Explore the shape of a square after it is transformed by the action of a matrix.
How would you go about estimating populations of dolphins?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Analyse these beautiful biological images and attempt to rank them in size order.
Match the descriptions of physical processes to these differential equations.
Which pdfs match the curves?
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore how matrices can fix vectors and vector directions.
Explore the properties of matrix transformations with these 10 stimulating questions.
Get further into power series using the fascinating Bessel's equation.
Can you match the charts of these functions to the charts of their integrals?
Can you find the volumes of the mathematical vessels?
Invent scenarios which would give rise to these probability density functions.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Which of these infinitely deep vessels will eventually full up?
How do you choose your planting levels to minimise the total loss at harvest time?
Can you make matrices which will fix one lucky vector and crush another to zero?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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?
Use vectors and matrices to explore the symmetries of crystals.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Who will be the first investor to pay off their debt?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
This problem explores the biology behind Rudolph's glowing red nose.
Explore the properties of perspective drawing.
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?
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?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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.
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?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Was it possible that this dangerous driving penalty was issued in error?
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.
Can you match these equations to these graphs?
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.
A problem about genetics and the transmission of disease.
Can you work out which processes are represented by the graphs?
Formulate and investigate a simple mathematical model for the design of a table mat.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Can you construct a cubic equation with a certain distance between its turning points?