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MTH 107 - Math in Society 3 |
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Associated Term:
Spring 2023
Learning Objectives: Upon successful completion of this course, the student 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 Required Materials: Technical Requirements: |

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