Course Description
Applications of modern mathematics to management and decision making including the solution of optimization problems using network theory, methods for optimal scheduling, voting methods, game theory, and related strategies. Applications include planning of postal delivery routes, placement of cable television lines, United States Congressional apportionment, and dispute resolution.
Athena Title
MAT DECISION MAKING
Semester Course Offered
Offered fall, spring and summer
Grading System
A - F (Traditional)
Course Objectives
Students should gain a working knowledge of the applications of modern discrete mathematics. They should be able to use network theory to model elementary optimization problems, and they should be able to analyze voting methods and legislative apportionment mathematically. They should know how to use game theory to plan strategies in situations of conflict. They should be able to describe and analyze mathematical models verbally.
Topical Outline
1. Management Science and Graph Theory: Graphs, finding Euler circuits, Hamiltonian circuits, sorted-edges algorithm, Kruskal's algorithm and minimum-cost spanning trees. Applications to routing long-distance telephone calls. Critical path analysis. Planning and Scheduling: List-processing algorithm, critical-path scheduling, decreasing-time-list algorithm. Graph coloring and applications to scheduling exams. 2. Voting and Social Choice: Majority rule and Condorcet's method, voting systems with more than two candidates, sequential pairwise voting, Hare system. Arrow's impossibility theorem, approval voting. The Manipulability of Voting Systems. Weighted Voting Systems: Shapley-Shubik and Banzhaf power indices, permutations and combinatorial reasoning. Comparing voting systems, winning coalitions. 3. Fairness and Apportionment. Fair Division: Adjusted winner allocation, Knaster inheritance procedure, taking turns, divide- and-choose. Cake division procedures: proportionality and envy. Apportionment methods, quotas. Congressional apportionment: Hamilton's method, Jefferson's method, divisor methods, Webster's method, Hill-Huntington method. What's fairest? Extra topics to be chosen from the following: 4. Linear Programming: Feasible region, optimal production policy, simplex method, tableaux. 5. Game Theory: The Mathematics of Competition: Winning strategies, maximum and minimum strategies. Zero-sum and variable-sum games. Prisoners' Dilemma, chicken. Winning games. 6. Identification Numbers and Information Science: Check digits, bank ID and ISBN numbers, UPC bar codes. Binary codes, parity-check sums, data compression. Cryptography, public-key cryptography and modular arithmetic, RSA encryption.
General Education Core
CORE III: Quantitative ReasoningSyllabus