Can you find the volumes of the mathematical vessels?
Who will be the first investor to pay off their debt?
Can you make matrices which will fix one lucky vector and crush another to zero?
Use vectors and matrices to explore the symmetries of crystals.
Which of these infinitely deep vessels will eventually full up?
Match the charts of these functions to the charts of their integrals.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Which pdfs match the curves?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the properties of perspective drawing.
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?
How would you go about estimating populations of dolphins?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Explore how matrices can fix vectors and vector directions.
How do you choose your planting levels to minimise the total loss at harvest time?
Go on a vector walk and determine which points on the walk are closest to the origin.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the shape of a square after it is transformed by the action of a matrix.
Can you sketch these difficult curves, which have uses in mathematical modelling?
How much energy has gone into warming the planet?
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.
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.
Why MUST these statistical statements probably be at least a little bit wrong?
Can you construct a cubic equation with a certain distance between its turning points?
Was it possible that this dangerous driving penalty was issued in error?
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?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Invent scenarios which would give rise to these probability density functions.
This problem explores the biology behind Rudolph's glowing red nose.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
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.
Can you match these equations to these graphs?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Get further into power series using the fascinating Bessel's equation.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Build up the concept of the Taylor series
How efficiently can you pack together disks?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
A problem about genetics and the transmission of disease.
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 possibilities for reaction rates versus concentrations with this non-linear differential equation
Explore the relationship between resistance and temperature