Recognize patterns within a problem |
Use basic logical thinking to solve a problem |
Apply basic number sense to solve problem |
Model a problem using basic geometry |
Recognize a preference schedule |
Determine a Plurality/Majority Winner |
Determine a winner using a Borda Count |
Determine a winner using a runoff or a sequential runoff |
Determine a winner using the Condorcet method |
Determine a winner using approval voting |
Indentify a paradox |
Understand and apply Arrow's conditions |
Use the concept of weighted voting and voting power to determine which candidates have the most power |
Use the concept of Estate Division to fairly divide items/cash amongst heirs of an estate |
Use Apportionment algorithms in appropriate situations |
Model the timeline of a project using a diagram |
Determine the critical paths of a project |
Define important vocabulary of graphs |
Recognize different representation of graphs |
Find Euler and Hamilton Circuits and Paths within a graph |
Apply graph coloring techniques to solve problems |
Determine the planarity of a graph |
Solve a Traveling Salesman Problem |
Determine the shortest route between two points of a graph |
Identify a tree and properties of it |
Determine the minimum spanning tree |
Model different situations using a binary tree |
Determine an expression tree from a binary tree |
Perform a traversal on an expression tree |
Apply basic matrix operations to different situations |
Model the population growth of a group using a Leslie Matrix |
Use the Leontief Input-Output Model to model different economic situations |
Solve systems of equations using matrices |
Use the concept of Markov Chains to model problems |
Apply the concept of game theory to different situations |
What are the strategies to solving various problems? |
What are the fundamentals to group-decision making? |
What are the concepts to dividing discrete and continuous objects fairly amongst people? |
What are the essential concepts of graph theory as it pertains to scheduling meeting or coloring a map? |
How do we create an efficient network using a variety of mathematical models and algorithms? |
How do we work with matrices and use them in a variety of mathematical models to apply to real-life applications? |
Preference Schedule | Graph | Decision Tree | Column Maximum |
Plurality Winner | Vertices | Spanning Tree | Maximin |
Majority Winner | Edges | Breadth-First Search | Minimax |
Borda Count | Critical Paths | Minimum Spanning Tree | Saddle Point |
Paradox | Earliest-Start Time | Rooted Tree | Expected Payoff |
Condorcet Paradox | Latest-Start Time | Parent-Child | |
Pairwise Voting | Connected Graphs | Binary Tree | |
Arrow’s Conditions | Complete Graphs | Traversal | |
Approval Voting | Adjacent | Postorder Traversal | |
Weighted Voting | Degree/Valence | Reverse Polish notation | |
Power Index | Order | ||
Winning Coalitions | Multiple Edges | Dimension | |
Discrete | Multigraph | Element | |
Continuous | Euler circuit | Square Matrix | |
Fair Share | Euler path | Column/Row Matrix | |
Estate Cash | Digraph | Zero Matrix | |
Final Settlement | Indegree | Main Diagonal | |
Ideal Ratio | Outdegree | Transpose of Matrix | |
Quota | Hamiltonian Path | Symmetric | |
Hamiltonian Circuit | Inverse of Matrix | ||
Transmitter | Leslie Matrix | ||
Adjusted Ratio | Tournaments | Super Diagonal | |
Webster Method | Receiver | Long-Term Growth Rate | |
Hill Method | Dominances | Demand Matrix | |
Arithmetic Mean | Coloring the Graph | Production Matrix | |
Geometric Mean | Chromatic number | Consumption Matrix | |
Cut-and-Choose Method | Eulerizing Graphs | Markov Chain | |
Inspection Method | Planar Graph | Transition Matrix | |
Moving-Knife Method | Bipartite | Transition Digraph | |
Subgraph | Complement | Steady-State Distribution | |
Traveling Salesman Problem | Weighted Graph | Game Theory | |
Brute Force Method | Nearest-Neighbor Algorithm | Strategies | |
Heuristic Method | Shortest Path Algorithm | Strictly Determined | |
Cycle | Tree | Payoff Matrix | |
Leaf | Row Minimum |
PATTERN RECOGNITION |
BASIC GEOMETRY |
NUMBER SENSE |
BASIC LOGIC |
MODEL-MAKING |
PREFERENCE SCHEDULE |
PLURALITY WINNER |
MAJORITY WINNER |
BORDA COUNT |
RUNOFF/SEQUENTIAL |
CONDORCET |
PARADOX |
ARROW’S CONDITIONS |
APPROVAL VOTING |
WEIGHTED VOTING |
VOTING POWER |
APPORTIONMENT ALGORITHMS |
CAKE CUTTING – APPLICATIONS |
CRITICAL PATHS |
ESTATE DIVISION |
MODELING PROJECTS |
VOCABULARY OF GRAPHS |
REPRESENTATIONS OF GRAPHS |
EULER CIRCUITS AND PATHS |
GRAPH COLORING |
PLANARITY AND COLORING |
THE TRAVELING SALESPERSON PROBLEM |
FINDING THE SHORTEST ROUTE |
TREES AND THEIR PROPERTIES |
MINIMUM SPANNING TREES |
BINARY AND EXPRESSION TREES |
TRAVERSALS |
