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Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.

Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...

Some simple ideas about graph theory with a discussion of a proof of Euler's formula relating the numbers of vertces, edges and faces of a graph.

Written for teachers, this article discusses mathematical representations and takes, in the second part of the article, examples of reception children's own representations.

The human genome is represented by a string of around 3 billion letters. To deal with such large numbers, genome sequencing relies on clever algorithms. This article investigates.

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.

Alf and Tracy explain how the Kingsfield School maths department use common tasks to encourage all students to think mathematically about key areas in the curriculum.

This article looks at the importance in mathematics of representing places and spaces mathematics. Many famous mathematicians have spent time working on problems that involve moving and mapping. . . .

An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.

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. . . .

This article sets some puzzles and describes how Euclid's algorithm and continued fractions are related.

This article for teachers looks at some suggestions taken from the NRICH website that offer a broad view of data and ask some more probing questions about it.

Step back and reflect! This article reviews techniques such as substitution and change of coordinates which enable us to exploit underlying structures to crack problems.

Having a good grasp of trigonometry is important for solving advanced mathematics examinations questions.

Jenny Murray describes the mathematical processes behind making patchwork in this article for students.

A small change can have a big effect! Read all about Chaos Theory in this short article.

What do you need to know about discrete and continuous random variables to tackle STEP and other advanced mathematics examinations Statistics?

An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.

The Four Colour Conjecture was first stated just over 150 years ago, and finally proved conclusively in 1976. It is an outstanding example of how old ideas can be combined with new discoveries. prove. . . .

Read about the problem that tickled Euler's curiosity and led to a new branch of mathematics!

Introducing a geometrical instrument with 3 basic capabilities.

This short article offers some advice for tackling STEP and other advanced mathematics examinations questions on integration

This article describes investigations that offer opportunities for children to think differently, and pose their own questions, about shapes.

The first of three articles on the History of Trigonometry. This takes us from the Egyptians to early work on trigonometry in China.

In this article, Malcolm Swan describes a teaching approach designed to improve the quality of students' reasoning.

An article for teachers which discusses the differences between ratio and proportion, and invites readers to contribute their own thoughts.

Here is a proof of Euler's formula in the plane and on a sphere together with projects to explore cases of the formula for a polygon with holes, for the torus and other solids with holes and the. . . .

How do decisions about scoring affect who wins a combined event such as the decathlon?

By following through the threads of algebraic thinking discussed in this article, we can ensure that children's mathematical experiences follow a continuous progression.

Noticing the regular movement of the Sun and the stars has led to a desire to measure time. This article for teachers and learners looks at the history of man's need to measure things.

This is the second article in a two part series on the history of Algebra from about 2000 BCE to about 1000 CE.