How do these modelling assumption affect the solutions?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Look at the calculus behind the simple act of a car going over a
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
Work in groups to try to create the best approximations to these
See how the motion of the simple pendulum is not-so-simple after
Second in our series of problems on population dynamics for advanced students.
First in our series of problems on population dynamics for advanced students.
Third in our series of problems on population dynamics for advanced students.
At what positions and speeds can the bomb be dropped to destroy the
Fifth in our series of problems on population dynamics for advanced students.
Sixth in our series of problems on population dynamics for advanced students.
Invent scenarios which would give rise to these probability density functions.
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
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 problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
chemNRICH is the area of the stemNRICH site devoted to the
mathematics underlying the study of chemistry, designed to help
develop the mathematics required to get the most from your study. . . .
An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
Why MUST these statistical statements probably be at least a little
Fourth in our series of problems on population dynamics for advanced students.
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
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
You have two bags, four red balls and four white balls. You must
put all the balls in the bags although you are allowed to have one
bag empty. How should you distribute the balls between the two. . . .
Your school has been left a million pounds in the will of an ex-
pupil. What model of investment and spending would you use in order
to ensure the best return on the money?
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. . . .
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
This is the section of stemNRICH devoted to the advanced applied
mathematics underlying the study of the sciences at higher levels
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
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. . . .
A brief video explaining the idea of a mathematical knot.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Explain why, when moving heavy objects on rollers, the object moves
twice as fast as the rollers. Try a similar experiment yourself.
This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
In four years 2001 to 2004 Arsenal have been drawn against Chelsea
in the FA cup and have beaten Chelsea every time. What was the
probability of this? Lots of fractions in the calculations!
Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .
Given the graph of a supply network and the maximum capacity for
flow in each section find the maximum flow across the network.
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.
An account of how mathematics is used in computer games including
geometry, vectors, transformations, 3D graphics, graph theory and
Bricks are 20cm long and 10cm high. How high could an arch be built
without mortar on a flat horizontal surface, to overhang by 1
metre? How big an overhang is it possible to make like this?
Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?
Explore the transformations and comment on what you find.