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?
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
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.
Can you make matrices which will fix one lucky vector and crush another to zero?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
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.
Explore the meaning of the scalar and vector cross products and see how the two are related.
How would you go about estimating populations of dolphins?
Invent scenarios which would give rise to these probability density functions.
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?
Use vectors and matrices to explore the symmetries of crystals.
How much energy has gone into warming the planet?
Who will be the first investor to pay off their debt?
Which pdfs match the curves?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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.
This problem explores the biology behind Rudolph's glowing red nose.
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?
Analyse these beautiful biological images and attempt to rank them in size order.
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?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Was it possible that this dangerous driving penalty was issued in error?
The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?
Formulate and investigate a simple mathematical model for the design of a table mat.
Look at the advanced way of viewing sin and cos through their power series.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Which line graph, equations and physical processes go together?
Can you work out which processes are represented by the graphs?
Get some practice using big and small numbers in chemistry.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
A problem about genetics and the transmission of disease.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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?
Can you construct a cubic equation with a certain distance between its turning points?