MA 240   Discrete Mathematics,  Fall 2017,  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. Multi-step word problems, where two or more decisions must be made.   E.g., the Quadpod fighter question in HW7.
    3. Number of shortest paths through a grid.   Number of such paths through a single junction in the grid.  (sort of "Darkwood prep")
  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. The Binary Hypercube (of course!).
    7. DAGs (Directed Acyclic Graphs), for POSets (Partially Ordered Sets), as discussed last week of class, e.g., prefernce graphs
    8. Tree Topics