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

How would you go about estimating populations of dolphins?

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?

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

Which units would you choose best to fit these situations?

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

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

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

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

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

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

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

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

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

Which of these infinitely deep vessels will eventually full up?

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

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?

Use vectors and matrices to explore the symmetries of crystals.

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

Various solids are lowered into a beaker of water. How does the water level rise in each case?

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

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

Which line graph, equations and physical processes go together?

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

Work out the numerical values for these physical quantities.

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

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

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

Which dilutions can you make using only 10ml pipettes?

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

Match the descriptions of physical processes to these differential equations.

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

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.

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

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.

Get some practice using big and small numbers in chemistry.

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

Explore the relationship between resistance and temperature

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