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.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
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.
Formulate and investigate a simple mathematical model for the design of a table mat.
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 dilutions can you make using only 10ml pipettes?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work out the numerical values for these physical quantities.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Which line graph, equations and physical processes go together?
Get further into power series using the fascinating Bessel's equation.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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. . . .
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Get some practice using big and small numbers in chemistry.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Can you make matrices which will fix one lucky vector and crush another to zero?
How efficiently can you pack together disks?
Explore the shape of a square after it is transformed by the action of a matrix.
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.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Look at the advanced way of viewing sin and cos through their power series.
Build up the concept of the Taylor series
When you change the units, do the numbers get bigger or smaller?
Explore the relationship between resistance and temperature
Which units would you choose best to fit these situations?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
A problem about genetics and the transmission of disease.
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...
Invent scenarios which would give rise to these probability density functions.
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.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
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 how matrices can fix vectors and vector directions.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
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.
Explore the properties of perspective drawing.
This problem explores the biology behind Rudolph's glowing red nose.