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.
First of all, pick the number of times a week that you would like
to eat chocolate. Multiply this number by 2...
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.
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
It is possible to identify a particular card out of a pack of 15
with the use of some mathematical reasoning. What is this reasoning
and can it be applied to other numbers of cards?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Given the graph of a supply network and the maximum capacity for
flow in each section find the maximum flow across the network.
Fourth in our series of problems on population dynamics for advanced students.
Fifth in our series of problems on population dynamics for advanced students.
This is about a fiendishly difficult jigsaw and how to solve it
using a computer program.
Sixth in our series of problems on population dynamics for advanced students.
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!
First 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.
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
Invent scenarios which would give rise to these probability density functions.
An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.
Second in our series of problems on population dynamics for advanced students.
An account of how mathematics is used in computer games including
geometry, vectors, transformations, 3D graphics, graph theory and
Third 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. . . .
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.
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. . . .
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.
A brief video explaining the idea of a mathematical knot.
This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!
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. . . .
Explain why, when moving heavy objects on rollers, the object moves
twice as fast as the rollers. Try a similar experiment yourself.
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.
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. . . .
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
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Work in groups to try to create the best approximations to these
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. . . .
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
See how the motion of the simple pendulum is not-so-simple after
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. . . .
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
How many eggs should a bird lay to maximise the number of chicks
that will hatch? An introduction to optimisation.
Simple models which help us to investigate how epidemics grow and die out.
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.
At what positions and speeds can the bomb be dropped to destroy the
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?