MATH 445 -- ELEMENTARY MATHEMATICAL LOGIC

FALL 2008

Time and Room: MWF at 1:00 in MTH 1313

Instructor: Professor David W. Kueker
Office: MTH 2105
Phone: (301)405-5159
dwk@math.umd.edu
Office Hours: MW 2:00

Text: S. Hedman, A First Course in Logic, Oxford University Press, 2004.

Description: This course is an introduction to mathematical logic and some of its applications aimed at a broad audience. Logic is the study of reasoning. Mathematical Logic, more specifically, is the study of deductive reasoning -- that is, drawing correct inferences from given hypotheses. Several questions arise:

• What does it mean for an inference to be correct?
• How would you prove that an inference is correct?
• Can you decide whether or not an inference is correct?

We will discuss these questions for two formal systems: propositional logic, and first order logic.

Topics:

• Propositional logic: sections 1.1-1.3, 1.5-1.9.
• First order logic: sections 2.1-2.5, 3.2-3.5.
• Computability: selections from Chapter 7.

Note: the text defines two different (but equivalent) proof systems for each of propositional logic and first order logic -- "formal proofs" and resolution. In this course we will only discuss resolution. Especially in later sections our presentation will differ from that in the text.

Course Work: There will be regular homework assignments, two one-hour exams, and a two-hour final exam. The homeworks are worth a total of 100 points, the one-hour exams are worth 100 points apiece, and the final is worth 200 points, for a total of 500 points.

Exam Schedule:

• Exam 1: Monday 6 October on 1.1-1.3, 1.5-1.9.
• Exam 2: Friday 7 November on 2.1-2.4, 3.2-3.3.
• Final Exam: Tuesday 16 December, 1:30-3:30, on the entire course.

Collaboration on homework: You may freely discuss the homework with others, but the work submitted must be your own, written in your own words.