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

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

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.

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

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

Which dilutions can you make using only 10ml pipettes?

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.

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

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?

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?

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

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

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

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

Work out the numerical values for these physical quantities.

Which of these infinitely deep vessels will eventually full up?

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

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

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

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

Explore the relationship between resistance and temperature

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

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

Use vectors and matrices to explore the symmetries of crystals.

Build up the concept of the Taylor series

Get some practice using big and small numbers in chemistry.

Match the descriptions of physical processes to these differential equations.

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

Which units would you choose best to fit these situations?

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

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

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

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

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

Which line graph, equations and physical processes go together?

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

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

Have you ever wondered what it would be like to race against Usain Bolt?

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

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

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