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Formal logic as a tool for mathematical proofs. Propositional
calculus—Boolean expressions, logic connectives, axioms, and
theorems. Predicate calculus—universal and existential
quantification, modeling English propositions. Application to program
specification, verification, and derivation.
| 1.5 |
Textual
substitution |
| 1.0 |
Leibniz rule and
function evaluation |
| 0.5 |
The assignment
statement |
|
Boolean
Expressions (5 hours) |
| 1.5 |
Syntax and evaluation of boolean expressions |
| 0.5 |
Equality vs equivalence |
| 1.0 |
Satisfiability, validity, and duality |
| 2.0 |
Modeling English propositions |
|
Propositional
Calculus (6 hours) |
| 1.0 |
Equational logic and inference rules |
| 0.5 |
Equivalence |
| 1.0 |
Negation and inequivalence |
| 2.0 |
Disjunction and conjunction |
| 1.5 |
Implication |
|
Proof
Techniques and Applications (4 hours) |
| 1.0 |
Monotonicity, deduction theorem, case analysis |
| 0.5 |
Proof by contradiction |
| 0.5 |
Proof by contrapositive |
| 2.0 |
Solving word problems |
| 0.5 |
Types |
| 1.0 |
Syntax and interpretation of general quantification |
| 1.5 |
General quantification axioms |
| 1.0 |
Quantification range theorems |
|
Predicate
Calculus (5 hours) |
| 1.5 |
Universal quantification |
| 1.5 |
Existential quantification |
| 2.0 |
Formalizing English statements |
|
Predicates and
Programming (8 hours) |
| 2.0 |
Specification of programs |
| 2.0 |
Reasoning about the assignment statement |
| 2.0 |
Calculating parts of assignments |
| 2.0 |
Conditional statements and expressions |
Total: 35.0 hours, excluding holidays, review sessions, and exams
*Fifty-minute class hours
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