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

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

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

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

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

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

Which units would you choose best to fit these situations?

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?

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

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

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

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

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

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?

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

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

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.

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

Which line graph, equations and physical processes go together?

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

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

Build up the concept of the Taylor series

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

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

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?

Which dilutions can you make using only 10ml pipettes?

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

Work out the numerical values for these physical quantities.

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

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?

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

Is it really greener to go on the bus, or to buy local?

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

Use trigonometry to determine whether solar eclipses on earth can be perfect.

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

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

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

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

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

Which of these infinitely deep vessels will eventually full up?

Explore the relationship between resistance and temperature

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

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.