Combining, Dividing & Defining 2D and 3D Vectors

I have written about Vectors back in Feb 2020 (in this post called Introduction to Vectors) but seeing as that was so long ago I wanted to refresh my mind on the topic by writing a bit of a meatier post (as we covered more of this than we did at UWE). // Notes taken from my lectures at the University of Kent 2022 Starting at the beginning, what is a vector? A vector is a line that has been...Read more
Introduction to Logarithms (Logs)

Introduction to Logarithms (Logs)

Logarithms or logs are another way of expressing indices and is a bit like the inverse of dealing with powers. Logs were used to perform difficult calculations before there were calculators. To understand how logs work we could just look at a simple to understand example: We know that , so if we wanted to know the value of the indices that would make into (how many times multiplied by itself gives us i.e. ) then we could use the...Read more

Introduction to Computer Arithmetic (Changing Bases, Sums & Multiplication)

This post is going to be an intorduction to computer arithmetic and will give us a bit of background of what bases are and how to switch between them without first converting to base 10 (which is how our brains usually deal with numbers). We’re also going to look at performing sums with different bases without first changing to base 10 (great fun). Changing bases When is comes to computer arithmetic, we need to be able to play with changing...Read more

Application of Matrices

Following on from the last couple of posts on the subject, today we’re going to look at the application matrix operations and how they help us in the real world. Below I have constructed the diagram of a network which we can imagine has something flowing through it (like a railway system or water system etc.) and an “ideal system” has input nodes, branches, paths or “arcs” and output nodes. In our diagram we have and input nodes; and ,...Read more

Matrix Operations

Provided two matrices are the same size we are able to add them together and their sum can be defined as . When adding two vectors together, the numbers in the same position will be added together i.e. and so on. A matrix can also be multiplied by a scalar. So if then . \\ If you already have no idea about what I’m talking about then read Introduction to Matrices first ? Worked examples: Given matrices a) . \\...Read more

Introduction to Matrices 🧮

A matrix is a grid of numbers or mathematical expressions that we use to store vast quantities of data in such a way that allows us to easily identify and manipulate each piece of information in the matrix. Engineering, science and computing all use matrices in a huge number of applications i.e. data analysis, search engines or game theory. The size of the matrices is observed by the number of rows and columns and can be described as an “”...Read more

Introduction to Vectors ⬇️

Quantities that completely describe their magnitude are called scalars. Some examples of scalars include: area, length, speed or temperature. Quantities that need both a physical size, and a direction associated with it to be completely described are called vectors. Some examples of vectors include: force, velocity, displacement and acceleration. This line has been represented as a vector. The arrow on the line indicates the direction and the length of the line its magnitude. The vector directed from to . Which...Read more