This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested 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.
Get some practice using big and small numbers in chemistry.
Look at the advanced way of viewing sin and cos through their power series.
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?
Which line graph, equations and physical processes go together?
Match the descriptions of physical processes to these differential equations.
Build up the concept of the Taylor series
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the properties of matrix transformations with these 10 stimulating questions.
Get further into power series using the fascinating Bessel's equation.
Why MUST these statistical statements probably be at least a little bit wrong?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How would you go about estimating populations of dolphins?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
When you change the units, do the numbers get bigger or smaller?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Who will be the first investor to pay off their debt?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Invent scenarios which would give rise to these probability density functions.
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
Analyse these beautiful biological images and attempt to rank them in size order.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Use vectors and matrices to explore the symmetries of crystals.
Can you find the volumes of the mathematical vessels?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Which pdfs match the curves?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
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?
Explore how matrices can fix vectors and vector directions.
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?
Explore the relationship between resistance and temperature
This problem explores the biology behind Rudolph's glowing red nose.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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 make matrices which will fix one lucky vector and crush another to zero?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
A problem about genetics and the transmission of disease.