This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Which line graph, equations and physical processes go together?
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?
Why MUST these statistical statements probably be at least a little bit wrong?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Invent scenarios which would give rise to these probability density functions.
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 physical contexts.
Get further into power series using the fascinating Bessel's equation.
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.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Get some practice using big and small numbers in chemistry.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
How much energy has gone into warming the planet?
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which pdfs match the curves?
Was it possible that this dangerous driving penalty was issued in error?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Can you find the volumes of the mathematical vessels?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the shape of a square after it is transformed by the action of a matrix.
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you sketch these difficult curves, which have uses in mathematical modelling?
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 meaning of the scalar and vector cross products and see how the two are related.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Use vectors and matrices to explore the symmetries of crystals.
Which units would you choose best to fit these situations?
Match the descriptions of physical processes to these differential equations.
When you change the units, do the numbers get bigger or smaller?
Who will be the first investor to pay off their debt?
How would you go about estimating populations of dolphins?
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
Look at the advanced way of viewing sin and cos through their power series.
Simple models which help us to investigate how epidemics grow and die out.
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.
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?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Can you work out what this procedure is doing?
This problem explores the biology behind Rudolph's glowing red nose.
Go on a vector walk and determine which points on the walk are closest to the origin.
Are these estimates of physical quantities accurate?