Why MUST these statistical statements probably be at least a little bit wrong?
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.
Who will be the first investor to pay off their debt?
Get further into power series using the fascinating Bessel's equation.
Was it possible that this dangerous driving penalty was issued in error?
Match the descriptions of physical processes to these differential equations.
Which pdfs match the curves?
Which line graph, equations and physical processes go together?
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?
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.
Explore the properties of matrix transformations with these 10 stimulating questions.
Use vectors and matrices to explore the symmetries of crystals.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
How much energy has gone into warming the planet?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Can you match the charts of these functions to the charts of their integrals?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Build up the concept of the Taylor series
Look at the advanced way of viewing sin and cos through their power series.
Can you construct a cubic equation with a certain distance between its turning points?
This problem explores the biology behind Rudolph's glowing red nose.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Work out the numerical values for these physical quantities.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Explore the shape of a square after it is transformed by the action of a matrix.
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore how matrices can fix vectors and vector directions.
Which of these infinitely deep vessels will eventually full up?
Can you find the volumes of the mathematical vessels?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Can you match these equations to these graphs?
When you change the units, do the numbers get bigger or smaller?
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.
Which units would you choose best to fit these situations?
Get some practice using big and small numbers in chemistry.
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?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?