Introduction to Mathematical Logic

This is an introductory course in mathematical logic. The subject is of interest to students in both Mathematics and Computer Science. Topics covered include propositional logic, first order logic, consistency, satisfiability, soundness, completeness, and compactness. We will also discuss some basic set theory and axiomatic number theory (Peano's arithmetic). If time permits we will discuss the famous incompleteness theorems of Godel.

• Students will be able to translate formulas of propositional logic to and from natural language statements, determine the satisfiability and validity of propositional formulas via truth-tables.
• Students will be able to translate formulas of first-order logic to and from natural language sentences, check the satisfiability and validity of formulas in a domain.
• Students will be able to prove and apply the soundness, completeness and compactness theorems for propositional and first-order logics.
• Students will be able to appreciate the use logic in formalizing mathematics through the introduction to formal number theory (Peano's arithmetic) and set theory.