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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

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an e 3 presentation ralph cox with special thanks to dr s butenko tamu and ronnie gonzales
An E3 Presentation

Ralph Cox

with Special Thanks to

Dr. S. Butenko

TAMU

and

Ronnie Gonzales

Lesson Plans: Applications of Graph Theory
overview
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
delta airline schedule
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
simplified version
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
simplified version6
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
lesson 1
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
activity 1
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
activity 19
Activity 1
  • Graph from Graphviz
activity 2
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
activity 3
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
activity 4
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
activity 419
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=
review lesson 1
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
lesson 2
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
activity 122
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.
review lesson 2
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
resources
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
games
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