![]() ![]() 01 Introduction to set theory Definition of a setĪ set is a collection of (mathematical) objects. Finally we study permutations - ways to rearrange or re-order a set - which are both interesting in their own right and widely applied, for example in linear algebra as you will see later in 0005. We move on to the idea of a function and to key function properties, useful for example whenever we want to compare the size of two sets. We’ll cover sets and relations, used whenever we discuss collections of objections and relations among them. The aim of this first part of 0005 is to introduce you to some of the key definitions and results from modern algebra that end up being used everywhere in mathematics and everywhere math is used. The notes are very similar to the video content, so you may find it helpful to read the notes before watching the video, or to have a copy of the notes open while you watch the videos. The notes are split into numbered sections, one for each teaching video. These are the lecture notes for the first part of MATH0005: Algebra 1. MATH0005 Algebra 1: sets, functions, and permutations
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