# 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 **