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

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

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

Which line graph, equations and physical processes go together?

Use vectors and matrices to explore the symmetries of crystals.

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

How would you go about estimating populations of dolphins?

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

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

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

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

Starting with two basic vector steps, which destinations can you reach on a vector walk?

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?

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

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

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

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

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.

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

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

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.

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

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?

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.

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

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

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.

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

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

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

Build up the concept of the Taylor series

Which units would you choose best to fit these situations?

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

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

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.

Explore the relationship between resistance and temperature

Which dilutions can you make using only 10ml pipettes?