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

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

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?

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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

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

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

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

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

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

Which of these infinitely deep vessels will eventually full up?

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

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

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

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

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

How would you go about estimating populations of dolphins?

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.

Match the descriptions of physical processes to these differential equations.

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

Explore the relationship between resistance and temperature

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

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

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

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

Use trigonometry to determine whether solar eclipses on earth can be perfect.

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.

Build up the concept of the Taylor series

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

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

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

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

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.