Discrete Mathematics

Other Texas Mathematics sets

• Grade K
• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• Algebra I (2012)
• Grade 8
• Algebra II
• Algebraic Reasoning
• Grade 9
• Statistics
• Advanced Quantitative Reasoning
• Geometry (2012)
• Grades 10, 11, 12
• Independent Study in Mathematics
• Mathematical Models with Applications
• Precalculus

The student applies the concept of graphs to determine possible solutions to real-world problemsDMPS.9-12.2

explain the concept of graphsDMPS.9-12.2.A

use graph models for simple problems in management scienceDMPS.9-12.2.B

determine the valences of the vertices of a graphDMPS.9-12.2.C

identify Euler circuits in a graphDMPS.9-12.2.D

solve route inspection problems by Eulerizing a graphDMPS.9-12.2.E

determine solutions modeled by edge traversal in a graphDMPS.9-12.2.F

compare the results of solving the traveling salesman problem (TSP) using the nearest neighbor algorithm and using a greedy algorithmDMPS.9-12.2.G

distinguish between real-world problems modeled by Euler circuits and those modeled by Hamiltonian circuitsDMPS.9-12.2.H

distinguish between algorithms that yield optimal solutions and those that give nearly optimal solutionsDMPS.9-12.2.I

find minimum-cost spanning trees using Kruskal's algorithmDMPS.9-12.2.J

use the critical path method to determine the earliest possible completion time for a collection of tasksDMPS.9-12.2.K

explain the difference between a graph and a directed graphDMPS.9-12.2.L

The student uses heuristic algorithms to solve real-world problemsDMPS.9-12.3

use the list processing algorithm to schedule tasks on identical processorsDMPS.9-12.3.A

recognize situations appropriate for modeling or scheduling problemsDMPS.9-12.3.B

determine whether a schedule is optimal using the critical path method together with the list processing algorithmDMPS.9-12.3.C

identify situations appropriate for modeling by bin packingDMPS.9-12.3.D

use any of six heuristic algorithms to solve bin packing problemsDMPS.9-12.3.E

solve independent task scheduling problems using the list processing algorithmDMPS.9-12.3.F

explain the relationship between scheduling problems and bin packing problemsDMPS.9-12.3.G

The student uses mathematical processes to apply decision-making schemes. The student analyzes the effects of multiple types of weighted voting and applies multiple voting concepts to real-world situationsDMPS.9-12.4

describe the concept of a preference schedule and how to use itDMPS.9-12.4.A

explain how particular decision-making schemes workDMPS.9-12.4.B

determine the outcome for various voting methods, given the voters' preferencesDMPS.9-12.4.C

explain how different voting schemes or the order of voting can lead to different resultsDMPS.9-12.4.D

describe the impact of various strategies on the results of the decision-making processDMPS.9-12.4.E

explain the impact of Arrow's Impossibility TheoremDMPS.9-12.4.F

relate the meaning of approval votingDMPS.9-12.4.G

explain the need for weighted voting and how it worksDMPS.9-12.4.H

identify voting concepts such as Borda count, Condorcet winner, dummy voter, and coalitionDMPS.9-12.4.I

compute the Banzhaf power index and explain its significanceDMPS.9-12.4.J

The student applies the adjusted winner procedure and Knaster inheritance procedure to real-world situationsDMPS.9-12.5

use the adjusted winner procedure to determine a fair allocation of propertyDMPS.9-12.5.A

use the adjusted winner procedure to resolve a disputeDMPS.9-12.5.B

explain how to reach a fair division using the Knaster inheritance procedureDMPS.9-12.5.C

solve fair division problems with three or more players using the Knaster inheritance procedureDMPS.9-12.5.D

explain the conditions under which the trimming procedure can be applied to indivisible goodsDMPS.9-12.5.E

identify situations appropriate for the techniques of fair divisionDMPS.9-12.5.F

compare the advantages of the divider and the chooser in the divider-chooser methodDMPS.9-12.5.G

discuss the rules and strategies of the divider-chooser methodDMPS.9-12.5.H

resolve cake-division problems for three players using the last-diminisher methodDMPS.9-12.5.I

analyze the relative importance of the three desirable properties of fair division: equitability, envy-freeness, and Pareto optimalityDMPS.9-12.5.J

identify fair division procedures that exhibit envy-freenessDMPS.9-12.5.K

The student uses knowledge of basic game theory concepts to calculate optimal strategies. The student analyzes situations and identifies the use of gaming strategiesDMPS.9-12.6

recognize competitive game situationsDMPS.9-12.6.A

represent a game with a matrixDMPS.9-12.6.B

identify basic game theory concepts and vocabularyDMPS.9-12.6.C

determine the optimal pure strategies and value of a game with a saddle point by means of the minimax techniqueDMPS.9-12.6.D

explain the concept of and need for a mixed strategyDMPS.9-12.6.E

compute the optimal mixed strategy and the expected value for a player in a game who has only two pure strategiesDMPS.9-12.6.F

model simple two-by-two, bimatrix games of partial conflictDMPS.9-12.6.G

identify the nature and implications of the game called "Prisoners' Dilemma"DMPS.9-12.6.H

explain the game known as "chicken"DMPS.9-12.6.I

identify examples that illustrate the prevalence of Prisoners' Dilemma and chicken in our societyDMPS.9-12.6.J

determine when a pair of strategies for two players is in equilibriumDMPS.9-12.6.K

The student analyzes the theory of moves (TOM). The student uses the TOM and game theory to analyze conflictsDMPS.9-12.7

compare and contrast TOM and game theoryDMPS.9-12.7.A

explain the rules of TOMDMPS.9-12.7.B

describe what is meant by a cyclic gameDMPS.9-12.7.C

use a game tree to analyze a two-person gameDMPS.9-12.7.D

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 theoryDMPS.9-12.7.E

describe the use of TOM in a larger, more complicated gameDMPS.9-12.7.F

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 TOMDMPS.9-12.7.G