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

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

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?

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

Which line graph, equations and physical processes go together?

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.

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

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

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

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

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

Build up the concept of the Taylor series

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

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

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?

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

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

Work out the numerical values for these physical quantities.

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

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?

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

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

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

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.

Get some practice using big and small numbers in chemistry.

Which of these infinitely deep vessels will eventually full up?

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

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

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?

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.

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.

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

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