How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Invent scenarios which would give rise to these probability density functions.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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?
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.
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.
Simple models which help us to investigate how epidemics grow and die out.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you find the volumes of the mathematical vessels?
Which line graph, equations and physical processes go together?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Who will be the first investor to pay off their debt?
Can you sketch these difficult curves, which have uses in mathematical modelling?
How do you choose your planting levels to minimise the total loss at harvest time?
How much energy has gone into warming the planet?
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.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Build up the concept of the Taylor series
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Use vectors and matrices to explore the symmetries of crystals.
Can you make matrices which will fix one lucky vector and crush another to zero?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which pdfs match the curves?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
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 out the numerical values for these physical quantities.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the shape of a square after it is transformed by the action of a matrix.
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?
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. . . .
Explore the properties of perspective drawing.
Can Jo make a gym bag for her trainers from the piece of fabric she has?
Formulate and investigate a simple mathematical model for the design of a table mat.
Get some practice using big and small numbers in chemistry.
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
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.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
A problem about genetics and the transmission of disease.
Explore the properties of matrix transformations with these 10 stimulating questions.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Get further into power series using the fascinating Bessel's equation.
When you change the units, do the numbers get bigger or smaller?