2 Summary of chapters
These notes contain three chapters: Algebra, Vectors and Matrices. Certain elements in the vectors chapter are useful for understanding the matrix chapter, and the general algebra rules apply to most areas of maths.
2.1 Algebra
This chapter will introduce you to a range of standard topics in Algebra, from working with mathematical operations, to solving a variety of different types of standard equations. It will no doubt start at a level you have seen before, but will hopefully also provide some more in depth discussions about topics you have seen before, and help build up your toolkit for tackling algebra.
2.2 Vectors
This chapter will introduce you to what may be a new type of mathematical object, a vector. They provide a way to store more than just a single number behind an object we might algebraically just call \(v\). Vectors will be a way to store both length and direction inside one object. This chapter will introduce you to the standard algebra possible on such objects, a variety of different (but equivalent) notations along with applications of their usage in two and three dimensions.
2.3 Introduction to Matrices
Matrices3 are another new type of mathematical object, this time grids of numbers. You will again check how to do basic algebra on matrices, before learning how matrix multiplication works. A wide range of adjectives used with matrices will be discussed, before introducing the idea of a matrix determinant and inverse. The chapter ends with direct applications of inverses to solving systems of linear equations.