Use your skill and judgement to match the sets of random data.
How do you choose your planting levels to minimise the total loss
at harvest time?
Which countries have the most naturally athletic populations?
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
A problem about genetics and the transmission of disease.
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
Estimate areas using random grids
Simple models which help us to investigate how epidemics grow and die out.
Starting with two basic vector steps, which destinations can you
reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
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.
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?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Which pdfs match the curves?
Can you construct a cubic equation with a certain distance between
its turning points?
Can you find the volumes of the mathematical vessels?
Which of these infinitely deep vessels will eventually full up?
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
Why MUST these statistical statements probably be at least a little
Explore the meaning of the scalar and vector cross products and see
how the two are related.
Which line graph, equations and physical processes go together?
Explore the properties of matrix transformations with these 10 stimulating questions.
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?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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?
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Explore the properties of perspective drawing.
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
Can you draw the height-time chart as this complicated vessel fills
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.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore how matrices can fix vectors and vector directions.
Can you sketch these difficult curves, which have uses in
How much energy has gone into warming the planet?
Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Match the descriptions of physical processes to these differential
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?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
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.