How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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.
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 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.
Invent scenarios which would give rise to these probability density functions.
Simple models which help us to investigate how epidemics grow and die out.
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.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
How would you go about estimating populations of dolphins?
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 pdfs match the curves?
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.
Was it possible that this dangerous driving penalty was issued in error?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How much energy has gone into warming the planet?
Explore the shape of a square after it is transformed by the action of a matrix.
Which units would you choose best to fit these situations?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
When you change the units, do the numbers get bigger or smaller?
Use vectors and matrices to explore the symmetries of crystals.
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?
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.
Build up the concept of the Taylor series
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Formulate and investigate a simple mathematical model for the design of a table mat.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Who will be the first investor to pay off their debt?
How do you choose your planting levels to minimise the total loss at harvest time?
Which of these infinitely deep vessels will eventually full up?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Go on a vector walk and determine which points on the walk are closest to the origin.
Can you make matrices which will fix one lucky vector and crush another to zero?
A problem about genetics and the transmission of disease.
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Get some practice using big and small numbers in chemistry.
Can you work out what this procedure is doing?
Can you work out which processes are represented by the graphs?