Available online
Description
In this session we will talk about different topics in the areas of Pure and Applied Mathematics. Pure Mathematics: The four-colour theorem Back in 1852, a mathematics student called Francis Guth...rie noticed that it was possible to colour the counties of England in such a way as no two neighbouring counties have the same colour, using just four colours. The problem gained notoriety as mathematicians tried – and failed – to prove it (“noticing” that it can always be done isn’t really enough for us!), including, rather famously, an 11-year period in the late 1800s when everyone believed an attempt at a proof by Alfred Kempe had resolved it. Using Kempe’s ideas, it was 124 years after it was first posed, in 1976, when a proof was finally announced by two mathematicians at the University of Illinois, Kenneth Appel and Wolfgang Haken, with the aid of a supercomputer. Applied Mathematics: Chaos theory and the butterfly effect Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas? This question, which was famously posed by meteorologist Ed Lorenz in 1972, encapsulates the concept of sensitive dependence on initial conditions, and has been extensively used to exemplify the notion of chaos. In this part of the session we will explore the motion of some simple mechanical systems to illustrate chaos, what does it mean to have sensitive dependence on initial conditions, and its consequences on weather prediction and other applications.
In this session we will talk about different topics in the areas of Pure and Applied Mathematics. Pure Mathematics: The four-colour theorem Back in 1852, a mathematics student called Francis Guth...rie noticed that it was possible to colour the counties of England in such a way as no two neighbouring counties have the same colour, using just four colours. The problem gained notoriety as mathematicians tried – and failed – to prove it (“noticing” that it can always be done isn’t really enough for us!), including, rather famously, an 11-year period in the late 1800s when everyone believed an attempt at a proof by Alfred Kempe had resolved it. Using Kempe’s ideas, it was 124 years after it was first posed, in 1976, when a proof was finally announced by two mathematicians at the University of Illinois, Kenneth Appel and Wolfgang Haken, with the aid of a supercomputer. Applied Mathematics: Chaos theory and the butterfly effect Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas? This question, which was famously posed by meteorologist Ed Lorenz in 1972, encapsulates the concept of sensitive dependence on initial conditions, and has been extensively used to exemplify the notion of chaos. In this part of the session we will explore the motion of some simple mechanical systems to illustrate chaos, what does it mean to have sensitive dependence on initial conditions, and its consequences on weather prediction and other applications.
| Series: | STEM Showcase Event; Series 2018 |
|---|---|
| Episode | 10 |
| Recording date: | 05-07-2018 |
| Published: | 2018 |
| Rights Statement: | Rights owned or controlled by The Open University |
| Restrictions on use: | This material can be used in accordance with The Open University conditions of use. A link to the conditions can be found at the bottom of all Digital Archive web pages. |
| Duration: | 00:32:02 |
| + Show more... | |
| Presenter: | Karen Foley |
| Contributors: | Marc Pradas; Robert Brignall |
| Publisher: | The Open University |
| Link to related site: | Internal url: http://studenthublive.open.ac.uk/abstract/mathematics-and-statistics?event=STEM%20Showcase%20Student%20Hub%20Live%20%28SHL%29%20Event%20%E2%80%93%20Thursday%205%20July%20%4010.00%20%E2%80%93%2017.00 |
| Production number: | SHL00338 |
| Available to public: | yes |
