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 shape of a square after it is transformed by the action
of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
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.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Why MUST these statistical statements probably be at least a little
Which pdfs match the curves?
Which line graph, equations and physical processes go together?
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?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Use vectors and matrices to explore the symmetries of crystals.
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
How do you choose your planting levels to minimise the total loss
at harvest time?
Can you find the volumes of the mathematical vessels?
Can you draw the height-time chart as this complicated vessel fills
Which countries have the most naturally athletic populations?
Can you construct a cubic equation with a certain distance between
its turning points?
Which of these infinitely deep vessels will eventually full up?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Explore the properties of perspective drawing.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Get some practice using big and small numbers in chemistry.
Invent scenarios which would give rise to these probability density functions.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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.
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Can you sketch these difficult curves, which have uses in
Was it possible that this dangerous driving penalty was issued in
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?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
How much energy has gone into warming the planet?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Match the charts of these functions to the charts of their integrals.
In this short problem, try to find the location of the roots of
some unusual functions by finding where they change sign.
Look at the advanced way of viewing sin and cos through their power series.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
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?
Estimate areas using random grids
Match the descriptions of physical processes to these differential
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
This problem explores the biology behind Rudolph's glowing red nose.
Explore the relationship between resistance and temperature