MATH 120  Topics For The Final Exam
Friday December 3, 2010 at 11:30

While the final exam will be comprehensive, covering the entire semester, there will be more emphasis on the material from Chapters 7, 8, and 9.

  CONCEPTS METHODS

Functions and Sequences

Recognizing onto or one-to-one functions
Recursive functions
Arithmetic and geometric sequences

Calculating a recursive function
The Integers

Congruence: iquo and mod
Divisors, multiples
Prime numbers
Relatively prime numbers

Converting between decimal and binary representation
Finding prime factorizations
Finding gcd and lcm
Boolean Expressions

Propositions
Operations: and, or, not, implies
DeMorgan's Laws

 Creating truth tables
Implication

When an implication is true
Converse and when it is true
Contrapositive and when it is true

Stating the converse
Stating the contrapositive
Finding the negation of an implication
Defining Sets and Tuples Subsets, the empty set, k-subsets

By listing the elements
By giving a property which describes the elements
Basic Operations on Sets

DeMorgan's Laws for sets
Cartesian product and ordered pairs

Complement, union, intersection, difference
Creating Venn diagrams
Inclusion-Exclusion for two or three sets
Quantifiers

Existential
Universal

Creating Venn diagrams
Negating a quantified statement
Proving or disproving quantified statements
Multiple quantifiers Interpreting statements with two or more quantifiers Negating these statements
Mathematical Induction

Predicates as functions
Induction implications
Base case

 Coordinating an induction proof
Counting Methods Permutations
Combinations (sets)
One-to-one correspondence

Multiplication Principle
Counting permutations
Counting combinations (the "n pick k" formula)
Relations

Reflexive, Symmetric, Transitive properties
Equivalence relations, equivalence classes

Drawing Cayley graphs
Domain and image
Graphs

Paths, circuits, trees
Bipartite graphs, complete graphs
Subgraphs

Spanning trees and Kruskal's Algorithm
Finding an Eulerian walk or a Hamiltonian circuit