Invent scenarios which would give rise to these probability density functions.
First in our series of problems on population dynamics for advanced students.
Two cyclists, practising on a track, pass each other at the starting line and go at constant speeds... Can you find lap times that are such that the cyclists will meet exactly half way round the. . . .
Second in our series of problems on population dynamics for advanced students.
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
First of all, pick the number of times a week that you would like
to eat chocolate. Multiply this number by 2...
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
At what positions and speeds can the bomb be dropped to destroy the
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Look at the calculus behind the simple act of a car going over a
How do these modelling assumption affect the solutions?
See how the motion of the simple pendulum is not-so-simple after
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
Third in our series of problems on population dynamics for advanced students.
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Why MUST these statistical statements probably be at least a little
Edward Wallace based his A Level Statistics Project on The Mean
Game. Each picks 2 numbers. The winner is the player who picks a
number closest to the mean of all the numbers picked.
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!
A brief video explaining the idea of a mathematical knot.
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and record your findings in truth tables.
Formulate and investigate a simple mathematical model for the design of a table mat.
An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.
Fifth in our series of problems on population dynamics for advanced students.
Fourth in our series of problems on population dynamics for advanced students.
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?
The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to. . . .
Sixth in our series of problems on population dynamics for advanced students.
bioNRICH is the area of the stemNRICH site devoted to the
mathematics underlying the study of the biological sciences,
designed to help develop the mathematics required to get the most
from your. . . .
This is the section of stemNRICH devoted to the advanced applied
mathematics underlying the study of the sciences at higher levels
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
This article explains the concepts involved in scientific
mathematical computing. It will be very useful and interesting to
anyone interested in computer programming or mathematics.
Simple models which help us to investigate how epidemics grow and die out.
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Work in groups to try to create the best approximations to these
In this article for teachers, Alan Parr looks at ways that
mathematics teaching and learning can start from the useful and
interesting things can we do with the subject, including. . . .
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
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.
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
To win on a scratch card you have to uncover three numbers that add
up to more than fifteen. What is the probability of winning a
An account of how mathematics is used in computer games including
geometry, vectors, transformations, 3D graphics, graph theory and
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
This is about a fiendishly difficult jigsaw and how to solve it
using a computer program.
At Holborn underground station there is a very long escalator. Two
people are in a hurry and so climb the escalator as it is moving
upwards, thus adding their speed to that of the moving steps. . . .