Go on a vector walk and determine which points on the walk are closest to the origin.
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
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 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.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Which of these infinitely deep vessels will eventually full up?
Who will be the first investor to pay off their debt?
Use vectors and matrices to explore the symmetries of crystals.
Which pdfs match the curves?
Can you find the volumes of the mathematical vessels?
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.
This problem explores the biology behind Rudolph's glowing red nose.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Was it possible that this dangerous driving penalty was issued in error?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Which line graph, equations and physical processes go together?
Get further into power series using the fascinating Bessel's equation.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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.
Match the descriptions of physical processes to these differential equations.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Build up the concept of the Taylor series
How much energy has gone into warming the planet?
Get some practice using big and small numbers in chemistry.
Work out the numerical values for these physical quantities.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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?
How do you choose your planting levels to minimise the total loss at harvest time?
Which units would you choose best to fit these situations?
Explore the relationship between resistance and temperature
Analyse these beautiful biological images and attempt to rank them in size order.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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.
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?