Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore how matrices can fix vectors and vector directions.
Which pdfs match the curves?
Can you find the volumes of the mathematical vessels?
Which of these infinitely deep vessels will eventually full up?
How do you choose your planting levels to minimise the total loss at harvest time?
Match the charts of these functions to the charts of their integrals.
Get further into power series using the fascinating Bessel's equation.
How efficiently can you pack together disks?
Can you match these equations to these graphs?
How would you go about estimating populations of dolphins?
Use vectors and matrices to explore the symmetries of crystals.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the shape of a square after it is transformed by the action of a matrix.
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?
Explore the properties of perspective drawing.
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Are these estimates of physical quantities accurate?
Can you make matrices which will fix one lucky vector and crush another to zero?
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.
How much energy has gone into warming the planet?
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.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Who will be the first investor to pay off their debt?
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.
Analyse these beautiful biological images and attempt to rank them in size order.
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.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Build up the concept of the Taylor series
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Invent scenarios which would give rise to these probability density functions.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Explore the relationship between resistance and temperature
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you work out which processes are represented by the graphs?
A problem about genetics and the transmission of disease.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Get some practice using big and small numbers in chemistry.