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

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

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

Match the descriptions of physical processes to these differential equations.

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

Get some practice using big and small numbers in chemistry.

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

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

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

Which line graph, equations and physical processes go together?

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

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.

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

Which units would you choose best to fit these situations?

Work out the numerical values for these physical quantities.

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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.

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

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

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?

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

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?

Explore the relationship between resistance and temperature

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

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

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

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

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

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

Which of these infinitely deep vessels will eventually full up?

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

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

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

How would you go about estimating populations of dolphins?

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?

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

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