Lectures

1. Propositional Logic
2. Propositional Equivalences
3. Predicates and Quantifiers
4. Nested Quantifiers
5. Rules of Inference and Valid Arguments
6. Introduction to Proofs
7. Sets
8. Set Operations and Identities
9. Functions
10. Progressions, Sequences, and Recurrences

Concepts

• atomic propositions
• axiom
• bijection
• cardinality
• cartesian product
• codomain
• composition
• conjecture
• contingency
• contradiction
• corollary
• domain
• elements
• empty set
• finite
• function
• graph
• image
• injection
• inverse
• lemma
• logically equivalent
• Negation
• power set
• preimage
• proof
• proper subset
• Proposition
• propositions
• range
• recurrence relation
• rules of inference
• satisfiable
• set
• string
• subset
• surjection
• tautology
• theorem
• tuple
• universal set
• valid argument

Sources

• Course slides §1.1: Propositions
• Course slides §11.1: Functions
• Course slides §12.1: Function Composition, Floor and Ceiling Functions
• Course slides §13.1: Geometric and Arithmetic Progressions, Recurrence
• Course slides §2.1: Logic Applications
• Course slides §3.2: Proving New Equivalences, Satisfibility
• Course slides §4.1: Predicates, Quantifiers, and De Morgan Laws
• Course slides §4.2: Distributing Quantifiers over Conjunctions and Disjunctions
• Course slides §5.1: Distributing Quantifiers over Conjunctions and Disjunctions
• Course slides §6.1: Rules of Inference and Valid Arguments
• Course slides §7.2: Sets
• Course slides §8.1: Power Set, Cartesian Product
• Course slides §8.2: Set Operations
• Course slides §9.1: Set Identities
• Course slides §9.2: Generalized Union and Intersection