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?

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

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.

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.

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

Which of these infinitely deep vessels will eventually full up?

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

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.

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.

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

Match the descriptions of physical processes to these differential equations.

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

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

Work with numbers big and small to estimate and calculate 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.

Build up the concept of the Taylor series

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

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?

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?

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

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

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

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

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

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

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

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?

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

Can you work out which processes are represented by the graphs?

Explore the relationship between resistance and temperature

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