MA 103 – Topics in Contemporary Mathematics

North Carolina State University , Prof.Tom Lada

Apportionment: Hamilton's Method

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Course Description

Contents:
Preference Ballots: plurality Borda Count – Plurality with Elimination – Ranking – Weighted Voting Systems – Banzhaf Power Index – Shapley Shubik Power Index – Fair Division: Divider Choose ane Lone Divider – Lone Choose Last Diminisher – Sealed Bids – Method of Markers – Apportionment: Hamilton’s Method – Jefferson’s, Adam’s Method – Webster’s Method-Review of Chapters 3 and 4 – Introduction Graph Theory – Euler Paths and Circuits

Eulerization – Hamilton Circuits – Traveling Salesman Problem: Brute Force Method Nearest Neighbor Algorithm – Repetitive Nearest Neighbor Algorithm and Cheapest Link Algorithm – Graph Coloring -Spanning Trees Kruskal’s Algorithm – steiner Points – Scheduling, Decreasing Time Algorithm – Critical Path Algorithm – Independent Tasks Bin Packing – Fibonacci Numbers – Gnomons – Linear Growth -Exponential Growth and Compound Interest – Fractals – Final Review

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