## Important Documents

Discrete Math Text - Digital

CoMap

CoMap

- Codebreaking
- The Math of Technology

## Links

Königsberg Bridge Problem

The Pregel River had two branches and flowed around an island through the center of the city of Königsberg. There were seven bridges connecting the various landmasses, as shown in this diagram.

The townspeople, who liked to stroll over the bridges, tried to figure out a path that would cross each of the seven bridges just once. You couldn’t miss any of the bridges, and you couldn’t cross any bridge more than once.

*In this puzzle we invite you to visit the bridges of the medieval city of Königsberg. Can you cross each bridge just once without missing any of them?*The Pregel River had two branches and flowed around an island through the center of the city of Königsberg. There were seven bridges connecting the various landmasses, as shown in this diagram.

The townspeople, who liked to stroll over the bridges, tried to figure out a path that would cross each of the seven bridges just once. You couldn’t miss any of the bridges, and you couldn’t cross any bridge more than once.

## Wolfram Projects - Demonstrations

## Click on the picture to try the Tower of Hanoi

The Tower of Hanoi

The puzzle was invented by the French mathematician Édouard Lucas in 1883. There is a legend about an Indian temple which contains a large room with three time-worn posts in it surrounded by 64 golden disks. Brahmin priests, acting out the command of an ancient prophecy, have been moving these disks, in accordance with the rules of the puzzle, since that time. The puzzle is therefore also known as the Tower of Brahma puzzle. According to the legend, when the last move of the puzzle is completed, the world will end. It is not clear whether Lucas invented this legend or was inspired by it.

If the legend were true, and if the priests were able to move disks at a rate of one per second, using the smallest number of moves, it would take them (2^64)−1 seconds or roughly 585 billion years; it would take 18,446,744,073,709,551,615 turns to finish.

The puzzle was invented by the French mathematician Édouard Lucas in 1883. There is a legend about an Indian temple which contains a large room with three time-worn posts in it surrounded by 64 golden disks. Brahmin priests, acting out the command of an ancient prophecy, have been moving these disks, in accordance with the rules of the puzzle, since that time. The puzzle is therefore also known as the Tower of Brahma puzzle. According to the legend, when the last move of the puzzle is completed, the world will end. It is not clear whether Lucas invented this legend or was inspired by it.

If the legend were true, and if the priests were able to move disks at a rate of one per second, using the smallest number of moves, it would take them (2^64)−1 seconds or roughly 585 billion years; it would take 18,446,744,073,709,551,615 turns to finish.

## Mega Penny Project

MegaPenny site

What does 1 Quadrillion pennies look like?

The Secret Universe Within - Multiples of 10

What does 1 Quadrillion pennies look like?

The Secret Universe Within - Multiples of 10

## Circuits

## Euler

## Hamiltonian

Hamiltonian Circuit - Algorithms

click picture for link

click picture for link

## Urban Planning Project - assignments

- Designing Your Own City: Maps and Google Sketchup
- The Unsuspecting Bridge Inspector: Eulerizing the Königsberg Bridge
- Designing Recycling Routes: Onitsha, Ghana
- What's the Shortest Route?: A Hamiltonian Circuit between all the cities in the class - include NNA, Brute Force Trees, and final optimized answer.
- Bus Route: Setup Optimized routes for bus lines that cover 75%+ of your cities streets.
- Tendency To Be Tardy: Using A2Tech layout (link), layout a critical path between any two classrooms and find a maximum passing time needed. (Need hallway measurements, walking times etc)
- Ted the Taxi Man: Euler circuit of the city for coverage and pickups, then Hamiltonian for a teacher set 5 point driving tour with ETA.
- Transportation Dilemma: Scheduling

## Urban Planning Project - Resources

The Urban Planning Project - Wiki

Every thing you need to know about the project.

We will publish materials here when the project is complete.

Webquest - Construction

Building a Sustainable (Green) City Urban Spawl

Every thing you need to know about the project.

We will publish materials here when the project is complete.

Webquest - Construction

Building a Sustainable (Green) City Urban Spawl

## Estate Division

Estate Division

Rent Division

Chore Division

The Moving Knife - physical division.

Rent Division

Chore Division

The Moving Knife - physical division.

fairdivision_2011.ppt | |

File Size: | 640 kb |

File Type: | ppt |

## Voting Theory

## Voting Visualization: Borda, Condorcet, RO, SRO, Plurality, and Approval

## Electoral College

Electoral College votes by state - U.S. Map scaled by population. KEY: 1 grid square per vote (or IR multiple).

## Code Breaking

Code Breaking WebQuest and information source

## Codebreaking - how it works

## Enigma Machine/History

Overview of WW2 codebreaking

DvD encryption and general codebreaking

Overview of Codebreaking - Ohio State

DvD encryption and general codebreaking

Overview of Codebreaking - Ohio State

## Cryptography

## Facial Recognition

## Codebreaking Challenge

## CodeBreaking

Try your skillz here.

## Game Theory

Info

http://www.gametheory.net/

http://en.wikipedia.org/wiki/List_of_games_in_game_theory

Courses in Game Theory

http://oyc.yale.edu/economics/econ-159

https://www.coursera.org/course/gametheory

http://www.gametheory.net/

http://en.wikipedia.org/wiki/List_of_games_in_game_theory

Courses in Game Theory

http://oyc.yale.edu/economics/econ-159

https://www.coursera.org/course/gametheory

## Class Presentations and Math Casts

Seige Math wiki