the text easier to read. You can also download an offline copy of these notes in various formats. Please get in touch if you’ve got any accessibility requirements that aren’t met.

I hope you enjoy the course. If you have any questions, comments, or corrections then please email me.