Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore how matrices can fix vectors and vector directions.
Can you make matrices which will fix one lucky vector and crush another to zero?
Go on a vector walk and determine which points on the walk are closest to the origin.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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.
Get further into power series using the fascinating Bessel's equation.
Get some practice using big and small numbers in chemistry.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you match these equations to these graphs?
How would you go about estimating populations of dolphins?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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.
Can you find the volumes of the mathematical vessels?
Which of these infinitely deep vessels will eventually full up?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
How much energy has gone into warming the planet?
Which pdfs match the curves?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which line graph, equations and physical processes go together?
Use vectors and matrices to explore the symmetries of crystals.
Work out the numerical values for these physical quantities.
Can you work out which processes are represented by the graphs?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which units would you choose best to fit these situations?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
Which dilutions can you make using only 10ml pipettes?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Build up the concept of the Taylor series
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.
Match the descriptions of physical processes to these differential equations.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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?
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
Who will be the first investor to pay off their debt?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
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?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Why MUST these statistical statements probably be at least a little bit wrong?