MATH 4810 - Mathematical Logic

(crosslisted) PHIL 4310
(MQR-AS)

Fall (offered alternate years). 4 credits. Student option grading.

Forbidden Overlap: due to an overlap in content, students will receive credit for only one course in the following group: CS 4860, MATH 4810, MATH 4860, PHIL 4310.
Prerequisite: MATH 2220 or MATH 2230 and preferably some additional course involving proofs in mathematics, computer science, or philosophy.

Staff.

First course in mathematical logic providing precise definitions of the language of mathematics and the notion of proof (propositional and predicate logic). The completeness theorem says that we have all the rules of proof we could ever have. The Gödel incompleteness theorem says that they are not enough to decide all statements even about arithmetic. The compactness theorem exploits the finiteness of proofs to show that theories have unintended (nonstandard) models. Possible additional topics: the mathematical definition of an algorithm and the existence of noncomputable functions; the basics of set theory to cardinality and the uncountability of the real numbers.