MAT 431 Mathematical Logic
Fall 2018, MWF 2:00-2:50, Bacon 214A
Prerequisite: MAT 300 or PHI 307

Lecture Notes
Syllabus Homework   
Exams Textbook
Honor Principle
Instructor
Articles Grades

Logic is the study of the process of reasoning. Mathematical logic uses mathematical methods to study the reasoning process of mathematics.
Mathematics is powerful enough to answer questions concerning the nature, the strength, and the weakness of mathematics.


Lectures Notes

Table of Contents
Chapter 0
Section 1.1 The Language of Sentential Logic
Section 1.2 Truth Assignments (Some homework solutions)
Section 1.3 Omitting Parentheses
Section 1.4 Induction and Recursion
Section 1.5 Sentential Connectives
Section 1.7 Compactness
Chapter 1 Review Problems
Section 2.1 First-Order Languages
Section 2.2.1-2.2.2 Structures and Satisfaction   Tarski's Definition of Truth
Section 2.2.3-2.2.4 Satisfaction Relation for Sentences, and Logical Implication
Section 2.2 Review Problems  Work only on #1-5, 7-14, 16.  Basic Definitions
Section 2.4.1 Tautologies in First-Order Logic
Section 2.4.2 Generalizations and Substitution
Section 2.4.3 The Logical Axioms
Section 2.4.4 Formal Deductions
Section 2.4.5-6 Metatheorems about Deductions; Strategies for Showing that Deductions Exist
Section 2.4.7 Equality
Section 2.4.8 More Metatheorems about Deductions
Section 2.4 Review Problems
Section 2.5 The Soundness and Completeness Theorems

Textbook

A Mathematical Introduction to Logic by Herbert B. Enderton, 2nd edition.  (Author's commentary) (A Review) (Author's errata)

Articles

    A 1996 article by Leon Henkin on "The discovery of my completeness proofs."
    An article on the life and work of Alonzo Church, by Herbert B. Enderton.  
    Godel on Tarski, by Stanislaw Krajewski.
    Guidlines for logic education, by the Association for Symbolic Logic.

Instructor

Professor Daniel Cunningham
Office: Buckham A255
Office Hours: Th 12-3 and by appointment
Send Email to Me
Telephone: 878-6422 (leave messagee)

Homework: On each Friday, a take-home quiz will be distributed. The quiz will consist of a few previously assigned homework problems. Your quiz solutions will be submitted to me on the due date.

Written homework will be graded on content and clarity. Again, clear and understandable proofs are crucial in mathematical logic. Late homework submissions will not be accepted.

  1. Section 1.1 on page 36 of notesQuiz 1: Due Friday Sept. 7
  2. Section 1.2 on page 40 of notesQuiz 2: Due Friday Sept. 14                
  3. Section 1.3 on pages 41-42 of notesQuiz 3: Due Friday Sept. 21
  4. Section 1.4 on page 44 of notes
  5. Section 1.5 on page 46 of notes.
  6. Section 1.7 on page 50 of notes.   Quiz 4: Due Friday Sept. 28
  7. Section 2.1 on page 61 of notes.   Quiz 5: Due Friday Oct. 12
  8. Section 2.2.2 on page 66 of notes. Quiz 6: Due Friday Oct. 19 (distributed in class on Oct. 12)
  9. Section 2.2.3 on page 69 of notes. Quiz 7: Due Friday Oct. 26 (distributed in class on Oct. 19)
  10. Section 2.2.4 on page 71 in notes. Quiz 8: Due Friday Nov. 2 (distributed in class on Oct. 26)
  11. Section 2.4.1 on page 87 in notes.
  12. Section 2.4.2 on page 90 in notes. Quiz 9: Due Friday Nov. 9 (distributed in class on Nov. 2)
  13. Section 2.4.3 on page 92 in notes. Quiz 10: Due Friday Nov. 16 (distributed in class on Nov. 9)
  14. Section 2.4.4 on page 95 in notes
  15. Section 2.4.6 on page 101 in notes. Quiz 11 and Quiz 12 Due Friday Nov. 30 (distributed in class on Nov. 14)
  16. Section 2.4.7 on page 103 of notes.
  17. Section 2.4.8 on page 107 of notes.
  18. Section 2.5.1 on page 111 of notes.
  19. Section 2.5.2 on page 112 of notes.
  20. Section 2.5.3-5 on page 122 of notes.
Exams

All exams in this class will (tentatively) be take-home exams. There will be three midterms and a final. Written exams will be graded on their content and clarity. Clear and understandable proofs are critical in all areas of mathematics, and are particularly crucial in mathematical logic. Late take-home exams will not be accepted. Note: Exam 1 will cover topics from Chapter 1, and Exam 2 will cover topics in Chapter 2.

The Honor Principle

Academic integrity and intellectual honesty are essential in academic practice.

Grades

A link to your exam grades, listed under your Secret ID, are available here.