Was it possible that this dangerous driving penalty was issued in error?
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 physical contexts.
Get further into power series using the fascinating Bessel's equation.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which of these infinitely deep vessels will eventually full up?
Get some practice using big and small numbers in chemistry.
How do you choose your planting levels to minimise the total loss at harvest time?
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?
How would you go about estimating populations of dolphins?
Match the charts of these functions to the charts of their integrals.
Can you find the volumes of the mathematical vessels?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore how matrices can fix vectors and vector directions.
Use vectors and matrices to explore the symmetries of crystals.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Work out the numerical values for these physical quantities.
Which pdfs match the curves?
Build up the concept of the Taylor series
Who will be the first investor to pay off their debt?
Are these estimates of physical quantities accurate?
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?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Explore the relationship between resistance and temperature
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Estimate areas using random grids
Match the descriptions of physical processes to these differential equations.
Look at the advanced way of viewing sin and cos through their power series.
Analyse these beautiful biological images and attempt to rank them in size order.
Go on a vector walk and determine which points on the walk are closest to the origin.
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.
Can you make matrices which will fix one lucky vector and crush another to zero?
Which units would you choose best to fit these situations?
A problem about genetics and the transmission of disease.
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.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Explore the properties of perspective drawing.
Formulate and investigate a simple mathematical model for the design of a table mat.