This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
How efficiently can you pack together disks?
Which of these infinitely deep vessels will eventually full up?
How do you choose your planting levels to minimise the total loss at harvest time?
Why MUST these statistical statements probably be at least a little bit wrong?
Which line graph, equations and physical processes go together?
Can you construct a cubic equation with a certain distance between its turning points?
Which pdfs match the curves?
Match the charts of these functions to the charts of their integrals.
How would you go about estimating populations of dolphins?
Can you match these equations to these graphs?
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 vectors and matrices to explore the symmetries of crystals.
Can you find the volumes of the mathematical vessels?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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?
Invent scenarios which would give rise to these probability density functions.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
Explore the properties of perspective drawing.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you make matrices which will fix one lucky vector and crush another to zero?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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?
Go on a vector walk and determine which points on the walk are closest to the origin.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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.
Match the descriptions of physical processes to these differential equations.
Who will be the first investor to pay off their debt?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
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.
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?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
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.
Are these estimates of physical quantities accurate?
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
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 biological contexts.
Explore how matrices can fix vectors and vector directions.
Can Jo make a gym bag for her trainers from the piece of fabric she has?
Explore the relationship between resistance and temperature
Which dilutions can you make using only 10ml pipettes?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?