G.DM.1 The student will model problems, using vertex-edge graphs. The concepts of valence, connectedness, paths, planarity, and directed graphs will be investigated.
G.DM.2 The student will solve problems through investigation and application of circuits, cycles, Euler paths, Euler circuits, Hamilton paths, and Hamilton circuits. Optimal solutions will be sought using existing algorithms and student-created algorithms.
G.DM.3 The student will apply graphs to conflict-resolution problems, such as map coloring, scheduling, matching, and optimization.
G.DM.4 The student will apply algorithms relating to trees, networks, and paths. Appropriate technology will be used to determine the number of possible solutions and generate solutions when a feasible number exists.
ETFD Election Theory and Fair Division
ETFD.DM.5 The student will analyze and describe the issue of fair division in discrete and continuous cases.
ETFD.DM.6 The student will investigate and describe weighted voting and the results of various election methods. These may include approval and preference voting as well as plurality, majority, runoff, sequential runoff, Borda count, and Condorcet winners.
ETFD.DM.7 The student will identify apportionment inconsistencies that apply to issues such as salary caps in sports and allocation of representatives to Congress. Historical and current methods will be compared.
CM Computer Mathematics
CM.DM.8 The student will describe and apply sorting algorithms and coding algorithms used in sorting, processing, and communicating information.
CM.DM.9 The student will select, justify, and apply an appropriate technique to solve a logic problem.
RO.DM.10 The student will use algorithms to schedule tasks in order to determine a minimum project time. The algorithms will include critical path analysis, the list-processing algorithm, and student-created algorithms.
RO.DM.11 The student will solve linear programming problems.