Real, rational, irrational, imaginary. An explanation of numbers of different kinds, a little about infinite series and an surprising relationship. Types of integers: odd, even, squares; perfect, amicable and prime numbers.
How letters are used to solve equations. Notation and rules. Simple, simultaneous and quadratic equations covered for the beginner. Biquadratics, simple cubics and complex roots.
A number triangle known by the Chinese and named after a French mathematician. This triangle is used for algebra, probabilities, and calculations. The Binomial Theorem and series.
Right-angled triangles. Introducing the trigonometric functions: Sine, Cosine and Tangent. Trigonometrical calculations, formulas and series. Cosine and Sine rules. Secants, Cosecants and Cotangents.
An introductory look at the strange world of logarithms, how they are used for calculations, how they are evaluated with series, and using logarithms to solve algebraic equations. Definitions of index and base.
Graphs are a way of visualising algebraic functions. The Cartesian coordinate system is introduced along with a description of graph drawing from first principles. There are examples of different types of graphs.
An introduction to Calculus. An introduction to differentiation - measuring rates of change. Using Newton's Method of Approximations to solve equations.
Spherical Trigonometry is the trigonometry of triangles drawn on a sphere. It is used for many areas in geography and astronomy including navigation, mapping and sundials.
More algebra. Determinants and their use in solving simultaneous equations. Partial fractions. An introduction to Limits, including L'Hôpital's Rule.
Coming soon...
A brief History of Mathematics
Integration (Definite and Indefinite)
Complex Numbers
Hyperbolic Functions
Solving Differential Equations
Vector Algebra
