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STANDARDS

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US-AL

Math

Alabama Math

Applications of Finite Mathematics: Networks

Complex problems can be modeled using vertex and edge graphs and characteristics of the different structures are used to find solutions.

AFM.16

Use vertex and edge graphs to model mathematical situations involving networks.

AFM.16.a

Not covered
Identify properties of simple graphs, complete graphs, bipartite graphs, complete bipartite graphs, and trees.
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AFM.17

Solve problems involving networks through investigation and application of existence and nonexistence of Euler paths, Euler circuits, Hamilton paths, and Hamilton circuits. Note: Real-world contexts modeled by graphs may include roads or communication networks.

AFM.17.a

Not covered
Develop optimal solutions of application-based problems using existing and student-created algorithms.
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AFM.17.b

Not covered
Give an argument for graph properties.
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AFM.18

Apply algorithms relating to minimum weight spanning trees, networks, flows, and Steiner trees.

AFM.18.a

Not covered
Use shortest path techniques to find optimal shipping routes.
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AFM.18.b

Not covered
Show that every connected graph has a minimal spanning tree.
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AFM.18.c

Not covered
Use Kruskal’s Algorithm and Prim’s Algorithm to determine the minimal spanning tree of a weighted graph.
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AFM.19

Not covered
Use vertex-coloring, edge-coloring, and matching techniques to solve application-based problems involving conflict.
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AFM.20

Not covered
Determine the minimum time to complete a project using algorithms to schedule tasks in order, including critical path analysis, the list-processing algorithm, and student-created algorithms.
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AFM.21

Not covered
Use the adjacency matrix of a graph to determine the number of walks of length n in a graph.
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