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.

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

Which line graph, equations and physical processes go together?

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

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

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

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

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

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

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

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

Can you match the charts of these functions to the charts of their integrals?

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

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

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.

Use vectors and matrices to explore the symmetries of crystals.

Build up the concept of the Taylor series

Which units would you choose best to fit these situations?

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

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

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

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

Match the descriptions of physical processes to these differential equations.

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

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

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?

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

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

Work out the numerical values for these physical quantities.

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

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

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

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

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.

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?

Which of these infinitely deep vessels will eventually full up?

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

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

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

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

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.