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?

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

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

How would you go about estimating populations of dolphins?

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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

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.

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

Match the charts of these functions to the charts of their integrals.

Match the descriptions of physical processes to these differential equations.

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?

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

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

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

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

Which of these infinitely deep vessels will eventually full up?

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

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

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

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?

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

Explore the relationship between resistance and temperature

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

Which line graph, equations and physical processes go together?

Why MUST these statistical statements probably be at least a little bit wrong?

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

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.

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?

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

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

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.

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

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

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

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