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A problem about genetics and the transmission of disease.
Estimate areas using random grids
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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.
Simple models which help us to investigate how epidemics grow and die out.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Why MUST these statistical statements probably be at least a little bit wrong?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Work out the numerical values for these physical quantities.
Which line graph, equations and physical processes go together?
How do you choose your planting levels to minimise the total loss at harvest time?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Get further into power series using the fascinating Bessel's equation.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
Get some practice using big and small numbers in chemistry.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
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.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
How much energy has gone into warming the planet?
When you change the units, do the numbers get bigger or smaller?
Use your skill and judgement to match the sets of random data.
Build up the concept of the Taylor series
Look at the advanced way of viewing sin and cos through their power series.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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?
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 how matrices can fix vectors and vector directions.
Explore the properties of matrix transformations with these 10 stimulating questions.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Invent scenarios which would give rise to these probability density functions.
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.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Looking at small values of functions. Motivating the existence of the Taylor expansion.