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

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

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

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

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

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

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

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.

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.

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

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

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

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

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

How would you go about estimating populations of dolphins?

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

Match the descriptions of physical processes to these differential equations.

Build up the concept of the Taylor series

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

Which line graph, equations and physical processes go together?

Work out the numerical values for these physical quantities.

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

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

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

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

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?

Which dilutions can you make using only 10ml pipettes?

Explore the relationship between resistance and temperature

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

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

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

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.

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

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.

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

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

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

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

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

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