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

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

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

How would you go about estimating populations of dolphins?

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

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.

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.

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

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

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

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

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

Explore the relationship between resistance and temperature

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?

Which line graph, equations and physical processes go together?

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

Work out the numerical values for these physical quantities.

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.

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?

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

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

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

Which dilutions can you make using only 10ml pipettes?

Get some practice using big and small numbers in chemistry.

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.

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

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

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

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

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

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

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

Which units would you choose best to fit these situations?

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

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

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