MATH 4810 - [Mathematical Logic]

(crosslisted) PHIL 4310
(MQR)

Fall. Next offered 2016-2017 (offered alternate years). 4 credits.

Forbidden Overlap: Due to an overlap in content, students will not receive credit for both MATH 4810 and MATH 4860.
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.