Explore how matrices can fix vectors and vector directions.
Which pdfs match the curves?
Look at the advanced way of viewing sin and cos through their power series.
Go on a vector walk and determine which points on the walk are closest to the origin.
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?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How much energy has gone into warming the planet?
Was it possible that this dangerous driving penalty was issued in error?
Get further into power series using the fascinating Bessel's equation.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Are these estimates of physical quantities accurate?
Can you work out what this procedure is doing?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
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.
Which line graph, equations and physical processes go together?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Invent scenarios which would give rise to these probability density functions.
Use vectors and matrices to explore the symmetries of crystals.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Which of these infinitely deep vessels will eventually full up?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Explore the properties of perspective drawing.
Analyse these beautiful biological images and attempt to rank them in size order.
Explore the meaning of the scalar and vector cross products and see how the two are related.
This problem explores the biology behind Rudolph's glowing red nose.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Explore the properties of matrix transformations with these 10 stimulating questions.
How do you choose your planting levels to minimise the total loss at harvest time?
Can you construct a cubic equation with a certain distance between its turning points?
Can you find the volumes of the mathematical vessels?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Who will be the first investor to pay off their debt?
Work with numbers big and small to estimate and calulate 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.
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?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Match the descriptions of physical processes to these differential equations.
Formulate and investigate a simple mathematical model for the design of a table mat.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Explore the shape of a square after it is transformed by the action of a matrix.