CS 2233 Discrete Mathematical Structures – Fall 08
Material relevant for the Final Exam
•Homeworks 1–8
•1.1–1.4 Logic:
–Propositions and operators (and, or, not, implication, etc.), truth tables
–Predicates and quantifiers (for-all, exists), nested quantifiers
–Translating a formula (with or without quantifiers) into English, and
translating an English sentence into a formula
–Equivalences of formulas (e.g., De Morgan’s Laws)
– NOT: Rules of inference (1.5)
•1.6–1.7 Proofs
–Different types of proofs (see handout; e.g., direct proof, proof by
contradiction, proof by cases)
–Know how to apply different proof techniques to prove a theorem. (This
includes, as a first step, translating an English statement into a
propositional formula.)
–Know how to disprove a theorem (e.g., find a counterexample to disprove a
for-all statement)
•2.1–2.4 Sets, Functions, Sequences, Summations
–Sets: Definition, operators (intersection, union,...), power set, cartesian
product
–Functions: Definition of a function, one-to-one/injective, onto/surjective,
one-to-one correspondence/bijection, inverse, composition, graphs
–Sequences: Definition (functions with domain N)
–Summations: Know how to read the Psymbol, arithmetic series, geometric
series, index substitution
•3.1-3.3 Algorithms and Complexity:
–O, Ω,Θ. (E.g., use definitions to show that 4n+ 5 ∈O(n2).)
–Code snippets
•4.1-4.2 Induction
–Weak and strong induction
– NOT: Program correctness and loop invariants (4.5)
•4.3, 7.1 Recursive Definitions and Recurrence Relations
–Recursive functions, sequences, and algorithms
Know how to develop a recursive solution (i.e., function, sequence, or
algorithm) for a problem. (E.g., recursive function for 2n, or a recursive
definition for the sequence 1,5,9,13,17, . . ..)
–Every recursive definition has a base case and a recursive case.
