This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
Which line graph, equations and physical processes go together?
Why MUST these statistical statements probably be at least a little bit wrong?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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?
Which pdfs match the curves?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How much energy has gone into warming the planet?
Was it possible that this dangerous driving penalty was issued in error?
Get further into power series using the fascinating Bessel's equation.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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.
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?
Build up the concept of the Taylor series
Work out the numerical values for these physical quantities.
Explore the shape of a square after it is transformed by the action of a matrix.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Which units would you choose best to fit these situations?
Explore how matrices can fix vectors and vector directions.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
When you change the units, do the numbers get bigger or smaller?
Look at the advanced way of viewing sin and cos through their power series.
Are these estimates of physical quantities accurate?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Get some practice using big and small numbers in chemistry.
Use vectors and matrices to explore the symmetries of crystals.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Simple models which help us to investigate how epidemics grow and die out.
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?
Is it really greener to go on the bus, or to buy local?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you work out what this procedure is doing?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Go on a vector walk and determine which points on the walk are closest to the origin.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Explore the properties of matrix transformations with these 10 stimulating questions.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Which of these infinitely deep vessels will eventually full up?