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.

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

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?

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

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

How would you go about estimating populations of dolphins?

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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

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?

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.

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

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

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.

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

Which line graph, equations and physical processes go together?

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

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

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

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?

Can you match the charts of these functions to the charts of their integrals?

Which of these infinitely deep vessels will eventually full up?

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

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

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

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.

Build up the concept of the Taylor series

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

Match the descriptions of physical processes to these differential equations.

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

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

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

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

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

Work out the numerical values for these physical quantities.