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

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

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.

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?

Which line graph, equations and physical processes go together?

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

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?

How would you go about estimating populations of dolphins?

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

Get some practice using big and small numbers in chemistry.

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

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

Work out the numerical values for these physical quantities.

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

Build up the concept of the Taylor series

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

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

Match the descriptions of physical processes to these differential equations.

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

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

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

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

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

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

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

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?

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

Explore the relationship between resistance and temperature

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

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

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

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

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

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

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

Match the charts of these functions to the charts of their integrals.

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