MATH 481 - Introduction to Mathematical Logic
Fall 2013, Section 001
Instruction Mode: Section 001 is (see other Sections below)
Subject: Mathematics (MATH)
Department: LSA Mathematics
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Details

Credits:
3
Requirements & Distribution:
BS
Waitlist Capacity:
5
Advisory Prerequisites:
MATH 412 or 451 or equivalent experience with abstract mathematics.
Other Course Info:
F.
BS:
This course counts toward the 60 credits of math/science required for a Bachelor of Science degree.
Repeatability:
May not be repeated for credit.
Primary Instructor:

Description

All of modern mathematics involves logical relationships among mathematical concepts. In this course we focus on these relationships themselves rather than the ideas they relate. Inevitably this leads to a study of the (formal) languages suitable for expressing mathematical ideas. The explicit goal of the course is the study of propositional and first-order logic; the implicit goal is an improved understanding of the logical structure of mathematics. Students should have some previous experience with abstract mathematics and proofs, both because the course is largely concerned with theorems and proofs and because the formal logical concepts will be much more meaningful to a student who has already encountered these concepts informally. No previous course in logic is prerequisite. In the first third of the course the notion of a formal language is introduced and propositional connectives (and, or, not, implies), tautologies, and tautological consequence are studied. The heart of the course is the study of first-order predicate languages and their models. The new elements here are quantifiers ('there exists' and 'for all'). The study of the notions of truth, logical consequence, and provability lead to the completeness and compactness theorems. The final topics include some applications of these theorems, usually including non-standard analysis. MATH 681, the graduate introductory logic course, also has no specific logic prerequisite but does presuppose a much higher general level of mathematical sophistication. PHIL 414 may cover much of the same material with a less mathematical orientation. MATH 481 is not explicitly prerequisite for any later course, but the ideas developed have application to every branch of mathematics.

Schedule

MATH 481 - Introduction to Mathematical Logic
Schedule Listing
001 (LEC)
 In Person
12151
Open
10
 
-
MWF 12:00PM - 1:00PM

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Syllabi

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