MA 240   Discrete Mathematics,  Fall 2013,  Instructor:  Jeffrey Horn   GUIDE TO THE FINAL EXAM


GENERAL

TOPICS  (not necessarily complete, but I tried!)

  1. PROPOSITIONAL LOGIC
  2. PREDICATE LOGIC
  3. BASIC COUNTING
  4. COMBINATORICS AND PERMUTATIONS
    1. P(n) permutations, P(n,r) r-permutations, C(n,r) r-combinations
    2. Number of shortest paths through a grid.   Number of such paths through a single junction in the grid.
    3.  Growth rates.
  5. GRAPHS AND TREES
    1. Basic Graph Notation:  graph G = (V,E), where V is a set of vertices and E is a set of edges.
    2. Graph Terms:  Undirected and directed graphs, connected graph, simple graph (i.e., no self-loops, no multiple edges between a pair of vertices), circuit, degree of a vertex, etc.
    3. Euler Paths and Circuits
    4. Hamilton Paths and Circuits
    5. Graph Encodings:   Adjacency List, Adjacency Matrix
    6. DAGs (Directed Acyclic Graphs), as discussed last day of class. 
    7. Tree Topics
  6. OTHER TOPICS
    1. Inductive proof
    2. The Binary Hypercube (graphing it, labeling it, the combinatorics of it, etc.)