Resources tagged with: Mathematical modelling

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Broad Topics > Mathematical Thinking > Mathematical modelling

An Introduction to Computer Programming and Mathematics

Age 16 to 18

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.

Fixing the Odds

Age 14 to 16 Challenge Level:

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. . . .

Scratch Cards

Age 14 to 16 Challenge Level:

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?

Snooker

Age 16 to 18 Challenge Level:

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

Twenty20

Age 7 to 16 Challenge Level:

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

FA Cup

Age 16 to 18 Challenge Level:

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!

The Use of Mathematics in Computer Games

Age 16 to 18

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

Maximum Flow

Age 16 to 18 Challenge Level:

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.

Problem Solving, Using and Applying and Functional Mathematics

Age 5 to 18 Challenge Level:

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.

Ramping it Up

Age 16 to 18 Challenge Level:

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

Population Dynamics - Part 3

Age 16 to 18 Challenge Level:

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

The Legacy

Age 14 to 16 Challenge Level:

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?

Stringing it Out

Age 14 to 16 Challenge Level:

Explore the transformations and comment on what you find.

Population Dynamics - Part 2

Age 16 to 18 Challenge Level:

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

The Wrong Stats

Age 16 to 18 Challenge Level:

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

Modelling Assumptions in Mechanics

Age 16 to 18

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

Predator - Prey Systems

Age 16 to 18 Challenge Level:

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

Age 16 to 18 Challenge Level:

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

Chemnrich

Age 14 to 18 Challenge Level:

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. . . .

Where to Land

Age 14 to 16 Challenge Level:

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?

Bionrich

Age 14 to 18 Challenge Level:

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. . . .

Physnrich

Age 14 to 18 Challenge Level:

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

Engnrich

Age 16 to 18 Challenge Level:

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

Big and Small Numbers in Physics - Group Task

Age 16 to 18 Challenge Level:

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

The Not-so-simple Pendulum 1

Age 16 to 18 Challenge Level:

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

Population Dynamics - Part 1

Age 16 to 18 Challenge Level:

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

Stemnrich - the Physical World

Age 11 to 16 Challenge Level:

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

Branching Processes and Extinction

Age 16 to 18 Challenge Level:

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

Spot the Card

Age 14 to 16 Challenge Level:

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?

Slippage

Age 14 to 16 Challenge Level:

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. . . .

Investigating Epidemics

Age 11 to 16 Challenge Level:

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

Circuit Training

Age 14 to 16 Challenge Level:

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .

Guessing the Graph

Age 14 to 16 Challenge Level:

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

Population Dynamics Collection

Age 16 to 18 Challenge Level:

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

Stonehenge

Age 16 to 18 Challenge Level:

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

Population Ecology Using Probability

Age 16 to 18 Challenge Level:

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

Chocolate 2010

Age 14 to 16 Challenge Level:

First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...

The Mean Game

Age 16 to 18

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.

Cushion Ball

Age 16 to 18 Challenge Level:

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?

Impuzzable

Age 16 to 18

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

Lap Times

Age 14 to 16 Challenge Level:

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

Time to Evolve 2

Age 16 to 18 Challenge Level:

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

Population Dynamics - Part 6

Age 16 to 18 Challenge Level:

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

Population Dynamics - Part 5

Age 16 to 18 Challenge Level:

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

Shaping the Universe II - the Solar System

Age 11 to 16

The second in a series of articles on visualising and modelling shapes in the history of astronomy.

Shaping the Universe I - Planet Earth

Age 11 to 16

This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.

Truth Tables and Electronic Circuits

Age 11 to 18

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

Population Dynamics

Age 16 to 18 Challenge Level:

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

Ball Bearings

Age 16 to 18 Challenge Level:

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.

Population Dynamics - Part 4

Age 16 to 18 Challenge Level:

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