An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Use vectors and matrices to explore the symmetries of crystals.

Here are several equations from real life. Can you work out which measurements are possible from each equation?

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

When you change the units, do the numbers get bigger or smaller?

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

Which units would you choose best to fit these situations?

Get further into power series using the fascinating Bessel's equation.

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

Can you match the charts of these functions to the charts of their integrals?

See how enormously large quantities can cancel out to give a good approximation to the factorial function.

Work with numbers big and small to estimate and calculate various quantities in biological contexts.

Why MUST these statistical statements probably be at least a little bit wrong?

Which line graph, equations and physical processes go together?

Invent scenarios which would give rise to these probability density functions.

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

Formulate and investigate a simple mathematical model for the design of a table mat.

Which dilutions can you make using only 10ml pipettes?

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

Build up the concept of the Taylor series

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

Explore the meaning of the scalar and vector cross products and see how the two are related.

Is it really greener to go on the bus, or to buy local?

Where should runners start the 200m race so that they have all run the same distance by the finish?

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.

Starting with two basic vector steps, which destinations can you reach on a vector walk?

Can you make matrices which will fix one lucky vector and crush another to zero?

Explore the properties of matrix transformations with these 10 stimulating questions.

Can you sketch these difficult curves, which have uses in mathematical modelling?

Go on a vector walk and determine which points on the walk are closest to the origin.

Looking at small values of functions. Motivating the existence of the Taylor expansion.

Explore the shape of a square after it is transformed by the action of a matrix.

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

Simple models which help us to investigate how epidemics grow and die out.

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

Get some practice using big and small numbers in chemistry.

Can Jo make a gym bag for her trainers from the piece of fabric she has?