MATH 120  Topics For The Final Exam
Friday December 7, 2010 at 11:30

While the final exam will be comprehensive, covering the entire semester,about half of the exam will be 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)

 

A1, A3, A4, A5, A6, A7

E1, E2, E7, E8, E9, E10, E11, E13, E15, E17, E20,
E21, E23, E24, E25
Relations

Reflexive, Symmetric, Transitive properties
Equivalence relations, equivalence classes

Drawing Cayley graphs
Domain and image

  A2, A3, A5, A6, A7, A8, A9, A10 E1, E5, E8a, E11, E12, E13, E15, E20
Graphs

Paths, circuits, trees
Bipartite graphs, complete graphs
Subgraphs

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

  A2, A3, A4, A5, A6, A7, A8, A9 E1, E5, E8, E10, E12, E13, E15, E16, E19, E20