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Natural Science Division

Formal Methods: MATH 220 (3)

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.

Hours Topic
Preliminaries (3 hours)
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
Quantification (4 hours)
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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