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

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

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

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

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

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

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

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?

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

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

Which dilutions can you make using only 10ml pipettes?

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

Looking at small values of functions. Motivating the existence of the Taylor expansion.

Get some practice using big and small numbers in chemistry.

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

Which line graph, equations and physical processes go together?

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

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

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

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

Build up the concept of the Taylor series

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

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

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

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.

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

Explore the relationship between resistance and temperature

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

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

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.

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 properties of matrix transformations with these 10 stimulating questions.

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.

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

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

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.

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

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?

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

Which units would you choose best to fit these situations?