Oct 06, 2022  
2020-2021 Lane Community College Catalog 
    
2020-2021 Lane Community College Catalog [ARCHIVED CATALOG]

Add to Portfolio (opens a new window)

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 , MTH 098 , or equivalent course with a grade of C- or better within the past two years, or placement test.
Learning Outcomes
  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.



Add to Portfolio (opens a new window)