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# MTH 325 Learning Targets

## Proof

• P.1: I can set up a framework of assumptions and conclusions for proofs using direct proof, proof by contraposition, and proof by contradiction.
• P.2: I can identify the predicate being used in a proof by mathematical induction and use it to set up a framework of assumptions and conclusions for an induction proof.
• P.3: I can identify the parts of a proof, including the technique used and the assumptions being made.
• P.4: I can perform a critical analysis of a written proof and provide a detailed explanation of the steps used in the proof.

## Graphs

• G.1: I can create a graph given information or rules about nodes and edges.
• G.2: I can give examples of graphs having combinations of various properties and examples of graphs of special ("named") types.
• G.3: I can represent a graph in different ways and change representations from one to another.
• G.4: I can take any representation of a graph and determine information about the entire graph or parts of the graph.
• G.5: I can determine whether two graphs are isomorphic.
• G.6: I can give a valid vertex coloring for a graph and determine a graph's chromatic number.
• G.7: I can determine whether a graph has an Euler path or cycle, and whether it has a Hamilton path or cycle.
• G.8: I can construct a spanning tree for a (connected) graph, and I can construct a minimal spanning tree for a weighted graph using Prim's Algorithm and Kruskal's Algorithm.

## Relations

• R.1: I can represent a relation in different ways and change representations from one to another.
• R.2: I can give examples of relations on a set that have combinations of the properties of reflexivity, symmetry, antisymmetry, and transitivity.
• R.3: I can compute the composition of two relations (and determine when a composition cannot be computed) and raise a relation on a set to a positive integer power.
• R.4: I can determine whether two points in a set with a relation belong to the transitive closure of that relation, and I can use Warshall’s Algorithm to find the matrix for the transitive closure of a relation.
• R.5: I can determine when a relation is an equivalence relation, and I can determine the equivalence class for an element and determine whether two elements belong to the same equivalence class.
• R.6: I can determine when a set with a relation is a partially ordered set, a totally ordered set, and a well-ordered set.

## Trees

• T.1: I can give examples of trees with combinations of important properties and determine information about a tree as a whole or about parts of the tree.
• T.2: I can list the nodes of a tree in the correct order when visited using preorder, postorder, and inorder traversals.
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