- What is a proposition?
- Truth tables (sorry!)
- Negations of propositions (¬p)
- Conjunctions (p ∧ q)
- Disjunctions (p ∨ q)
- Exclusive OR (p ⊕ q)
- Logic and Bit operations (1’s and 0’s)
- Conditionals
- Conditional statements (p → q)
- Contrapositive, converse, inverse
- Biconditional statements (p ↔ q)

- Translating English Sentences
- System specifications and consistency
- Logic Gates

- Tautologies, contradictions, and contingencies
- Logical equivalences
- Laws (Tables 6 and 7).
- Demorgan’s Laws
- Finding new logical equivalences without using a truth table.

- Propositional Satisfiability

- What is a predicate?
- Predicate functions
- Quantifiers
- Universal and Existential
- Uniqueness quantifier expressed with Universal/Existential
- Negations (Demorgan’s Laws)

- Logical equivalences with quantifiers
- Expressing in English

- Order of quantifiers
- Translating mathematical statements
- Translating nested quantifiers to English and vice versa.
- Negations of nested quantifiers.

- Premises and valid arguments
- Rules of inference for propositional logic
- Table 1
- Modus Ponens, Modus Tollens, etc.
- Resolution
- Using these rules to build arguments.
- Logical fallacies

- Rules of inference for quantifiers
- Universal generalization/instantiation
- Existential generalization/instantiation

- Theorems/Axioms/Postulates
- Proof strategies
- Direct proofs
- Proof by contraposition
- Proof by contradiction
- Vacuous and trivial proofs

- Disproving statements: Counterexamples

- What is a set?
- Roster notation and set-builder notation
- Sets of numbers and their notation (natural numbers, integers, positive integers)
- Empty sets
- Subsets, proper subsets, and equality
- Cardinality of a set.
- Power sets
- Cartesian products and n-tuples.
- Set notation and quantifiers.

- Union of two sets.
- Intersection of two sets and disjoint sets.
- Difference of two sets.
- The universal set U and the complement of a set.
- Table 1: Set Identities

- What is a function (in the more abstract sense)?
- Domains, Codomains, Ranges
- One to One functions (injective)
- Onto functions (surjective)
- One to One Correspondence functions (bijective) and inverses.
- Composition of functions.
- Special functions: floor, ceiling, modulo.

- What is a sequence?
- What is a recurrence relation?
- Initial conditions
- Closed formulas of recurrence relations
- Strategies for finding sequences.

- Summations
- Summation notation with upper/lower limits
- Infinite series
- Formulas for calculating sum of terms
- Double summations

- What is a matrix?
- m rows by n columns
- Order of indices

- Adding/subtracting matrices
- Matrix multiplication
- First row * first column, second row * second column, etc.
- Identity matrix and inverses of square matrices.
- Powers of square matrices.

- Zero-One matrices
- Join/Meet
- Boolean product