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.
Winter 2021
- 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.
Fall 2012
A few mathematical logic resources available online:
Maintained by Stefan Bilaniuk. Last updated 2021-05-16.