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

Use your skill and judgement to match the sets of random data.

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

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

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

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

How would you go about estimating populations of dolphins?

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

Which of these infinitely deep vessels will eventually full up?

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

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

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

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

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

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

Match the descriptions of physical processes to these differential equations.

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

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

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?

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

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

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

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

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

Which dilutions can you make using only 10ml pipettes?

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

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

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.

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

How would you design the tiering of seats in a stadium so that all spectators have a good view?

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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

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

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

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

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

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?