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?

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

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

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

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

Which line graph, equations and physical processes go together?

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.

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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.

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

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

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

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

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

Which units would you choose best to fit these situations?

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

Build up the concept of the Taylor series

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?

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

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

Match the descriptions of physical processes to these differential equations.

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

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.

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

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

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

Work out the numerical values for these physical quantities.

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

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

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

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

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

Get some practice using big and small numbers in chemistry.

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?

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