Mat 3361, Introduction to Mathematical Logic
Fall 2004
Peter Selinger

Professor: Peter Selinger.
Office: KED 205D.
Phone: 562-5800 ext. 3510
Email: (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,

Peter Selinger / Department of Mathematics and Statistics / Dalhousie University / PGP key