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.

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

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.

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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

Match the descriptions of physical processes to these differential equations.

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

Which line graph, equations and physical processes go together?

Explore the relationship between resistance and temperature

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

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

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

How would you go about estimating populations of dolphins?

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

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

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

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

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

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

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

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

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.

Get some practice using big and small numbers in chemistry.

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

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?

Work out the numerical values for these physical quantities.

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

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

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

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

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

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

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

Which units would you choose best to fit these situations?

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.