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

Which line graph, equations and physical processes go together?

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

Match the descriptions of physical processes to these differential equations.

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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

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?

Can you match the charts of these functions to the charts of their integrals?

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

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

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

Build up the concept of the Taylor series

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

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

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.

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

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

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

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

Which of these infinitely deep vessels will eventually full up?

Which units would you choose best to fit these situations?

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

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.

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

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

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 physical contexts.

Explore the relationship between resistance and temperature

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

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

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