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

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

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.

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.

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

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

Which of these infinitely deep vessels will eventually full up?

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.

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

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

Match the descriptions of physical processes to these differential equations.

Which line graph, equations and physical processes go together?

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

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?

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

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

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

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

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

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.

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

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

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

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 biological contexts.

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.

Which units would you choose best to fit these situations?

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

Work out the numerical values for these physical quantities.

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

Explore the relationship between resistance and temperature

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