This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Was it possible that this dangerous driving penalty was issued in error?
Are these estimates of physical quantities accurate?
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.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work out the numerical values for these physical quantities.
Which line graph, equations and physical processes go together?
Why MUST these statistical statements probably be at least a little bit wrong?
Invent scenarios which would give rise to these probability density functions.
Which pdfs match the curves?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Formulate and investigate a simple mathematical model for the design of a table mat.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Explore the properties of matrix transformations with these 10 stimulating questions.
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?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Which units would you choose best to fit these situations?
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.
Match the descriptions of physical processes to these differential equations.
When you change the units, do the numbers get bigger or smaller?
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?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Analyse these beautiful biological images and attempt to rank them in size order.
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
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.
Use vectors and matrices to explore the symmetries of crystals.
This problem explores the biology behind Rudolph's glowing red nose.
Explore the relationship between resistance and temperature
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Can you make matrices which will fix one lucky vector and crush another to zero?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Explore how matrices can fix vectors and vector directions.
Can you find the volumes of the mathematical vessels?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Can you match the charts of these functions to the charts of their integrals?
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 would you go about estimating populations of dolphins?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?