Skip to content

Instantly share code, notes, and snippets.

@RobertTalbert
Created April 28, 2017 20:56
Show Gist options
  • Star 1 You must be signed in to star a gist
  • Fork 0 You must be signed in to fork a gist
  • Save RobertTalbert/30a00ecce9a91ec3d21c8e818831480f to your computer and use it in GitHub Desktop.
Save RobertTalbert/30a00ecce9a91ec3d21c8e818831480f to your computer and use it in GitHub Desktop.

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.
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment