Secondary Catalogue

Series: Professor Dave Explains Mathematics


Addition and Subtraction

Addition and Subtraction

Alright, so we've decided to learn all of the maths, but where shall we start? Well, let's start at the beginning. The first kind of math we developed was simple arithmetic. We needed this at the dawn of civilisation to communicate very simple...Show More
Addition and Subtraction of Fractions

Addition and Subtraction of Fractions

We know about addition and subtraction, we know about fractions, so let's learn to add and subtract fractions! This is now possible because we know how to find the least common multiple of two numbers, which we will need to do to be able to get...Show More
Algebraic Equations with Variables

Algebraic Equations with Variables

Now that we know the basics about solving algebraic equations, we will start looking at more and more difficult examples. But don't worry, just one step at a time! First, a few that are just a little more complicated than the easiest ones.
Circles: Radius, Diameter, Chords, Circumference, and Sectors

Circles: Radius, Diameter, Chords, Circumference, and Sectors

Is there anything more aesthetically pleasing than a perfect circle? It may seem like the king of shapes, but it's also arguably the simplest. Define a central point and a radius, and you've got a circle. What else can we say about circles? Let's...Show More
Divisibility, Prime Numbers, and Prime Factorisation

Divisibility, Prime Numbers, and Prime Factorisation

Now that we understand division, we can talk about divisibility. A number is divisible by another if their quotient is a whole number. The smaller number is a factor of the larger one, but are there numbers with no factors at all? There's some...Show More
History of Greek Geometry

History of Greek Geometry

I have to tell you, Ancient Greece is my favorite era of history. Socrates, Plato, Aristotle, plus all of the mathematicians, like Pythagoras. He loved math so much, he made a religion out of it! I mean it makes sense, if you transport yourself...Show More
Multiplication and Division of Fractions

Multiplication and Division of Fractions

If we know how to add and subtract fractions, we should know how to multiply and divide them too, right? Don't worry, it's actually even easier than adding and subtracting them, because when we multiply two fractions, they don't have to have the...Show More
Multiplication and Division of Small Numbers

Multiplication and Division of Small Numbers

What came next after addition and subtraction? Why, multiplication and division, of course! Multiplication is kind of like addition, really. In fact, it's just repeated addition. Take a look at this early innovation in arithmetic, and the...Show More
Types of Angles

Types of Angles

What are angles? What kinds of angles are there and how do they relate? Vertical angles, supplementary angles, complementary angles, corresponding angles, we cover them all in here!
Types of Quadrilaterals

Types of Quadrilaterals

Shapes! They're so fun. But they're even more fun when you know precisely how to define them. What's a rhombus? What's a parallelogram? Did you know that squares are rectangles? And both squares and rectangles are parallelograms? There's a whole...Show More
Types of Triangles in Euclidean Geometry

Types of Triangles in Euclidean Geometry

If a shape is made of straight line segments, the minimum number of sides it can have is three. And three sides make a triangle! I'm sure you knew that. But do you know all the types of triangles?
Understanding Fractions, Improper Fractions, and Mixed Numbers

Understanding Fractions, Improper Fractions, and Mixed Numbers

Once we know how to divide, we must learn about fractions, because not all divisions will lead to whole number quotients. But there are proper fractions, improper fractions, mixed numbers...what are all these things? Just check this out!