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?
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.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Get some practice using big and small numbers in chemistry.
When you change the units, do the numbers get bigger or smaller?
Why MUST these statistical statements probably be at least a little bit wrong?
Which units would you choose best to fit these situations?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Look at the advanced way of viewing sin and cos through their power series.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Build up the concept of the Taylor series
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?
Get further into power series using the fascinating Bessel's equation.
Invent scenarios which would give rise to these probability density functions.
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 do you choose your planting levels to minimise the total loss at harvest time?
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?
Can you find the volumes of the mathematical vessels?
Which of these infinitely deep vessels will eventually full up?
Which pdfs match the curves?
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you make matrices which will fix one lucky vector and crush another to zero?
Use vectors and matrices to explore the symmetries of crystals.
This problem explores the biology behind Rudolph's glowing red nose.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Which dilutions can you make using only 10ml pipettes?
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.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Was it possible that this dangerous driving penalty was issued in error?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Match the descriptions of physical processes to these differential equations.
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.
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.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Explore the properties of perspective drawing.