# Course Descriptions

This course provides an introduction to some of the fundamental ideas of logic. Topics will include truth functional logic, quantificational logic, and logical decision problems.

Also Offered As: PHIL 1710 (005)

Notes: This is a Formal Reasoning course.

Topics will be drawn from some subjects in combinatorial analysis with applications to many other branches of math and science: graphs and networks, generating functions, permutations, posets, asymptotics.

Also Offered As: MATH 3400 (340)

Prerequisite: MATH 1410 (114) OR MATH 1510 (115) OR MATH 1610 (116)

Topics will be drawn from some subjects useful in the analysis of information and computation: logic, set theory, theory of computation, number theory, probability, and basic cryptography.

Also Offered As: MATH 3410 (341)

Prerequisite: MATH 3400 (340) OR LGIC 2100 (210)

Propositional logic: semantics, formal deductions, resolution method. First order logic: validity, models, formal deductions; Gödel's completeness theorem, Löwenheim-Skolem theorem: cut-elimination, Herbrand's theorem, resolution method. Computability: finite automata, Turing machines, Gödel's incompleteness theorems. Algorithmically unsolvable problems in mathematics.

Also Offered As: MATH 5700 (570), PHIL 4721 (410)

Prerequisite: MATH 3710 (371) OR MATH 5030 (503)

The second semester of a two-semester course on the fundamental results and techniques of mathematical logic. Topics will be drawn from model theory, proof theory, recursion theory, and set theory. Connections between logic and algebra, analysis, combinatorics, computer science, and the foundations of mathematics will be emphasized.

Also Offered As: MATH 5710 (571), PHIL 4722 (413)

Prerequisite: PHIL 4721 (410) OR MATH 5700 (570)

The course focuses topics drawn from the central areas of mathematical logic: model theory, proof theory, set theory, and computability theory.

Also Offered As: MATH 6710 (671), PHIL 4720 (412)

Student arranges with a faculty member to pursue an independent research project on a suitable topic.