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

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.

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

Which units would you choose best to fit these situations?

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

Work out the numerical values for these physical quantities.

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

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

Which line graph, equations and physical processes go together?

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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

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

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

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?

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?

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

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

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.

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

Build up the concept of the Taylor series

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?

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

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?

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?

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

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?

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

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

Can you construct a cubic equation with a certain distance between its turning points?

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

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