Here are several equations from real life. Can you work out which measurements are possible from each equation?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Why MUST these statistical statements probably be at least a little bit wrong?
Which pdfs match the curves?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Who will be the first investor to pay off their debt?
Which line graph, equations and physical processes go together?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Invent scenarios which would give rise to these probability density functions.
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you sketch these difficult curves, which have uses in mathematical modelling?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Use vectors and matrices to explore the symmetries of crystals.
How much energy has gone into warming the planet?
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?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Explore the shape of a square after it is transformed by the action of a matrix.
Analyse these beautiful biological images and attempt to rank them in size order.
Match the charts of these functions to the charts of their integrals.
Get further into power series using the fascinating Bessel's equation.
Explore the relationship between resistance and temperature
Can you find the volumes of the mathematical vessels?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Build up the concept of the Taylor series
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
Which of these infinitely deep vessels will eventually full up?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
How would you go about estimating populations of dolphins?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Match the descriptions of physical processes to these differential equations.
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Formulate and investigate a simple mathematical model for the design of a table mat.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Which dilutions can you make using only 10ml pipettes?
Look at the advanced way of viewing sin and cos through their power series.
Get some practice using big and small numbers in chemistry.
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?
Explore the properties of perspective drawing.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Go on a vector walk and determine which points on the walk are closest to the origin.