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

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

Which line graph, equations and physical processes go together?

Match the descriptions of physical processes to these differential equations.

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

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

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.

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 biological contexts.

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

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

Which units would you choose best to fit these situations?

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

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

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

Build up the concept of the Taylor series

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

How would you go about estimating populations of dolphins?

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.

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

Use vectors and matrices to explore the symmetries of crystals.

Work out the numerical values for these physical quantities.

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

Get some practice using big and small numbers in chemistry.

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.

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

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.

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

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

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

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.

Explore the relationship between resistance and temperature

Use trigonometry to determine whether solar eclipses on earth can be perfect.

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

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

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.