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

• MATH-COIS 4215H Course Outline
• Readings & Schedule
• Problem sets
• Take-Home Final Examination

Other sources

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.