Sep 27, 2022  
2021-2022 Lane Community College Catalog 
    
2021-2022 Lane Community College Catalog [ARCHIVED CATALOG]

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MTH 107 - Math in Society 3

4 Credit(s)

MTH 105, 106, and 107 are a three course sequence but may be taken in any order. These applications include at least three of the following topics: voting systems, methods of fair division, apportionment, networks, graph theory, or other topics approved by the Mathematics Division.

Prerequisite: MTH 095  or MTH 098 , or equivalent course completed with a grade of "C-" or better within the past two years or placement by the College's Math Placement Process.
Learning Outcomes
Students who successfully complete this course will be able to:

  1. Define the fairness criteria for elections and determine which of the criteria a given voting system satisfies
  2. Determine the outcome of a weighted voting system
  3. Explain the meaning and importance of fairness criteria for election methods
  4. Determine whether or not a particular apportionment falls prey to the New State paradox, the Population paradox, or the Alabama paradox
  5. Explain the meaning and importance of fairness criteria for election methods
  6. Determine whether or not a division is fair or envy-free
  7. Collaborate with group members to discuss and explain class concepts, solve application problems, and propose new problems and scenarios
  8. Reflect on successes, failures, and obstacles encountered in the problem-solving process
  9. Assess mistakes and rework solutions on certain assignments
  10. Construct and organize solutions in appropriate ways; clarify and explain thought process and solution
  11. Justify solutions with appropriate graphics, examples, and mathematical arguments
  12. Determine the winner of an election using a variety of different voting methods
  13. Determine if a coalition is a winning or losing coalition
  14. Use Euler's theorem to determine if a given graph contains an Euler path or an Euler circuit
  15. Determine which of the fairness criteria a voting method satisfies
  16. Determine the outcome of a weighted voting system
  17. Determine a modified quota and modified divisor, given the size of the population and the number of seats to be apportioned
  18. Determine whether or not a particular apportionment satisfies the Quota rule
  19. Compute the Banzhaf power index of a weighted voting system
  20. Fairly divide a quantity using divide-and-choose methods for two, three, or more players
  21. Fairly divide a collection of objects
  22. Apportion seats using a variety of methods
  23. Find the minimal spanning trees of a given graph
  24. Find approximate solutions to the traveling merchant problem



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