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

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

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

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.

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

Work out the numerical values for these physical quantities.

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

How would you go about estimating populations of dolphins?

Which line graph, equations and physical processes go together?

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

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

Which countries have the most naturally athletic populations?

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

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?

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

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

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

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

Which dilutions can you make using only 10ml pipettes?

Get some practice using big and small numbers in chemistry.

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

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

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

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

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.

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

Build up the concept of the Taylor series

Explore the relationship between resistance and temperature

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

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

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

Which units would you choose best to fit these situations?

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

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

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

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.

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

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

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?

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

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