This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Get further into power series using the fascinating Bessel's equation.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Which line graph, equations and physical processes go together?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Was it possible that this dangerous driving penalty was issued in error?
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you find the volumes of the mathematical vessels?
Match the charts of these functions to the charts of their integrals.
Get some practice using big and small numbers in chemistry.
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?
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you match these equations to these graphs?
Which of these infinitely deep vessels will eventually full up?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Explore the relationship between resistance and temperature
Invent scenarios which would give rise to these probability density functions.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Why MUST these statistical statements probably be at least a little bit wrong?
Which pdfs match the curves?
How do you choose your planting levels to minimise the total loss at harvest time?
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 problem explores the biology behind Rudolph's glowing red nose.
Use vectors and matrices to explore the symmetries of crystals.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Which dilutions can you make using only 10ml pipettes?
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?
Look at the advanced way of viewing sin and cos through their power series.
Match the descriptions of physical processes to these differential equations.
Explore the properties of perspective drawing.
Build up the concept of the Taylor series
Go on a vector walk and determine which points on the walk are closest to the origin.
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 possibilities for reaction rates versus concentrations with this non-linear differential equation
Explore the shape of a square after it is transformed by the action of a matrix.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which units would you choose best to fit these situations?
How efficiently can you pack together disks?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you make matrices which will fix one lucky vector and crush another to zero?
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.
Who will be the first investor to pay off their debt?