This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Get further into power series using the fascinating Bessel's equation.
Look at the advanced way of viewing sin and cos through their power series.
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
How much energy has gone into warming the planet?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Get some practice using big and small numbers in chemistry.
Build up the concept of the Taylor series
Invent scenarios which would give rise to these probability density functions.
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.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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?
Was it possible that this dangerous driving penalty was issued in error?
Which line graph, equations and physical processes go together?
Which units would you choose best to fit these situations?
Use vectors and matrices to explore the symmetries of crystals.
Explore the properties of matrix transformations with these 10 stimulating questions.
Why MUST these statistical statements probably be at least a little bit wrong?
Formulate and investigate a simple mathematical model for the design of a table mat.
Which pdfs match the curves?
Explore the relationship between resistance and temperature
When you change the units, do the numbers get bigger or smaller?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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?
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.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
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?
Can you make matrices which will fix one lucky vector and crush another to zero?
Can you work out what this procedure is doing?
Match the descriptions of physical processes to these differential equations.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Analyse these beautiful biological images and attempt to rank them in size order.
Explore the shape of a square after it is transformed by the action of a matrix.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
How would you go about estimating populations of dolphins?
Explore how matrices can fix vectors and vector directions.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Are these estimates of physical quantities accurate?
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.