1 / 26

Lesson Plans: Applications of Graph Theory

An E 3 Presentation Ralph Cox with Special Thanks to Dr. S. Butenko TAMU and Ronnie Gonzales. Lesson Plans: Applications of Graph Theory. Overview. Ronnie & I studied Delta Airlines Converted flight schedules to a matrix Calculated and plotted Teach the TEKS through Graph Theory

paul2
Download Presentation

Lesson Plans: Applications of Graph Theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. An E3 Presentation Ralph Cox with Special Thanks to Dr. S. Butenko TAMU and Ronnie Gonzales Lesson Plans: Applications of Graph Theory

  2. Overview • Ronnie & I studied Delta Airlines • Converted flight schedules to a matrix • Calculated and plotted • Teach the TEKS through Graph Theory • Lesson 1 • Create graphs • Count edges • Create pie charts and histograms • Lesson 2 • Solve two step equations • Miscellaneous Resources

  3. Delta Airline Schedule • Flight schedule to matrix • Undirected graph • Each city a node • Each flight an edge • Calculate edge density • Calculate Degree vs Node Regression • Plot the graph • Convert from matrix to .dot file • Define Edge: Dallas--Houston is an edge. • Use Graphviz to generate plot

  4. Delt Flight Map

  5. Simplified Version • Lesson 1 • Student learns to draw graph given edge • Student learns to draw graph given matrix • Student learns to count edges to find degrees • Student practices making table of degrees and nodes • Student practices making pie chart out of table • Student practices making histogram out of table • Student practices making scatter plot out of table • Student uses calculator to find linear and exponential regression

  6. Simplified Version • Lesson 2 • Student practices solving linear equation using concrete methods • Student makes graph of processes that can be used to solve linear equation • Student sees simple path is standard algorithm • Student learns to solve simple linear equation • Computer Time • Students can play on computer with graphviz and make graphs • Students can go to website for tutorial • Students can play logic games

  7. Lesson 1 • Analyze small set flight data • Start with list of edges • Create list of nodes • Create Graph • Larger set of data from airline.xls • Start with matrix • Create list of nodes and edges • Figure out degree vs. nodes • Draw pie chart and histogram • Calculate regression

  8. Activity 1 • Draw the graph for this set of edges • Louisville – OrlandoTampa – ColumbusColumbus – OrlandoKey West – OrlandoOrland -- Fort LauderdaleOrlando – Nassau • List the nodes • Draw the several different graphs

  9. Activity 1 • Graph from Graphviz

  10. Activity 2 • Given the data in Matrix from • List Nodes • List Edges • Draw Graph • Count edges on each node to find degree • Make table • List Degrees • How many nodes of each degree • Color the nodes • No adjacent node same color • Minimum color

  11. Activity 2

  12. Activity 3 • Start with Table created in prior activity • Identify dependent and independent variable • Identify domain and range • Bin data • Combine a few degrees into one point • For example count every 5 • Make Pie chart • Figure percentage for each interval • How many degrees for each interval • Make Histogram • Look at range to figure out scale

  13. Activity 3

  14. Activity 3

  15. Activity 3

  16. Activity 4 • Make a linear scatter plot • What is independent variable and domain • What is the dependent variable and range • Label axis • Make sure to review how to number axis! • Make Log-Log scatter plot • Same except for on Log paper • Exponential becomes a line! • Use a ruler to draw best line

  17. Activity 4

  18. Activity 4

  19. Activity 4 • Enter data into the calculator • Reset calculator 2nd mem 7,1,2 • Press stat and select edit • Enter data in L1 and L2 • Adjust window and turn on plot with 2nd 'stat plot' • Check out graph • Calculate regression • Linear regression: Stat Calc linreg • Exponential: Stat Calc expreg • Enter both equations into y=

  20. Review Lesson 1 • Convert list to list of edges and list of nodes • Make a graph • Count edges on each node • Create Table • Not necessary to bin • Create Pie Chart and Histogram • Create Scatter Plot • Calculate regression

  21. Lesson 2 • Student discovers optimal solution for solving simple linear equation • Use graphs to show several processes • Start with any equation • Student suggest steps • Continue until reach an answer • Examine graph • Graph will have several paths that lead to the solution • One will be shorter than the rest

  22. Activity 1 • Start by solving equations using concrete techniques • Then graph various processes • Start with 2x+3=7 • Accept student suggestions, write in graph form • Continue until have several paths from equation to solution. • Which path is shortest? • Student should move from guess and check to optimal process • At end student should be able to apply standard algorithm.

  23. Activity 1

  24. Review lesson 2 • Review solving linear equations using concrete methods • Start graphing process to solve linear equation • Choose shortest path for best process • Generalize to standard algorithm • Practice applying algorithm

  25. Resources • Graphviz • Uses simple text files and simple commands • Students can make own graphs on computer • See .dot files in lesson. • American Scientist- Practical Graph Theory • http://www.americanscientist.org/template/AssetDetail/assetid/14708 • Graph theory tutorial • http://www.utm.edu/cgi-bin/caldwell/tutor/departments/math/graph/intro

  26. Games! • Logic games • http://plastelina.net/ • Wolf sheep and cabbage • Family Crisis • Missionary and Cannibals • Four Random Books • Plait, Philip; Bad Astronomy; 2002 • Levin, Janna; How the Universe Got it's Spots; 2002 • Kranz, Gene; Failure is not an Option; 2001 • Murray, Margaret; Women Becoming Mathematicians; 2000

More Related