Which line graph, equations and physical processes go together?

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.

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

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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

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.

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?

Can you work out which processes are represented by the graphs?

Work out the numerical values for these physical quantities.

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

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.

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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

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

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?

Which of these infinitely deep vessels will eventually full up?

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

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

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?

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

Match the descriptions of physical processes to these differential equations.

Which units would you choose best to fit these situations?

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

Explore the relationship between resistance and temperature

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.

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

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

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