Starting with two basic vector steps, which destinations can you reach on a vector walk?
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?
Can you find the volumes of the mathematical vessels?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Is it really greener to go on the bus, or to buy local?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Explore the properties of matrix transformations with these 10 stimulating questions.
Use vectors and matrices to explore the symmetries of crystals.
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?
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?
Which pdfs match the curves?
Which line graph, equations and physical processes go together?
Work out the numerical values for these physical quantities.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Explore the relationship between resistance and temperature
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
Where should runners start the 200m race so that they have all run the same distance by the finish?
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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.
Get some practice using big and small numbers in chemistry.
Can you draw the height-time chart as this complicated vessel fills with water?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Which units would you choose best to fit these situations?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Who will be the first investor to pay off their debt?
Estimate areas using random grids
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.