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Texas TEKS Discrete Mathematics for Problem Solving
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(Random) (2.A) Graph Theory. Explain the concept of graphs;

(Random) (2.B) Graph Theory. Use graph models for simple problems in management science; (Random) (2.C) Graph Theory. Determine the valences of the vertices of a graph; (Random) (2.D) Graph Theory. Identify Euler circuits in a graph; (Random) (2.E) Graph Theory. Solve route inspection problems by Eulerizing a graph; (Random) (2.F) Graph Theory. Determine solutions modeled by edge traversal in a graph; (Random) (2.G) Graph Theory. Compare the results of solving the traveling salesman problem (TSP) using the nearest neighbor algorithm and using a greedy algorithm; (Random) (2.H) Graph Theory. Distinguish between real-world problems modeled by Euler circuits and those modeled by Hamiltonian circuits; (Random) (2.I) Graph Theory. Distinguish between algorithms that yield optimal solutions and those that give nearly optimal solutions; (Random) (2.J) Graph Theory. Find minimum-cost spanning trees using Kruskal's algorithm; (Random) (2.K) Graph Theory. Use the critical path method to determine the earliest possible completion time for a collection of tasks; and (Random) (2.L) Graph Theory. Explain the difference between a graph and a directed graph. (Random) (3.A) Planning and Scheduling. Use the list processing algorithm to schedule tasks on identical processors; (Random) (3.B) Planning and Scheduling. Recognize situations appropriate for modeling or scheduling problems; (Random) (3.C) Planning and Scheduling. Determine whether a schedule is optimal using the critical path method together with the list processing algorithm; (Random) (3.D) Planning and Scheduling. Identify situations appropriate for modeling by bin packing;
and (3.G) Explain the relationship between scheduling problems and bin packing problems. (Random) (3.E) Planning and Scheduling. Use any of six heuristic algorithms to solve bin packing problems; (Random) (3.F) Planning and Scheduling. Solve independent task scheduling problems using the list processing algorithm; (Random) (4.A) Group decision making. Describe the concept of a preference schedule and how to use it; (Random) (4.B) Group decision making. Explain how particular decision-making schemes work; (Random) (4.C) Group decision making. Determine the outcome for various voting methods, given the voters' preferences; (Random) (4.D) Group decision making. Explain how different voting schemes or the order of voting can lead to different results; (Random) (4.E) Group decision making. Describe the impact of various strategies on the results of the decision-making process;
(Random) (4.F) Group decision making. Explain the impact of Arrow's Impossibility Theorem; (Random) (4.G) Group decision making. Relate the meaning of approval voting; (Random) (4.H) Group decision making. Explain the need for weighted voting and how it works; (Random) (4.I) Group decision making. Identify voting concepts such as Borda count, Condorcet winner, dummy voter, and coalition; and (Random) (4.J) Group decision making. Compute the Banzhaf power index and explain its significance. (Random) (5.A) Fair Division. Use the adjusted winner procedure to determine a fair allocation of property; (Random) (5.B) Fair Division. Use the adjusted winner procedure to resolve a dispute; (Random) (5.C) Fair Division. Explain how to reach a fair division using the Knaster inheritance procedure; and (5.D) Solve fair division problems with three or more players using the Knaster inheritance procedure; (Random) (5.E) Fair Division. Explain the conditions under which the trimming procedure can be applied to indivisible goods; and (5.K) Identify fair division procedures that exhibit envy-freeness. (Random) (5.F) Fair Division. Identify situations appropriate for the techniques of fair division; (Random) (5.G) Fair Division. Compare the advantages of the divider and the chooser in the divider-chooser method; (Random) (5.H) Fair Division. Discuss the rules and strategies of the divider-chooser method; (Random) (5.I) Fair Division. Resolve cake-division problems for three players using the last-diminisher method; (Random) (5.J) Fair Division. Analyze the relative importance of the three desirable properties of fair division: equitability, envy-freeness, and Pareto optimality; and (Random) (6.A) Game Theory. Recognize competitive game situations;
and (6.B) Represent a game with a matrix; (Random) (6.C) Game Theory. Identify basic game theory concepts and vocabulary;
and (6.D) Determine the optimal pure strategies and value of a game with a saddle point by means of the minimax technique; (Random) (6.E) Game Theory. Explain the concept of and need for a mixed strategy;
and (6.F) Compute the optimal mixed strategy and the expected value for a player in a game who has only two pure strategies; (Random) (6.G) Game Theory. Model simple two-by-two, bimatrix games of partial conflict;
(6.H) Identify the nature and implications of the game called "Prisoners' Dilemma";
(6.I) Explain the game known as "chicken";
and (6.J) Identify examples that illustrate the prevalence of Prisoners' Dilemma and chicken in our society; (Random) (6.K) Game Theory. Determine when a pair of strategies for two players is in equilibrium. (Random) (7.A) Theory of Moves. Compare and contrast TOM and game theory;
and (7.B) Explain the rules of TOM; (Random) (7.C) Theory of Moves. Describe what is meant by a cyclic game;
and (7.D) Use a game tree to analyze a two-person game; (Random) (7.E) Theory of Moves. Determine the effect of approaching Prisoners' Dilemma and chicken from the standpoint of TOM and contrast that to the effect of approaching them from the standpoint of game theory; (Random) (7.F) Theory of Moves. Describe the use of TOM in a larger, more complicated game; and (7.G) Model a conflict from literature or from a real-life situation as a two-by-two strict ordinal game and compare the results predicted by game theory and by TOM.

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