The determinant of a matrix is a scalar value (ie a single number) calculated from the elements of the matrix. In this article, we will look at the definition and some of the uses of determinants. We will also look at some properties of determinants. The determinant is only defined…

Of course you can! The painter’s paradox is a paradox relating to an interesting 3D shape called Gabriel’s horn. Gabriel’s horn Gabriel’s horn is based on the function:

Integration is a method that can be used to calculate lengths, areas, and volumes defined by mathematical functions. It also has many applications in pure mathematics, physics, statistics, and many other fields. According to the Fundamental theorem of calculus integration and differentiation are (loosely speaking) inverse processes. This article is…

The travelling salesman problem (often abbreviated to TSP) is a classic problem in graph theory. It has many applications, in many fields. It also has quite a few different solutions. The problem The problem is usually stated in terms of a salesman who needs to visit several towns before eventually returning to…

The quotient rule allows us to find the derivative of the quotient of 2 functions. It has similarities with the product rule, and it may be worth studying the product rule before the tackling quotient rule if you haven’t already done so. Here is an example of the sort of…

In the article i to the power i we took a deep dive into the topic of raising a complex number to a complex power, which has a surprising result for the particular case of raised to the power of i. This time we will look at the general case…

A flip-flop is a particular arrangement of logic gates that uses positive feedback to store persistent information about previous states of its inputs. Most simple arrangements of logic gates can be described by a truth table that defines all its output values as a logical function of its current input…

Bayes’ theorem allows us to calculate probabilities based on relevant prior knowledge. In this article, we will start by looking at how prior knowledge can be applied to probabilities, and derive Bayes’ theorem from that. A probability experiment Imagine you have a bag containing 100 plastic tokens. Some are square, some are circular…

In this article, we will look at a simple dynamical system representing constrained growth. For illustration, we will assume this represents the year-by-year population of rabbits in an environment where the amount of available food and space prevents the population from growing to an unlimited size. As we will see…