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?
Invent scenarios which would give rise to these probability density functions.
Was it possible that this dangerous driving penalty was issued in error?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Which line graph, equations and physical processes go together?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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.
Which units would you choose best to fit these situations?
How much energy has gone into warming the planet?
When you change the units, do the numbers get bigger or smaller?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Work out the numerical values for these physical quantities.
Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
This problem explores the biology behind Rudolph's glowing red nose.
Get further into power series using the fascinating Bessel's equation.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Use vectors and matrices to explore the symmetries of crystals.
Which pdfs match the curves?
Can you make matrices which will fix one lucky vector and crush another to zero?
Can you find the volumes of the mathematical vessels?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you match the charts of these functions to the charts of their integrals?
Explore how matrices can fix vectors and vector directions.
Match the descriptions of physical processes to these differential equations.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
How would you go about estimating populations of dolphins?
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.
Are these estimates of physical quantities accurate?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Analyse these beautiful biological images and attempt to rank them in size order.
Can you match these equations to these graphs?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the relationship between resistance and temperature
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore the shape of a square after it is transformed by the action of a matrix.