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
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Why MUST these statistical statements probably be at least a little bit wrong?
Which line graph, equations and physical processes go together?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Explore the properties of matrix transformations with these 10 stimulating questions.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Get further into power series using the fascinating Bessel's equation.
How would you go about estimating populations of dolphins?
Can you find the volumes of the mathematical vessels?
Use vectors and matrices to explore the symmetries of crystals.
Which pdfs match the curves?
Work out the numerical values for these physical quantities.
Can you make matrices which will fix one lucky vector and crush another to zero?
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
Which dilutions can you make using only 10ml pipettes?
Get some practice using big and small numbers in chemistry.
Explore the shape of a square after it is transformed by the action of a matrix.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Explore the meaning of the scalar and vector cross products and see how the two are related.
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?
How much energy has gone into warming the planet?
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.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Explore the relationship between resistance and temperature
Who will be the first investor to pay off their debt?
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.
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?
Match the descriptions of physical processes to these differential equations.
Explore the properties of perspective drawing.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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?
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.
Which units would you choose best to fit these situations?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
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.
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 these equations to these graphs?