Trent University

Mathematics-Computer Science 4215H

*Mathematical Logic*

MATH-COIS 4215H is an introduction to the study of propositional and first-order logics as mathematical objects in their own right, through the Soundness, Completeness, and Compactness Theorems. The course uses the modified Moore method: given the definitions and statements of results, some examples, and some hints, students will prove most of the results for themselves.

**Prerequisite:** MATH 2200H, or the permission of the instructor.

- MATH-COIS 4215H Course Outline
- A Problem Course in Mathematical Logic, Version 1.6, by Stefan Bilaniuk. The textbook; we'll be working through Parts I & II, on propositional and first-order logic, respectively.
- Assignment # 1,
2,
3,
4,
5,
π+
*e*, 6, 7, 8, 9, 10, 11, Extra

and Solutions to Assignment # 1, 2, 3, 4, 5 - Take-Home Final Examination
- Lectures and Notes
*The Language of Propositional Logic*- video, notes*The Language of Propositional Logic II*- video, notes*Truth Assignments*- video, notes*Truth Assignments II*- video, notes*Truth Assignments III*- video, notes*Deductions*- video, notes*Deductions II*- video, notes*Deductions III*- video, notes*Consistency*- video, notes*Consistency II*- video, notes*Consistency III*- video, notes*Consistency IV*- video, notes*First-Order Logic - An Overview*- video, notes*First-Order Logic: An Example of a Language*- video, notes*First-Order Logic: Free variables and extension languages*- video, notes*Structures for First-Order Languages*- video, notes*Structures for First-Order Languages II*- video, notes*Structures for First-Order Languages III*- video, notes*Structures for First-Order Languages IV*- video, notes*Structures for First-Order Languages V*- video, notes*Structures for First-Order Languages VI*- video, notes*Deductions in First-Order Logic*- video, notes*Deductions in First-Order Logic II*- video, notes*Deductions in First-Order Logic III*- video, notes*Completeness of First-Order Logic*- video, notes*Completeness of First-Order Logic II*- video, notes*Completeness of First-Order Logic III*- video, notes*Completeness of First-Order Logic IV*- video, notes*Completeness of First-Order Logic V*- video, notes*Completeness of First-Order Logic VI*- video, notes*Applications of the Compactness Theorem*- video, notes

In case you're wondering about the long gap between 2012 and 2021, the course was offered as a reading course several times in between, but there were too few students interested and/or too many other demands on staffing resources to offer it as a regular course.

A few mathematical logic resources available online:

- Mathematical logic, article at Wikipedia.
- Elementary Calculus: An Approach Using Infinitesimals, a calculus text using non-standard analysis by H. Jerome Keisler.
- Mathematical Logic [pdf], notes for a logic course by Helmut Schwichtenberg.

Maintained by Stefan Bilaniuk. Last updated 2021-05-16.