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 |

Mathematics is powerful enough to answer questions concerning the nature, the strength, and the weakness of mathematics.

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

Articles |
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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 |
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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. |
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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.

- 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 notes.
- Section 1.5 – on page 46 of notes.
- 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
notes.
**Quiz 6: Due****Friday****Oct. 19 (distributed in class on Oct. 12)** - Section 2.2.3 – on page 69 of
notes.
**Quiz 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.

Exams |
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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.

**Exam 1 on sections 1.1–3, and 1.7. Passed out on Friday Oct. 5. Due Oct. 10. Cover Page**- 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.**

The Honor Principle |
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Academic integrity and intellectual honesty are essential in
academic practice.

- 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**).

Grades |
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