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

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

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

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?

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?

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

Use vectors and matrices to explore the symmetries of crystals.

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.

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

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

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

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

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

How would you go about estimating populations of dolphins?

Match the descriptions of physical processes to these differential equations.

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

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

Build up the concept of the Taylor series

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

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

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

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 physical contexts.

Explore the relationship between resistance and temperature

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

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

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

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

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.

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

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

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

Get some practice using big and small numbers in chemistry.

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