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?

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

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

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

How would you go about estimating populations of dolphins?

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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 out the numerical values for these physical quantities.

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

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?

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

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

Which line graph, equations and physical processes go together?

Build up the concept of the Taylor series

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

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

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

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

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

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.

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

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.

Can you draw the height-time chart as this complicated vessel fills with water?

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

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

Get some practice using big and small numbers in chemistry.

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

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?

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

Which units would you choose best to fit these situations?

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

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

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

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