Which line graph, equations and physical processes go together?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
How much energy has gone into warming the planet?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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?
Get some practice using big and small numbers in chemistry.
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?
Get further into power series using the fascinating Bessel's equation.
Invent scenarios which would give rise to these probability density functions.
Why MUST these statistical statements probably be at least a little
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which units would you choose best to fit these situations?
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?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Build up the concept of the Taylor series
Look at the advanced way of viewing sin and cos through their power series.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
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...
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Explore the relationship between resistance and temperature
Go on a vector walk and determine which points on the walk are
closest to the origin.
Which dilutions can you make using only 10ml pipettes?
How would you go about estimating populations of dolphins?
Was it possible that this dangerous driving penalty was issued in
Match the descriptions of physical processes to these differential
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.
Are these estimates of physical quantities accurate?
Formulate and investigate a simple mathematical model for the design of a table mat.
How efficiently can you pack together disks?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Is it really greener to go on the bus, or to buy local?
Explore the properties of perspective drawing.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Can you work out what this procedure is doing?
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.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?