# MA 103 - Topics in Contemporary Mathematics

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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

### Course Curriculum

 Preference Ballots: plurality Borda Count Details Plurality with Elimination Details Ranking Details Weighted Voting Systems Details Banzhaf Power Index Details Shapley Shubik Power Index Details Chapter 1 and 2 Review Details Chapter 1 and 2 Review Details Fair Division: Divider Choose ane Lone Divider Details Lone Choose Last Diminisher Details Sealed Bids Details Method of Markers Details Apportionment: Hamilton’s Method Details Jefferson’s, Adam’s Method Details Webster’s Method Details Review of Chapters 3 and 4 Details Introduction Graph Theory Details Euler Paths and Circuits Details Eulerization Details Hamilton Circuits Details Traveling Salesman Problem: Brute Force Method Nearest Neighbor Algorithm Details Repetitive Nearest Neighbor Algorithm and Cheapest Link Algorithm Details Graph Coloring Details Review of Chapter 5 and 6 Details Spanning Trees Kruskal’s Algorithm Details Steiner Points Details Steiner Points II Details Scheduling, Decreasing Time Algorithm Details Critical Path Algorithm Details Independent Tasks Bin Packing Details Review of Chapter 7 and 8 Details Review of Chapter 7 and 8 Details Fibonacci Numbers Details Gnomons Details Linear Growth Details Exponential Growth and Compound Interest Details Exponential Growth and Compound Interest Details Fractals Details Final Review Details

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