Tuesday, January 24, 2005

First Class!

First Class!

- Discussion of course details:

- handout course description

- Discussion of the many course features:

- In class activities.
- Homework
- Reading
- On-Line Quizzes

- Portfolios
- Projects
- The Tool kit

- personal info sheet.

- Flatland as social commentary/satire.

- Why focus on Visual Mathematics?
- Mathematics that studies topics related to visual experience. [Geometry,
Topology, Motion]

- Visualization of mathematics that is not inherently visual. [Visualizing Counting]
- Classification: Triangles, circles: congruence and similarity. What common features are shared by circles and triangles?... They divide the plane into two sectors: "inside and outside". Not in the same class as the symbol. 8.

- Example of "visual Math" and counting:
- My Name: Martin Flashman
- How to start a letter to me: Hi ___________

- How many different openings are possible?

- We can visualize this problem with a "tree"
- This visualization allows us to count the possibilities easily...
- There were several alternative countings suggested for this problem. This may be connected to some ambiguity in the statement of what would be an acceptable opening for the letter. So- if the assumption is made that some entry must be made then the choice of an omission for each selection would be eliminated from the tally, giving 25 possibilities. A distinction:
- "vague" meaning "Not clear in meaning or application." and
- "ambiguious" meaning "Open to more than one interpretation.
*Ambiguous*indicates the presence of two or more possible meanings." - This is an example of a visualization used to understand and solve a problem that initially is not connected to anything visual .

Professor | Martin | Flashman |

Doctor | Marty | Flash |

Mister | Omit | Omit |

Omit |

seeing there are 9 possibilities for each of 4 title branches

so that the total is 9*4 = 36 possibilities.