A problem about genetics and the transmission of disease.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Simple models which help us to investigate how epidemics grow and die out.
Which pdfs match the curves?
How do you choose your planting levels to minimise the total loss at harvest time?
Why MUST these statistical statements probably be at least a little bit wrong?
Which line graph, equations and physical processes go together?
Use vectors and matrices to explore the symmetries of crystals.
Which of these infinitely deep vessels will eventually full up?
Can you find the volumes of the mathematical vessels?
Get further into power series using the fascinating Bessel's equation.
Can you match these equations to these graphs?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Match the charts of these functions to the charts of their integrals.
How would you go about estimating populations of dolphins?
Can you make matrices which will fix one lucky vector and crush another to zero?
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.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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?
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 perspective drawing.
Invent scenarios which would give rise to these probability density functions.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you sketch these difficult curves, which have uses in mathematical modelling?
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.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
How much energy has gone into warming the planet?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Who will be the first investor to pay off their debt?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Match the descriptions of physical processes to these differential equations.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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?
Are these estimates of physical quantities accurate?
Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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?
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
Which units would you choose best to fit these situations?
Build up the concept of the Taylor series
Get some practice using big and small numbers in chemistry.