# Mathematical Introductions

### An Introduction to Tree Diagrams

##### Stage: 3 and 4

This article explains how tree diagrams are constructed and helps you to understand how they can be used to calculate probabilities.

### An Introduction to Modular Arithmetic

##### Stage: 4

An introduction to the notation and uses of modular arithmetic

### An Introduction to Differentiation

##### Stage: 4 and 5

An article introducing the ideas of differentiation.

### An Introduction to Irrational Numbers

##### Stage: 4 and 5

Tim Rowland introduces irrational numbers

### An Introduction to Polar Coordinates

##### Stage: 4 and 5

This introduction to polar coordinates describes what is an effective way to specify position. This article explains how to convert between polar and cartesian coordinates and also encourages the creation of some attractive curves from some relatively easy equations.

### An Introduction to Proof by Contradiction

##### Stage: 4 and 5

An introduction to proof by contradiction, a powerful method of mathematical proof.

### An Introduction to Vectors

##### Stage: 4 and 5

The article provides a summary of the elementary ideas about vectors usually met in school mathematics, describes what vectors are and how to add, subtract and multiply them by scalars and indicates why they are useful.

### An Introduction to Complex Numbers

##### Stage: 5

A short introduction to complex numbers written primarily for students aged 14 to 19.

### An Introduction to Galois Theory

##### Stage: 5

This article only skims the surface of Galois theory and should probably be accessible to a 17 or 18 year old school student with a strong interest in mathematics.

### An Introduction to Mathematical Induction

##### Stage: 5

This article gives an introduction to mathematical induction, a powerful method of mathematical proof.

### An Introduction to Mathematical Structure

##### Stage: 5

An introduction to the sort of algebra studied at university, focussing on groups.

### An Introduction to Number Theory

##### Stage: 5

An introduction to some beautiful results of Number Theory