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?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you find the volumes of the mathematical vessels?
Explore how matrices can fix vectors and vector directions.
How would you go about estimating populations of dolphins?
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.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
How do you choose your planting levels to minimise the total loss at harvest time?
Which of these infinitely deep vessels will eventually full up?
Are these estimates of physical quantities accurate?
Match the charts of these functions to the charts of their integrals.
Which pdfs match the curves?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the shape of a square after it is transformed by the action of a matrix.
Go on a vector walk and determine which points on the walk are closest to the origin.
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?
Who will be the first investor to pay off their debt?
Explore the properties of perspective drawing.
Use vectors and matrices to explore the symmetries of crystals.
How much energy has gone into warming the planet?
Match the descriptions of physical processes to these differential equations.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which line graph, equations and physical processes go together?
Why MUST these statistical statements probably be at least a little bit wrong?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
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.
This problem explores the biology behind Rudolph's glowing red nose.
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?
Get further into power series using the fascinating Bessel's equation.
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.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Can you match these equations to these graphs?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Estimate areas using random grids
A problem about genetics and the transmission of disease.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Explore the relationship between resistance and temperature
How efficiently can you pack together disks?
Build up the concept of the Taylor series
Can you sketch these difficult curves, which have uses in mathematical modelling?
Analyse these beautiful biological images and attempt to rank them in size order.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?