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

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

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?

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

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.

Simple models which help us to investigate how epidemics grow and die out.

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

Which line graph, equations and physical processes go together?

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

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

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

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

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

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

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

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

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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

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

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

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

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

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.

Use vectors and matrices to explore the symmetries of crystals.

Which units would you choose best to fit these situations?

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

When you change the units, do the numbers get bigger or smaller?

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

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

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

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

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

Build up the concept of the Taylor series

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.

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?

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

Which dilutions can you make using only 10ml pipettes?

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

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?

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

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

Get some practice using big and small numbers in chemistry.