Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Which line graph, equations and physical processes go together?
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Which units would you choose best to fit these situations?
When you change the units, do the numbers get bigger or smaller?
How much energy has gone into warming the planet?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Can you match these equations to these graphs?
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?
Invent scenarios which would give rise to these probability density functions.
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you draw the height-time chart as this complicated vessel fills with water?
Get some practice using big and small numbers in chemistry.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Get further into power series using the fascinating Bessel's equation.
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.
Can you match the charts of these functions to the charts of their integrals?
Can you work out which processes are represented by the graphs?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Can you find the volumes of the mathematical vessels?
Explore the shape of a square after it is transformed by the action of a matrix.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Why MUST these statistical statements probably be at least a little bit wrong?
Work out the numerical values for these physical quantities.
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
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?
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.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which pdfs match the curves?
How would you go about estimating populations of dolphins?
Who will be the first investor to pay off their debt?
Explore the relationship between resistance and temperature
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Build up the concept of the Taylor series
Match the descriptions of physical processes to these differential equations.
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.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Which dilutions can you make using only 10ml pipettes?
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.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Go on a vector walk and determine which points on the walk are closest to the origin.