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?
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?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Invent scenarios which would give rise to these probability density functions.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How much energy has gone into warming the planet?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Get further into power series using the fascinating Bessel's equation.
Explore the properties of matrix transformations with these 10 stimulating questions.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which units would you choose best to fit these situations?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Formulate and investigate a simple mathematical model for the design of a table mat.
How would you go about estimating populations of dolphins?
Work out the numerical values for these physical quantities.
Analyse these beautiful biological images and attempt to rank them in size order.
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 sketch these difficult curves, which have uses in mathematical modelling?
Was it possible that this dangerous driving penalty was issued in error?
Look at the advanced way of viewing sin and cos through their power series.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Are these estimates of physical quantities accurate?
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.
Build up the concept of the Taylor series
When you change the units, do the numbers get bigger or smaller?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Is it really greener to go on the bus, or to buy local?
Simple models which help us to investigate how epidemics grow and die out.
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
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?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Use vectors and matrices to explore the symmetries of crystals.
Go on a vector walk and determine which points on the walk are closest to the origin.
Can you work out what this procedure is doing?