Match the descriptions of physical processes to these differential equations.

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.

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

Which line graph, equations and physical processes go together?

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

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

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

Build up the concept of the Taylor series

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

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

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

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?

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.

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

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

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

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

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.

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

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

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

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

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.

Work out the numerical values for these physical quantities.

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

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

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

Which of these infinitely deep vessels will eventually full up?

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

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.

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?

How would you go about estimating populations of dolphins?

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

Get some practice using big and small numbers in chemistry.

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

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

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

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

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