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

Build up the concept of the Taylor series

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

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

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

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

Match the descriptions of physical processes to these differential equations.

Which line graph, equations and physical processes go together?

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

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

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

Which units would you choose best to fit these situations?

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

Get some practice using big and small numbers in chemistry.

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

How would you go about estimating populations of dolphins?

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?

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

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

Work out the numerical values for these physical quantities.

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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?

Explore the relationship between resistance and temperature

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

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 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.

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

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

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

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