Leadership Program:

During the summer institute, program participants learn about discrete mathematics and review and prepare materials that they can use to introduce these topics in their classes. The following web sites will help teachers to explore the topics farther.

Directed Graphs

• Directed Graphs - An introduction to terminology used with directed graphs.
• Special Graph Problems - Euler Circuits and di-graphs.
• Eulerian Path and Circuit - Algorithm for finding Euler Circuits in directed or non-directed graphs.
• Tournaments - A fun application of di-graphs to an unusual dice game.
• Low-Tech Game Systems - Scroll down to see a fun expansion of “Rock-Paper-Scissors”!

Sorting

• Sorting Networks and the END Search Algorithm - with a convenient graphical representation of sorting networks.
• Sorting Bricks and Sticks - Follow the links to “Sorting Bricks and Sticks” for a truly wonderful, interactive tutorial.
• Sorting Algorithms - A sampling of many different sorting algorithms.

Voting, Elections, and Selection

• The Center for Voting and Democracy - The Center educates the public about the impact of different voting systems on voter turnout, representation, accountability and the influence of money in elections. The Center has particular expertise in systems of proportional representation and instant runoff voting in winner-take-all elections.
• Readings in Proportional Representation - A source of information on proportional representation elections -- including beginning readings, in-depth articles by scholars and activists, an extensive bibliography, and a guide to related Web sites.
• Multiple Selection - This proposal is for a "multiple-selection, winner-take-all" voting system as an alternative to our current voting system, which I call "single-selection, winner-take-all".
• Mathematics of Voting - Introduction to voting theory.
• A Fourth Grade Experience - Decision-making and voting theory in a 4 th grade classroom.
• Will the Best Candidate Win? - Detailed lesson for exploring voting systems with students.
• Election Methods - Links to many good sites about voting.
• Voting Methods - Leads into much detail about voting.
• Discrete Math: Social Choice - Voting and apportionment activities through the Math Forum.
• Making Sense Out Of Consensus - A bit of a long read, but interesting discussion of voting in the U.S. in recent years.
• Approval Voting and The Good Society - A detailed look at several advantages of approval voting.

Patterns in Nature and Numbers

• Fibonacci Numbers and Nature - including bees, flowers, pine cones, rabbits, shells and more.
• Fibonacci Numbers and the Golden Ratio - University of Surrey Home page for the Fibonacci numbers.
• Fibonacci Celebrates Halloween - A Middle School Moment article from PCTM Magazine.
• Golden Ratio, Fibonacci Sequence - from the Math Forum archives of Dr. Math.
• Fibonacci Gateway - Gateway to lots of good Fibonacci-related material.
• Fibonacci  Numbers And How They Relate to Flowers, Pine Cones, Etc - Very clearly written and nicely illustrated—countless Fibonacci examples.
• Fibonacci Numbers in Nature - Colorful slides illustrating Fibonacci numbers in nature.
• Science Mysteries: Fibonacci Numbers in Nature - Nature's numbering system.
• The Fibonacci Sequence - Middle school lesson plan around the Fibonacci series.
• Patterns in Nature - Fibonacci and other remarkable patterns found in nature.

Fair Divison

• Ivars Peterson's MathLand - Divider-Chooser and its potential in professional sports drafts.
• Fair Division Problems and Fair Division Schemes - Somewhat wordy but a good survey of Fair Division schemes.
• Discrete Mathematics Project Fair Division Activities - Activities for exploring Fair Division in the classroom.
• How to Get Your Fair Share - Three fun interactive student activities related to Fair Division.
• What is "Fair Division"? - Java applet for a Fair Division “calculator.”
• Fair Division - The “Quick Summary” at the end is particularly helpful to review Fair Division methods.
• The Mediator - A downloadable conflict-resolution demo.

Scheduling

• Tournament Scheduling - Math Forum discussions about scheduling tournaments.
• Discrete Mathematics Project: Graph Theory Activity - Student activity about scheduling a checkers tournament.

Codes

• The Digital Revolution (I) - Barcodes: Introduction - Detailed explanation of codes in everyday life (zip, bar, ISBN, etc.)
• Barcodes - How do barcodes work?
• Can You Decode a Barcode? - Fun barcode questions for kids.
• Barcode Activity - Classroom activity about UPC numbers.
• Canadian Postal Codes - Explanation of Canadian postal codes.
• Take a Break - Error detection . . . very well written--by a high school student!

Drawing Graphs Without Crossings (Isomorphism and Planarity)

• Graph Drawing Definition - An introduction to graph drawing and planar graphs
• Graph Without Crossing Lines - The classic three utilities & three hous es problem.
• 3 Utilities Puzzle - The ultilities puzzle: a closer look.
• Utilities/House Problem - An explanation of why the utilities/houses problem is impossible.
• Graph Drawing - A very clear introduction that also goes into much greater detail.
• Graph Drawing Tutorial - Highly technical, but very detailed and clearly presented .
• Automatic Graph Drawing - Crossing minimizations--nicely illustrated.

DIMACS || Leadership Program || LP Web Pages || The Math Forum

Created by Ann Brown, Brian Rollfinke, and Gail Holmes
Last Update: April 21, 2008