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.

Which line graph, equations and physical processes go together?

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?

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

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

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?

Work out the numerical values for these physical quantities.

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

How would you go about estimating populations of dolphins?

Use vectors and matrices to explore the symmetries of crystals.

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

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

Get some practice using big and small numbers in chemistry.

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

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.

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

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

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.

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

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

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.

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

Explore the relationship between resistance and temperature

Build up the concept of the Taylor series

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

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

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

Which units would you choose best to fit these situations?

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

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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

Which dilutions can you make using only 10ml pipettes?

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.

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?