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?
Why MUST these statistical statements probably be at least a little bit wrong?
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.
Which line graph, equations and physical processes go together?
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?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Can you work out what this procedure is doing?
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.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Build up the concept of the Taylor series
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?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which pdfs match the curves?
Work out the numerical values for these physical quantities.
Simple models which help us to investigate how epidemics grow and die out.
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
Can you find the volumes of the mathematical vessels?
How do you choose your planting levels to minimise the total loss at harvest time?
Match the descriptions of physical processes to these differential equations.
Use vectors and matrices to explore the symmetries of crystals.
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.
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.
Get some practice using big and small numbers in chemistry.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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.
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?
Was it possible that this dangerous driving penalty was issued in error?
Which of these infinitely deep vessels will eventually full up?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Who will be the first investor to pay off their debt?
Are these estimates of physical quantities accurate?
Which units would you choose best to fit these situations?
Match the charts of these functions to the charts of their integrals.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you match these equations to these graphs?
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?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?