MA 240 Discrete
Mathematics, Fall 2017, Instructor: Jeffrey
Horn GUIDE TO THE
FINAL EXAM
GENERAL
- SCOPE: The final exam for MA 240 is
comprehensive. It will focus on the topics covered in our eight
homeworks and seven quizzes, so the best way to study is to look over
the assignments and quizzes including your submissions and the
solutions.
- TIME: I try to design the exam so that it
is easily completed within one hour, leaving students with plenty
of time (total time allocated for NMU final exams is 1 hour and
50 minutes) to go over the test, double-checking, etc.
- OPEN
BOOK: The final, like all of our assessments, is open book,
open notes, open use of computers, but you must do your own
work! (Don't be tempted to use your laptop to communicate
with others (other humans, that is!). Help from anyone but the
instructor is forbidden and must be punished (pretty darn harshly) if
detected.
- COMPUTER USE:
A laptop is not absolutely required to complete this test (which for
reasons of reliability will be pencil-and-paper. But it
is a good idea to have a laptop with you. You will be
allowed to use it to look things up. But once again, you
must do your own work, so don't be tempted to use your laptop to
communicate with others (other humans, that is!).
- FORMAT:
Mostly multiple choice and fill-in-the-blank. Maybe a few short
answer (one or two sentences) questions. Very much like our quiz questions!
TOPICS
(not necessarily complete, but I tried!)
- PROPOSITIONAL LOGIC
- Truth Tables (up to four inputs). Proof by truth
table (enumeration)
- Logical Equivalence (proof by truth table, proof by boolean
algebra axioms)
- Translating between natural language (English) statements and
prop. logic statements.
- Boolean Expressions:
- Operators: Negation, Implication, AND, OR, NAND,
NOR, XOR, etc.
- Compound Boolean Expressions
- SOME TERMS: Tautology, Contradiction, Satisfiable,
Unsatisfiable, Inverse, Converse, Contrapositive
- DeMorgan's Laws (both of them!)
- PREDICATE LOGIC
- The two quantifiers: Universal and Existential (or
"upsidedown A" and "backwards E")
- Domain of Discourse
- Translating between natural language (English) statements and
quantified logic statements.
- DeMorgan's Laws (both of them!) for the two quantifiers
- Nested quantifiers (e.g., Everybody loves somebody!)
- BASIC COUNTING
- Know when to multiply and when to add!
- Decision trees.
- Little Gauss' formula: Sum of integers 1 to n is
n(n+1)/2
- COMBINATORICS AND PERMUTATIONS
- P(n) permutations, P(n,r) r-permutations,
C(n,r) r-combinations
- Multi-step word problems, where two or more decisions must be made. E.g., the Quadpod fighter question in HW7.
- Number of shortest paths through a grid. Number
of such paths through a single junction in the grid. (sort of "Darkwood prep")
- GRAPHS AND TREES
- Basic Graph Notation: graph G = (V,E), where V is a set
of vertices and E is a set of edges.
- 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.
- Euler Paths and Circuits
- Hamilton Paths and Circuits
- Graph Encodings: Adjacency List, Adjacency Matrix
- The Binary Hypercube (of course!).
- DAGs (Directed Acyclic Graphs), for POSets (Partially Ordered Sets), as
discussed last week of class, e.g., prefernce graphs
- Tree Topics