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.

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

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.

Build up the concept of the Taylor series

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

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

Which units would you choose best to fit these situations?

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

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

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 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.

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

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?

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

Work out the numerical values for these physical quantities.

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?

Get some practice using big and small numbers in chemistry.

Which line graph, equations and physical processes go together?

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

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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?

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

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

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.

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.

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

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

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

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

Which of these infinitely deep vessels will eventually full up?

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

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

Explore the relationship between resistance and temperature

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

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