Topics in Mathematical Logic

(3 Credit Hours) · Undergraduate

Mathematical proofs are the cornerstone of truth. Proofs verify medical devices and spacecraft work properly. They help establish guilt or innocence. The theme of this class is to explore the notion of proof with certain logical systems with the motivation of understanding mathematical proofs or reasoning. We will study proofs in extended syllogistic logics, propositional logic, other logical systems close to natural language, and first-order logic. We will show some of these systems are complete (every true statement is provable) and decidable (there is an algorithm for deciding truth) and others are not. We will explore what this means. Along the way we will hopefully learn more about how people reason. It would be good to have taken at least one proof-oriented class previously but no knowledge of formal logic is required. Assessment will be done by a combination of weekly sets of short answer questions, some written homework sets, a midterm exam or two and a final project with a presentation.