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Ergodic Mathematics

Carom Maths provides this resource for teachers and students of A Level mathematics.

Ergodic maths is a fairly new branch of mathematics which concerns itself with repeated processes and some of the basic theorems are introduced here.

The activity is designed to explore aspects of the subject which...

The Distribution of Prime Numbers

Carom Maths provides this resource for teachers and students of A Level mathematics.

In this activity the distribution of prime numbers, proved by Hadamard and de la Vallée Poussin in 1896, is investigated using an Excel spreadsheet program, Autograph and the Prime Number Theorem.

The resource is...

Infinity

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation highlights the concept of infinity and its implications, as well as introducing the mathematician Georg Cantor and the arguments relating to infinity that he came up with.

The resource is designed to...

Hyperbolic Geometry

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation introduces Euclid's axioms and theorems and provides historic information on the development of geometric principles, as well as discussing hyperbolic geometry. A link to Non-Euclid software, from Joel...

The Propositional Calculus

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation challenges students to use the rules they have been given to develop a logical system and deduce theorems which prove that the system is complete and consistent and introduces the idea of truth tables to...

The Mandelbrot Set

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation explores the Mandelbrot Set, a topic from Chaos Theory, which involves complex numbers and the Argand diagram. Following a set of rules, students use a spreadsheet to establish if complex numbers, on the...

The Game of Life

Carom Maths provides this resource for teachers and students of A Level mathematics. The Game of Life is a simulation of how a population might grow, if subject to a few simple rules. Initially students try the rules out for themselves on squared paper, before following a link to a computer program that shows the...

Mapping a Set to Itself

Carom Maths provides this resource for teachers and students of A Level mathematics.

In this presentation students are given a function and explore the mapping of natural numbers, as well as being challenged to find the inverse function. A link to the online encyclopaedia of integer sequences is provided for...

Pearl Tilings

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation explores the effect of placing a single tile into an existing pattern which tessellates, referred to as a pearl tiling. New descriptions and notation are introduced and questions regarding regular polygons...

Tangles

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation describes the concept of Tangles, which were the idea of John Conway. Students are given some rules from which they create the tangle representing 2/5, before creating their own tangle numbers for others to...

What Are You Implying?

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation provides students with an opportunity to explore their own grasp of logic and introduces a logical tautology called Modus Tollens.

This activity is designed to explore aspects of the subject which...

Conics

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation introduces the Conics and provides a Geogebra file for students to explore how, by changing the eccentricity of a curve, the locus of a point is altered. They are also challenged to vary the constants of an...

The Four Colour Theorem

Carom Maths provides this resource for teachers and students of A Level mathematics.

Colouring maps, so that no two countries sharing a border are shaded with the same colour, is the focus of this presentation, which includes both the history and mathematical proofs to this problem.

This activity is...

V, S and E

Carom Maths provides this resource for teachers and students of A Level mathematics.

There are six ways to write the total edge length, total surface area and volume of a cube, or cuboid, in order of size. This presentation challenges students to find a cube for each order. Autograph files are provided to...

The Logistic Map and Chaos

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation provides a spreadsheet, which models a population of mice, and allows students to vary the input and thus change the behaviour of the model. There are some surprising discoveries to be made when the results...

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