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
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.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Explore the properties of perspective drawing.
Which line graph, equations and physical processes go together?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Work out the numerical values for these physical quantities.
Match the charts of these functions to the charts of their integrals.
Get further into power series using the fascinating Bessel's equation.
Which units would you choose best to fit these situations?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
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?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Which dilutions can you make using only 10ml pipettes?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Get some practice using big and small numbers in chemistry.
Formulate and investigate a simple mathematical model for the design of a table mat.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Go on a vector walk and determine which points on the walk are
closest to the origin.
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 physical contexts.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
How much energy has gone into warming the planet?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
When you change the units, do the numbers get bigger or smaller?
Estimate areas using random grids
Build up the concept of the Taylor series
Look at the advanced way of viewing sin and cos through their power series.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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.
A problem about genetics and the transmission of disease.
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.
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you sketch these difficult curves, which have uses in
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?
Explore how matrices can fix vectors and vector directions.
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?
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.
This problem explores the biology behind Rudolph's glowing red
Explore the relationship between resistance and temperature