Explore how matrices can fix vectors and vector directions.
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?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Can you find the volumes of the mathematical vessels?
Are these estimates of physical quantities accurate?
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?
Which pdfs match the curves?
How would you go about estimating populations of dolphins?
Which dilutions can you make using only 10ml pipettes?
This problem explores the biology behind Rudolph's glowing red nose.
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 shape of a square after it is transformed by the action of a matrix.
Which line graph, equations and physical processes go together?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which of these infinitely deep vessels will eventually full up?
Get further into power series using the fascinating Bessel's equation.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Was it possible that this dangerous driving penalty was issued in error?
Work out the numerical values for these physical quantities.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
How much energy has gone into warming the planet?
Which units would you choose best to fit these situations?
Get some practice using big and small numbers in chemistry.
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the relationship between resistance and temperature
Analyse these beautiful biological images and attempt to rank them in size order.
Explore the properties of perspective drawing.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Build up the concept of the Taylor series
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.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
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
When you change the units, do the numbers get bigger or smaller?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Use vectors and matrices to explore the symmetries of crystals.
Here are several equations from real life. Can you work out which measurements are possible from each equation?