Available online
Description
This programme investigates the orbit-stabilizer theorem in group theory and shows how this leads to the counting theorem which is used to solve counting problems. (This programme was re-edited in ...1995 as FOUM483R)
This programme investigates the orbit-stabilizer theorem in group theory and shows how this leads to the counting theorem which is used to solve counting problems. (This programme was re-edited in ...1995 as FOUM483R)
| Module code and title: | M203, Introduction to pure mathematics |
|---|---|
| Item code: | M203; 05D |
| First transmission date: | 1990 |
| Published: | 1990 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:24:19 |
| + Show more... | |
| Producer: | Andrew Adamyk |
| Contributors: | Alan Best; Robin Wilson |
| Publisher: | BBC Open University |
| Keyword(s): | Art gallery; Chessboards; Cubes; Group; Group action; Orbit; Orbit-stabilizer theorem; Rings; Stabilizer |
| Footage description: | The programme begins with Alan Best (OU) posing three counting problems: how many different rings can you make from eleven beads, given beads of three different colours; how many different patterns can you make by colouring the squares of a chessboard arbitrarily black or white; and how many different ways can you paint the faces of a cube, given three colours of paint. Robin Wilson (OU) uses a simpler version of the chessboard problem to develop some group theory to help with the three problems. He constructs a group action table, and revises the ideas of orbit and stabilizer for a group action. He shows how this example illustrates the orbit-stabilizer theorem, and also how counting problems can be solved by finding the number of orbits in each case. Alan Best uses the orbit-stabilizer theorem to derive the Counting Theorem, which given an expression for the number of orbits in a group action. This is then used to solve each of the three problems posed at the beginning of the programme. |
| Master spool number: | HOU6524 |
| Production number: | FOUM356Y |
| Videofinder number: | 3789 |
| Available to public: | no |
