Mathematical Modelling - Advanced
chemNRICH
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 of chemistry at A-level and university.
physNRICH
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
bioNRICH
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 study of biology at A-level and university.
Elastic Maths
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.
What's That Graph?
Can you work out which processes are represented by the graphs?
Stonehenge
Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.
Snooker
A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?
10 Olympic Starters
10 intriguing starters related to the mechanics of sport.
Dangerous Driver?
Was it possible that this dangerous driving penalty was issued in error?
The Mean Game
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.
Bird-brained
How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.
The Use of Mathematics in Computer Games
An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.
Big and Small Numbers in Physics - Group Task
Work in groups to try to create the best approximations to these physical quantities.
engNRICH
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
An Introduction to Computer Programming and 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.
Maximum Flow
Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.
Advanced Scientific Mathematics
This is the section of stemNRICH devoted to the advanced applied mathematics underlying the study of the sciences at higher levels
Cushion Ball
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?
Population Dynamics Collection
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
The Wrong Stats
Why MUST these statistical statements probably be at least a little bit wrong?
Population Dynamics - Part 2
Second in our series of problems on population dynamics for advanced students.
Population Dynamics
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
Spinners
How do scores on dice and factors of polynomials relate to each other?
Population Dynamics - Part 4
Fourth in our series of problems on population dynamics for advanced students.
Modelling Assumptions in Mechanics
An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.
Ball Bearings
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.
Ramping it Up
Look at the calculus behind the simple act of a car going over a step.
pdf Stories
Invent scenarios which would give rise to these probability density functions.
Population Dynamics - Part 6
Sixth in our series of problems on population dynamics for advanced students.
Population Dynamics - Part 1
First in our series of problems on population dynamics for advanced students.
Population Dynamics - Part 5
Fifth in our series of problems on population dynamics for advanced students.
The Not-so-simple Pendulum 1
See how the motion of the simple pendulum is not-so-simple after all.
Population Dynamics - Part 3
Third in our series of problems on population dynamics for advanced students.
Population Ecology Using Probability
An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.
Time to Evolve 2
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Predator - Prey Systems
See how differential equations might be used to make a realistic model of a system containing predators and their prey.
Over-booking
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?
Branching Processes and Extinction
An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.
Impuzzable
This is about a fiendishly difficult jigsaw and how to solve it using a computer program.
Overarch 2
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?
FA Cup
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!