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

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

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

Work out the numerical values for these physical quantities.

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?

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

Get some practice using big and small numbers in chemistry.

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

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 calculate various quantities in biological contexts.

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

Which units would you choose best to fit these situations?

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

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

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

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

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

Explore the relationship between resistance and temperature

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?

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?

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

Build up the concept of the Taylor series

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

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

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.

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

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

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?

Which dilutions can you make using only 10ml pipettes?

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

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?

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.

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

Match the descriptions of physical processes to these differential equations.

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

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

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.