Match the descriptions of physical processes to these differential equations.

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

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.

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

Use vectors and matrices to explore the symmetries of crystals.

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

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?

Explore the relationship between resistance and temperature

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

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

Which of these infinitely deep vessels will eventually full up?

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

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

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

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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

How would you go about estimating populations of dolphins?

Work out the numerical values for these physical quantities.

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

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

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

Build up the concept of the Taylor series

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

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

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

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

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

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.

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

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?

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...