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