This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
Why MUST these statistical statements probably be at least a little bit wrong?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Explore the properties of matrix transformations with these 10 stimulating questions.
Who will be the first investor to pay off their debt?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Look at the advanced way of viewing sin and cos through their power series.
Get further into power series using the fascinating Bessel's equation.
Match the descriptions of physical processes to these differential equations.
Which pdfs match the curves?
Was it possible that this dangerous driving penalty was issued in error?
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 some practice using big and small numbers in chemistry.
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.
Which line graph, equations and physical processes go together?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work out the numerical values for these physical quantities.
How would you go about estimating populations of dolphins?
How much energy has gone into warming the planet?
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?
Which units would you choose best to fit these situations?
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Build up the concept of the Taylor series
Can you sketch these difficult curves, which have uses in mathematical modelling?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Explore the shape of a square after it is transformed by the action of a matrix.
Use vectors and matrices to explore the symmetries of crystals.
Explore how matrices can fix vectors and vector directions.
Explore the meaning of the scalar and vector cross products and see how the two are related.
A problem about genetics and the transmission of disease.
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?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Can you work out what this procedure is doing?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Can you make matrices which will fix one lucky vector and crush another to zero?
Simple models which help us to investigate how epidemics grow and die out.
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Explore the relationship between resistance and temperature
This problem explores the biology behind Rudolph's glowing red nose.