Mathematical Content of the DMP

I. Social Decision Making

A. Fair Division -- estates, algorithms, mathematical induction

B. Apportionment -- methods, Balinski and Young Theorem, paradoxes

C. Election Theory -- group-ranking, Arrow's Fairness Criteria, Approval and weighted voting, voting power, algorithms, paradoxes

II. Graph Theory

A. Structures -- vocabulary, basic concepts, representations (diagrams, adjacency matrix and lists), breadth and depth

B. Circuits / Paths -- Euler/Hamiltonian circuits and paths, critical paths, shortest paths, Dijkstra's Algorithm, the traveling salesperson problem

C. Trees -- properties, minimal spanning trees (Prim's and Kruskal's algorithms), binary and expression trees, transversals

D. Applications -- modeling projects, program evaluation, review technique methods (PERT)

E. Graph Coloring -- planarity

III. Counting Techniques

A. Logic and Sets -- Venn diagrams, disjunction and union, conjunction and intersection, negation and complement, inclusion and exclusion

B. Addition and Multiplication Principles

C. Permutations and Combinations

D. Discrete Probability -- mutually exclusive events (the addition rule), independent events (the multiplication rule), conditional probablities, expected value, applications

IV. Matrix Models

A. Structures -- basic concepts, representations, addition, subtraction, multiplication

B. Markov Chains

C. Population -- Leslie Model

D. Economy -- Leontief Input-Output Model

E. Game Theory

V. Mathematics of Iteration/Recursion

A. First-Order Recurrence Relations

B. Applications -- arithmetic and geometric sequences, exponential growth, finance, population dynamics

C. Mixed Recursion

D. Cobweb Diagrams