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

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.

Build up the concept of the Taylor series

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

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

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

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.

How would you go about estimating populations of dolphins?

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

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

Which line graph, equations and physical processes go together?

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

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?

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

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

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

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.

Work out the numerical values for these physical quantities.

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

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?

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

Which units would you choose best to fit these situations?

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

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

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

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

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

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

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

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

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

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

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?

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

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

Explore the relationship between resistance and temperature