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

Which of these infinitely deep vessels will eventually full up?

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

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

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.

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

Which units would you choose best to fit these situations?

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

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

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

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

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

Which line graph, equations and physical processes go together?

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

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?

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

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

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

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

Match the descriptions of physical processes to these differential equations.

Build up the concept of the Taylor series

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

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

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

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

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?

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

Work out the numerical values for these physical quantities.

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

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

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.

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?

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 calulate various quantities in biological contexts.

Get some practice using big and small numbers in chemistry.

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