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?
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.
Which line graph, equations and physical processes go together?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Why MUST these statistical statements probably be at least a little bit wrong?
Can you sketch these difficult curves, which have uses in mathematical modelling?
How much energy has gone into warming the planet?
Work out the numerical values for these physical quantities.
How do you choose your planting levels to minimise the total loss at harvest time?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Get further into power series using the fascinating Bessel's equation.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Can you match the charts of these functions to the charts of their integrals?
Was it possible that this dangerous driving penalty was issued in error?
Can you find the volumes of the mathematical vessels?
Which of these infinitely deep vessels will eventually full up?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Get some practice using big and small numbers in chemistry.
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
How would you go about estimating populations of dolphins?
Go on a vector walk and determine which points on the walk are closest to the origin.
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.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Who will be the first investor to pay off their debt?
Build up the concept of the Taylor series
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Look at the advanced way of viewing sin and cos through their power series.
When you change the units, do the numbers get bigger or smaller?
This problem explores the biology behind Rudolph's glowing red nose.
Which units would you choose best to fit these situations?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Explore the properties of perspective drawing.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Match the descriptions of physical processes to these differential equations.
Explore the meaning of the scalar and vector cross products and see how the two are related.
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.
Can you make matrices which will fix one lucky vector and crush another to zero?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Explore the relationship between resistance and temperature