Lesson Plans: Applications of Graph Theory

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# Lesson Plans: Applications of Graph Theory - PowerPoint PPT Presentation

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 &amp; I studied Delta Airlines Converted flight schedules to a matrix Calculated and plotted Teach the TEKS through Graph Theory

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Presentation Transcript
An E3 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
• Lesson 1
• Create graphs
• Count edges
• Create pie charts and histograms
• Lesson 2
• Solve two step equations
• Miscellaneous Resources
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
• 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 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
• Analyze small set flight data
• Create list of nodes
• Create Graph
• Larger set of data from airline.xls
• Create list of nodes and edges
• Figure out degree vs. nodes
• Draw pie chart and histogram
• Calculate regression
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 1
• Graph from Graphviz
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
• 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
• 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 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
• 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
• Student discovers optimal solution for solving simple linear equation
• Use graphs to show several processes
• 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 1
• Start by solving equations using concrete techniques
• Then graph various processes
• 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 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
• 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!
• 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