Mat 3361,
Introduction to Mathematical Logic
Fall 2004 Peter Selinger |

**Professor:** Peter Selinger.

**Office:** KED 205D.

**Phone:** 562-5800 ext. 3510

**Email:** selinger@mathstat.dal.ca (please put "3361" into the
subject line)

**Office Hours:** Mondays 1-2.

**Time:** Tue+Thu, 5:30-7pm.

**Location:** MNT 204.

**Special times:** I will be away on Tuesday, September 21 and
Thursday, September 30. We will reschedule each of these two classes
at a special time to be announced.

**Course Description:** Logic is the study of the formal principles
of reasoning. In this course, we will study *symbolic logic*. We
will introduce the formal languages of propositional and first-order
logic, and we will learn how to formalize the notions of *truth*
and *proof*. Logic is unlike any other branch of mathematics,
because we do not just use proofs as a tool for reasoning, but we also
reason *about* proofs. For this reason, logic is sometimes called
meta-mathematics.

**Topics:** In the first part of the course, we will introduce the
notion of a formal language. We will study the propositional
connectives, tautologies, and tautological consequences. We will
consider several different formal proof systems, including natural
deduction and analytic tableaux. The heart of the course is the study
of first order predicate logic and its models. We will study formal
proofs, establish soundness and completeness theorems, and explore
some of their applications. We will examples from algebra, geometry,
and arithmetic to see how mathematical theories can be formalized. By
the end of the course we should be able to state and understand
Gödel's First Incompleteness Theorem.

**Prerequisite:** MAT2343.

**Textbook:** Dirk Van Dalen, *Logic and Structure (4th edition)*. The
textbook should be available from the Agora
Bookstore, 135 1/2 Besserer Street.

**Course Work:** There will be regular homework, one in-class
midterms, and a final exam. The midterm will be on October 21.

**Course Homepage:** Updated information will be available from the
course homepage,
http://www.mathstat.dal.ca/~selinger/3361/

selinger@mathstat.dal.ca / PGP key