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INQ 241 website-revOct09

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					INQ 241: Mathematical Reasoning--Mathematics of Democracy
Western Perspective
Roland Minton (Math/Computer Science/Physics)
Overarching Goals
   1. Students will be able to analyze the roles of math in elections throughout American
      history, contrasting potential outcomes from a variety of voting methods and judging
      which methods best promote the principles of democracy.
   2. Students will be able to analyze quantitative information about different decision-
      making processes, identify underlying assumptions and evaluate ramifications of
      alternative processes.

Skills Goals
Writing: Students will be able to articulate the underlying assumptions in a variety of
decision-making processes; construct arguments, both formal and informal, supporting a
position on the benefits and flaws in a voting method or decision-making process.
Quantitative reasoning: Students will be able to formulate questions about a decision-
making situation in the language of mathematics, and identify and use appropriate
mathematical techniques to derive relevant information to evaluate the situation.

Broad Content               Topics                          Assignments
   1. Apportionment         Introduction/motivation        Informal writing
                            Methods                        Clicker votes
                            History                        Excel project/paper (below)
                            Outcomes and paradoxes
                            Census
   2. Elections             Introduction                     Clicker votes
                            Methods                          Feedback lectures
                            History                          Gerrymandering debate
                            Outcomes and paradoxes
                            Gerrymandering
                            Mathematical research
   3. Weighted voting       Introduction/motivation          Clicker votes
                            Methods of measuring             Informal writing
                              power                           NY state case study/paper
                            Outcomes and paradoxes
   4. Google ranking        Markov chains                    Feedback lectures
                            Page rank                        Jigsaw on case studies
                            Specific pages, abuses
   5. Who’s Hot             Introduction                     Student Questions
                            Examples: Amazon,                Informal writing
                              Netflix, Kroger,….              Paper: is this democracy?
Specific Assignment

Background:

     Work with Excel spreadsheet to apportion Congress using a variety of methods,
      with a column showing the effect on (e.g.) the 2000 Presidential election

     Readings detailing constitutional constraints on apportionment, past controversies
      about apportionment and current controversies.

Assignment:

     Write a “closing argument” for a court case challenging the legality of our current
      system. You may argue either for or against the current system. Assume that the
      jurors are intelligent but do not know the material or examples from our background
      work. Also, assume that the opposing lawyer will object (and the judge will sustain)
      to distortions of facts or misstatements. Start your argument by explaining why
      apportionment is important (use examples) and then indicate why your position is
      “better” in terms of historical and/or mathematical criteria.
INQ 241: Mathematical Reasoning--Exploring Mathematical Connections
Rebecca Wills (Math/Computer Science/Physics)



Overarching Goal

Students will be able to apply their knowledge of graph theory to formulate and solve a
variety of practical connectivity problems.

Ancillary Skills Goals

   Students will be able to classify problems and identify appropriate approaches to model
    problems.
   Students will be able to implement algorithms.


Content Topics (1/2 to 2/3 of course content)

   Euler circuit problems (Traversability problems)
   Traveling salesman problems
   Minimum spanning trees
   Social networks
   Web search engine rankings (Google’s PageRank algorithm)

Classroom Activity—variation of Gallery Walk (Speed Dating: “Date” a problem for 10
minutes)

       Content topic: Google’s PageRank Algorithm

       Number of problems: 4 (2 copies of each)

       Number of groups: 8 (groups of 3)

       Distribute 4 problems related to Google’s page rank algorithm to the groups. Each
       team spends 10 minutes examining each problem and writing or modifying
       solutions. After each group reviews 4 problems in a “speed date” setting, their
       original problems along with the modified solutions are returned to them. For the
       remainder of class, each group provides/presents modified solutions to the class.
INQ 241: Mathematical Reasoning--Mathematics in American Government
Bryan Snare (Math/Computer Science/Physics)

I want my students to be able to…

   1) support and criticize the use and misuse of mathematics as it applies to elections.

   2) propose a solution to a complex scheduling issue and justify it as optimal.

   3) take the mathematics they have learned and apply it to situations not covered in
      class.

   Broad Content
                                Sequence of Topics                Assignments/Activities
      Topics

                                                               house.gov: Research and write
                                House of
                                                               about the role of the House of
                                 Representatives-role
                                                               Representatives in our
                                 that it plays
                                                               government
                                Electoral College
Apportionment
                                History/present
                                                               Find an interesting topic talked
                                 apportionment
                                                               about
                                Apportionment methods

                                Paradoxes produced            Follow your topic


                                Weighted voting               What will it take for your topic
                                 (electoral college)           to pass?

Voting Theory                   Voting methods

                                Fairness criteria

                                Arrow’s impossibility         Favorite voting method? Swap
                                                               and critique.


                                Euler circuits, trash pick-
                                 up                            Find optimal paths for campus
                                                               walks
Management Science              Hamilton Circuits-TSP

                                Trees and Networks
                                 (lighting Alaska)
Detailed Assignments:

   1) Apportionment/weighted voting:

What if we would have used a different apportionment method in the 2000 election. A
different winner? Does mathematics affect/play a role in our lives?

   2) Voting Methods:

   a. Pick a voting method that you believe to be the best and defend it with a two page
      paper.

   b. Swap papers with somebody and write a one page paper raising problems in their
      arguments.

   c. Swap back and make corrections to strengthen argument.

   3) Find the most efficient way to light up Alaska.???
INQ 241: Mathematical Reasoning—How to Run the World Efficiently
Karin Saoub (Math/Computer Science/Physics)

                                             Goals

  At the end of the course, students will be able to:

     Understand the use of various types of graphs in modeling real world situations

     Understand the challenges behind efficiency and evaluate strategies for finding
      optimal solutions

     Compare scheduling techniques and algorithms

     Apply the correct algorithm/technique to a real world problem, determine an
      optimal solution, and defend their choices.

                                     Draft of Course Plan

Broad Content     Sequence of Topics             Ideas for Assignments/activities
   Topics            and Concepts
                   within Each Broad
                     Content Topic

      Efficient      Euler Tours         1. Find an Euler Tour for a town/city service
      Routes                                 (garbage removal, mail delivery, snow
                                             removal).
                     Hamiltonian         2. Find Hamiltonian Circuit for on/off campus
                      Circuits               delivery (flowers/packages/services).
                     Spanning Trees      3. Find shortest route between 4/5 cities given
                                             airplane/train routes.

      Bipartite      Resource            1. Assign tasks to employees, teachers to
      Graphs          Allocation             courses, etc.

                     Coloring            2. Stable Marriage examples

                     Stable Marriage

      Interval       Coloring            1. Using FF algorithm for coloring
      Graphs
                     Resource            2. Assigning meeting to rooms based on time
                      Allocation             restrictions.

                                          3. DSA example with computer or train seats.
                      Dynamic Storage


                                          Final Project

Students will find a real world problem that applies to one of the three topics above.
They will determine what an optimal solution entails and apply the correct
algorithm/technique. These findings will be presented in a final report, as well as a
defense of their choices and solution.

				
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