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

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

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

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

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

How do you choose your planting levels to minimise the total loss at harvest time?

How would you go about estimating populations of dolphins?

Which of these infinitely deep vessels will eventually full up?

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

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

Analyse these beautiful biological images and attempt to rank them in size order.

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

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

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

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

Was it possible that this dangerous driving penalty was issued in error?

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

This problem explores the biology behind Rudolph's glowing red nose.

Look at the advanced way of viewing sin and cos through their power series.

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

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?

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Match the descriptions of physical processes to these differential equations.

Can you construct a cubic equation with a certain distance between its turning points?

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

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

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

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

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

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

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

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

Which units would you choose best to fit these situations?

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

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

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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