By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
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.
Which dilutions can you make using only 10ml pipettes?
Why MUST these statistical statements probably be at least a little bit wrong?
A problem about genetics and the transmission of disease.
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?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Which pdfs match the curves?
Get further into power series using the fascinating Bessel's equation.
Which units would you choose best to fit these situations?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Which line graph, equations and physical processes go together?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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?
Simple models which help us to investigate how epidemics grow and die out.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Work out the numerical values for these physical quantities.
How much energy has gone into warming the planet?
Build up the concept of the Taylor series
When you change the units, do the numbers get bigger or smaller?
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
Estimate areas using random grids
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Go on a vector walk and determine which points on the walk are closest to the origin.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Can you sketch these difficult curves, which have uses in mathematical modelling?
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.
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?
Explore the shape of a square after it is transformed by the action of a matrix.
Explore how matrices can fix vectors and vector directions.
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Explore the properties of perspective drawing.
Where should runners start the 200m race so that they have all run the same distance by the finish?