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.

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

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

Which line graph, equations and physical processes go together?

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

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

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

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

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?

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

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

Get further into power series using the fascinating Bessel's 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?

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

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

How would you go about estimating populations of dolphins?

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

Get some practice using big and small numbers in chemistry.

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.

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

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

Which units would you choose best to fit these situations?

Use vectors and matrices to explore the symmetries of crystals.

Build up the concept of the Taylor series

Work out the numerical values for these physical quantities.

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

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

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

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.

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

Match the descriptions of physical processes to these differential equations.

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.

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

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 relationship between resistance and temperature

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

Simple models which help us to investigate how epidemics grow and die out.

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

Which dilutions can you make using only 10ml pipettes?

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

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 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.

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

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