Study Guide for the Final Exam

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