This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Why MUST these statistical statements probably be at least a little bit wrong?
Get further into power series using the fascinating Bessel's equation.
Which line graph, equations and physical processes go together?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Get some practice using big and small numbers in chemistry.
Invent scenarios which would give rise to these probability density functions.
Build up the concept of the Taylor series
Work out the numerical values for these physical quantities.
How much energy has gone into warming the planet?
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.
How would you go about estimating populations of dolphins?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Are these estimates of physical quantities accurate?
Was it possible that this dangerous driving penalty was issued in error?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
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.
Look at the advanced way of viewing sin and cos through their power series.
Analyse these beautiful biological images and attempt to rank them in size order.
Who will be the first investor to pay off their debt?
Explore the properties of perspective drawing.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Use vectors and matrices to explore the symmetries of crystals.
Which pdfs match the curves?
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.
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?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
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 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.
How do you choose your planting levels to minimise the total loss at harvest time?
Match the descriptions of physical processes to these differential equations.
Go on a vector walk and determine which points on the walk are closest to the origin.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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?
Can you find the volumes of the mathematical vessels?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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?