MAT 431 – Mathematical Logic
Fall 2018, MWF 2:00-2:50, Bacon 214A
Prerequisite: MAT 300 or PHI 307
Logic is the
study of the process of reasoning. Mathematical logic uses
mathematical methods to study the reasoning process of
Mathematics is powerful enough to answer questions concerning
the nature, the strength, and the weakness of mathematics.
Table of Contents
Section 1.1 The Language of Sentential
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
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
Section 2.4.1 Tautologies in
Section 2.4.2 Generalizations and
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
Section 2.4 Review Problems
Section 2.5 The Soundness and
A Mathematical Introduction to Logic
by Herbert B. Enderton, 2nd edition. (Author's
commentary) (A Review) (Author's
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.
|Professor Daniel Cunningham
|Office: Buckham A255
|Office Hours: Th 12-3 and by
|Send Email to Me
|Telephone: 878-6422 (leave messagee)
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
- Section 1.1 – on page 36 of notes. Quiz 1: Due
Friday Sept. 7
- Section 1.2 – on page 40 of notes. Quiz 2: Due
Friday Sept. 14
- Section 1.3 – on pages 41-42 of notes. Quiz 3: Due Friday Sept. 21
- Section 1.4 – on page 44 of
- Section 1.5 – on page 46 of
- Section 1.7 – on page 50 of notes. Quiz 4: Due Friday Sept. 28
- Section 2.1 – on page 61 of notes. Quiz 5: Due
Friday Oct. 12
- Section 2.2.2 – on page 66 of
6: Due Friday Oct. 19 (distributed
in class on Oct. 12)
- Section 2.2.3 – on page 69 of
7: Due Friday Oct. 26 (distributed
in class on Oct. 19)
- Section 2.2.4 – on page 71 in notes. Quiz 8: Due Friday Nov.
2 (distributed in class on Oct. 26)
- Section 2.4.1 – on page 87 in notes.
- Section 2.4.2 – on page 90 in notes. Quiz 9: Due Friday Nov.
9 (distributed in class on Nov. 2)
- Section 2.4.3 – on page 92 in notes. Quiz 10: Due Friday Nov.
16 (distributed in class on Nov. 9)
- Section 2.4.4 – on page 95 in notes.
- Section 2.4.6 – on page 101 in notes. Quiz 11 and Quiz 12 Due Friday Nov.
30 (distributed in class on Nov. 14)
- Section 2.4.7 – on page 103 of notes.
- Section 2.4.8 – on page 107 of notes.
- Section 2.5.1 – on page 111 of notes.
- Section 2.5.2 – on page 112 of notes.
- Section 2.5.3-5 – on
page 122 of notes.
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
- Exam 1 on
sections 1.1–3, and 1.7. Passed out on Friday Oct.
5. Due Oct. 10. Cover
- Exam 2 on Sections 2.1 and
2.2.1-2.2.4. Passed out
on Friday Nov. 2. Due Nov. 9. Cover Page
- Final Exam Sections
2.4 and 2.5.1-5.
Due Dec. 12 in Bacon 214A at 2:00 pm.
Academic integrity and intellectual honesty are essential in
- Homework: Feel free to
discuss homework problems with other students and to work
together on them. However, you must write up your
solutions without copying from anyone; that is, you must
compose your solutions completely in your own words.
- Examinations: No help may be given or received on exams. No written or verbal information may be exchanged
between students. You must compose your proofs and
solutions in your own words. The only sources that you may
consult are your textbook, your class notes, and this
instructor. I absolutely will
not tolerate any cheating on the take-home exams.
Cheating will result in a failing grade (see "Academic Misconduct" on BSC
Academic Policies page).
A link to your exam grades, listed under your Secret ID,
are available here.