Use vectors and matrices to explore the symmetries of crystals.

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

Which of these infinitely deep vessels will eventually full up?

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

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

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

How would you go about estimating populations of dolphins?

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

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

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

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

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

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

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

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

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

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

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

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

Which line graph, equations and physical processes go together?

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

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

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

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

Match the descriptions of physical processes to these differential equations.

Build up the concept of the Taylor series

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?

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

Get some practice using big and small numbers in chemistry.

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

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

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

Work out the numerical values for these physical quantities.

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

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

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

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?

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

Simple models which help us to investigate how epidemics grow and die out.

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

Which units would you choose best to fit these situations?

Explore the relationship between resistance and temperature

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?

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.