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

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

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

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

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

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

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

First 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.

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

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

Third in our series of problems 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.

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

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

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. . . .

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. . . .

Why MUST these statistical statements probably be at least a little bit wrong?

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

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

Fifth in our series of problems on 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?

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. . . .

An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.

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.

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

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. . . .

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

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?

This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!

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?

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.

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

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. . . .

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?

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. . . .

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!

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?

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

This is about a fiendishly difficult jigsaw and how to solve it using a computer program.