Explore the properties of matrix transformations with these 10 stimulating questions.
Which pdfs match the curves?
Who will be the first investor to pay off their debt?
Use vectors and matrices to explore the symmetries of crystals.
Can you find the volumes of the mathematical vessels?
How do you choose your planting levels to minimise the total loss at harvest time?
Explore the shape of a square after it is transformed by the action of a matrix.
Can you make matrices which will fix one lucky vector and crush another to zero?
Match the charts of these functions to the charts of their integrals.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
How would you go about estimating populations of dolphins?
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?
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 properties of perspective drawing.
Explore how matrices can fix vectors and vector directions.
Go on a vector walk and determine which points on the walk are closest to the origin.
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?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
How much energy has gone into warming the planet?
Match the descriptions of physical processes to these differential equations.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
Build up the concept of the Taylor series
Which line graph, equations and physical processes go together?
Why MUST these statistical statements probably be at least a little bit wrong?
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.
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?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
This problem explores the biology behind Rudolph's glowing red nose.
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 construct a cubic equation with a certain distance between its turning points?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Look at the advanced way of viewing sin and cos through their power series.
Can you match these equations to these graphs?
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?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
How efficiently can you pack together disks?
Analyse these beautiful biological images and attempt to rank them in size order.
A problem about genetics and the transmission of disease.
Was it possible that this dangerous driving penalty was issued in error?
Can you draw the height-time chart as this complicated vessel fills with water?