Invent scenarios which would give rise to these probability density functions.
Why MUST these statistical statements probably be at least a little bit wrong?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
How much energy has gone into warming the planet?
Which line graph, equations and physical processes go together?
Which of these infinitely deep vessels will eventually full up?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Was it possible that this dangerous driving penalty was issued in error?
How would you go about estimating populations of dolphins?
Use vectors and matrices to explore the symmetries of crystals.
Can you find the volumes of the mathematical vessels?
Get further into power series using the fascinating Bessel's equation.
Can you make matrices which will fix one lucky vector and crush another to zero?
Get some practice using big and small numbers in chemistry.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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 perspective drawing.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Which pdfs match the curves?
Build up the concept of the Taylor series
When you change the units, do the numbers get bigger or smaller?
Look at the advanced way of viewing sin and cos through their power series.
Are these estimates of physical quantities accurate?
Analyse these beautiful biological images and attempt to rank them in size order.
Who will be the first investor to pay off their debt?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Which units would you choose best to fit these situations?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Formulate and investigate a simple mathematical model for the design of a table mat.
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
Go on a vector walk and determine which points on the walk are closest to the origin.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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.
Can you work out what this procedure is doing?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?