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.

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

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

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

Build up the concept of the Taylor series

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?

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

Get some practice using big and small numbers in chemistry.

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

Which line graph, equations and physical processes go together?

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

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

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

Match the descriptions of physical processes to these differential equations.

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

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

Explore the relationship between resistance and temperature

Can you match the charts of these functions to the charts of their integrals?

Work out the numerical values for these physical quantities.

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?

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

Can you draw the height-time chart as this complicated vessel fills with water?

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

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?

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 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.

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.

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?

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 units would you choose best to fit these situations?

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

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

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

Where should runners start the 200m race so that they have all run the same distance by the finish?

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