How do these modelling assumption affect the solutions?

Fourth in our series of problems on population dynamics for advanced students.

Second in our series of problems on population dynamics for advanced students.

Sixth in our series of problems on population dynamics for advanced students.

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

See how differential equations might be used to make a realistic model of a system containing predators and their prey.

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.

At what positions and speeds can the bomb be dropped to destroy the dam?

Third in our series of problems on population dynamics for advanced students.

Fifth in our series of problems on population dynamics for advanced students.

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

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!

First in our series of problems on population dynamics for advanced students.

This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.

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?

PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics

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 bit wrong?

How do scores on dice and factors of polynomials relate to each other?

Look at the calculus behind the simple act of a car going over a step.

See how the motion of the simple pendulum is not-so-simple after all.

Work in groups to try to create the best approximations to these physical quantities.

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. . . .

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

Invent scenarios which would give rise to these probability density functions.

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

This is the section of stemNRICH devoted to the advanced applied mathematics underlying the study of the sciences at higher levels

A car is travelling along a dual carriageway at constant speed. Every 3 minutes a bus passes going in the opposite direction, while every 6 minutes a bus passes the car travelling in the same. . . .

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. . . .

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. . . .

An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.

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!

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. . . .

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

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. . . .

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?

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. . . .

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.

Formulate and investigate a simple mathematical model for the design of a table mat.

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.

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.

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 prize?

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. . . .

Investigate circuits and record your findings in this simple introduction to truth tables and logic.