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.
Can you make matrices which will fix one lucky vector and crush another to zero?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Match the descriptions of physical processes to these differential equations.
Use vectors and matrices to explore the symmetries of crystals.
How would you go about estimating populations of dolphins?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you find the volumes of the mathematical vessels?
Which of these infinitely deep vessels will eventually full up?
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the properties of matrix transformations with these 10 stimulating questions.
Analyse these beautiful biological images and attempt to rank them in size order.
Explore how matrices can fix vectors and vector directions.
Who will be the first investor to pay off their debt?
Can you match the charts of these functions to the charts of their integrals?
Was it possible that this dangerous driving penalty was issued in error?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
How do you choose your planting levels to minimise the total loss at harvest time?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Explore the shape of a square after it is transformed by the action of a matrix.
Get further into power series using the fascinating Bessel's equation.
Which pdfs match the curves?
This problem explores the biology behind Rudolph's glowing red nose.
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.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Can you construct a cubic equation with a certain distance between its turning points?
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.
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.
Can you sketch these difficult curves, which have uses in mathematical modelling?
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.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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?
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?
Can you match these equations to these graphs?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Can you work out which processes are represented by the graphs?
A problem about genetics and the transmission of disease.
Explore the relationship between resistance and temperature
Here are several equations from real life. Can you work out which measurements are possible from each equation?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Can you draw the height-time chart as this complicated vessel fills with water?
Build up the concept of the Taylor series
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.