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.
Can you match these equations to these graphs?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Why MUST these statistical statements probably be at least a little bit wrong?
Which line graph, equations and physical processes go together?
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.
Who will be the first investor to pay off their debt?
How much energy has gone into warming the planet?
Explore the relationship between resistance and temperature
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?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
How would you go about estimating populations of dolphins?
Build up the concept of the Taylor series
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?
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.
Can you make matrices which will fix one lucky vector and crush another to zero?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Go on a vector walk and determine which points on the walk are closest to the origin.
Get further into power series using the fascinating Bessel's equation.
Get some practice using big and small numbers in chemistry.
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.
Look at the advanced way of viewing sin and cos through their power series.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Which pdfs match the curves?
Use vectors and matrices to explore the symmetries of crystals.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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?
Can you find the volumes of the mathematical vessels?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Are these estimates of physical quantities accurate?
Formulate and investigate a simple mathematical model for the design of a table mat.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
This problem explores the biology behind Rudolph's glowing red nose.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.
Can you work out which processes are represented by the graphs?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
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?