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

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

Second 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.

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

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?

Fourth 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.

Fifth 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.

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

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

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

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

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .

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.

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

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

How do these modelling assumption affect the solutions?

engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering

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

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

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

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. . . .

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?

Can you find the lap times of the two cyclists travelling at constant speeds?

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. . . .

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.

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.

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.

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

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

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.

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. . . .

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

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. . . .

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

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.

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. . . .

Simple models which help us to investigate how epidemics grow and die out.

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. . . .

Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

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

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. . . .

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.

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.

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