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.
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 how matrices can fix vectors and vector directions.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Explore the meaning of the scalar and vector cross products and see how the two are related.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Explore the shape of a square after it is transformed by the action of a matrix.
Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Use vectors and matrices to explore the symmetries of crystals.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How much energy has gone into warming the planet?
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?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work out the numerical values for these physical quantities.
Is it really greener to go on the bus, or to buy local?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Which line graph, equations and physical processes go together?
Which pdfs match the curves?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Can you sketch these difficult curves, which have uses in mathematical modelling?
How do you choose your planting levels to minimise the total loss at harvest time?
Explore the properties of matrix transformations with these 10 stimulating questions.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Invent scenarios which would give rise to these probability density functions.
A problem about genetics and the transmission of disease.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Get some practice using big and small numbers in chemistry.
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Can you work out which processes are represented by the graphs?
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Can you construct a cubic equation with a certain distance between its turning points?
Which of these infinitely deep vessels will eventually full up?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Explore the relationship between resistance and temperature
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
Build up the concept of the Taylor series