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

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

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

Build up the concept of the Taylor series

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

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

Which line graph, equations and physical processes go together?

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

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

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

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

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

Match the descriptions of physical processes to these differential equations.

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

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

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

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.

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

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

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.

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

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

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

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.

Work out the numerical values for these physical quantities.

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?

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

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

Which dilutions can you make using only 10ml pipettes?

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

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

Explore the relationship between resistance and temperature

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

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.

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

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

Which of these infinitely deep vessels will eventually full up?

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

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

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?