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.
Can you make matrices which will fix one lucky vector and crush another to zero?
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 meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore the shape of a square after it is transformed by the action of a matrix.
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.
How much energy has gone into warming the planet?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Use vectors and matrices to explore the symmetries of crystals.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Was it possible that this dangerous driving penalty was issued in error?
Which of these infinitely deep vessels will eventually full up?
Which pdfs match the curves?
How do you choose your planting levels to minimise the total loss at harvest time?
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?
Can you match these equations to these graphs?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Explore the properties of matrix transformations with these 10 stimulating questions.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
How would you go about estimating populations of dolphins?
Can you find the volumes of the mathematical vessels?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Analyse these beautiful biological images and attempt to rank them in size order.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Explore the properties of perspective drawing.
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
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.
Match the descriptions of physical processes to these differential equations.
Who will be the first investor to pay off their debt?
This problem explores the biology behind Rudolph's glowing red nose.
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
Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Invent scenarios which would give rise to these probability density functions.
Explore the relationship between resistance and temperature
A problem about genetics and the transmission of disease.
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Get some practice using big and small numbers in chemistry.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?