# Essays on Mathematical Topics

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.

The trigonometric identities and graphs of Sine and Cosine. Solving equations containing Sines, Cosines and Tangents.

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

# Other Essays

A collection of mathematical, physical and astronomical formulas and the interesting stories behind them.

# External Mathematics Links

**Please note, these links will open in a separate window.**
SOS Mathematics

A superb site covering topics from algebra to differential equations.

MathWorld

Comprehensive mathematics site (up to University level).

McTutor History of Mathematics

An excellent mathematical site with history and a co-ordinate geometry section featuring mathematical curves.

Encyclopedia.Com

A reference resource on many subjects including mathematics.

Worksheet Library

School resource site for various ages.

GED Online Test

Prepare yourself for the GED math test with this fun online resource.

HappyChild

is an excellent educational resource for children, full of interesting information.