Explore how matrices can fix vectors and vector directions.
Can you make matrices which will fix one lucky vector and crush another to zero?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Which pdfs match the curves?
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
Explore the shape of a square after it is transformed by the action of a matrix.
Use vectors and matrices to explore the symmetries of crystals.
Who will be the first investor to pay off their debt?
Are these estimates of physical quantities accurate?
Which of these infinitely deep vessels will eventually full up?
Can you find the volumes of the mathematical vessels?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
How do you choose your planting levels to minimise the total loss at harvest time?
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.
Match the descriptions of physical processes to these differential equations.
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.
Analyse these beautiful biological images and attempt to rank them in size order.
This problem explores the biology behind Rudolph's glowing red nose.
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?
Invent scenarios which would give rise to these probability density functions.
Can you construct a cubic equation with a certain distance between its turning points?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Was it possible that this dangerous driving penalty was issued in error?
Can you match the charts of these functions to the charts of their integrals?
Get further into power series using the fascinating Bessel's equation.
How much energy has gone into warming the planet?
Can you match these equations to these graphs?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Estimate areas using random grids
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Explore the properties of perspective drawing.
Can you draw the height-time chart as this complicated vessel fills with water?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you work out which processes are represented by the graphs?
Get some practice using big and small numbers in chemistry.
A problem about genetics and the transmission of disease.
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?
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?