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?

Match the descriptions of physical processes to these differential equations.

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

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

Which line graph, equations and physical processes go together?

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

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

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

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

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

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

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

Which units would you choose best to fit these situations?

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

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

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.

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?

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

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

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.

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

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

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

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

Build up the concept of the Taylor series

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

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

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

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

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

Work out the numerical values for these physical quantities.

Use vectors and matrices to explore the symmetries of crystals.

Which dilutions can you make using only 10ml pipettes?

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

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

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

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

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

Which of these infinitely deep vessels will eventually full up?

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

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

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 would you go about estimating populations of dolphins?

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