## Fall 2008

## Math 570 / LGIC 310 / PHIL 006 / PHIL 506, MW 10:30-12, DRL 2N36

## Introduction to Logic and Computation

*Office*: Room 4E6 in David Rittenhouse Laboratory

*Telephone*: eight five nine eight three
( *Math. Dept. Office*: eight eight one seven eight )

*Fax:* three four zero six three

*E-mail*: lastname at math

*Office Hours*: By appointment

## About This Course

From
Encyclopaedia Britannica:
Gödel's proof, which states that within any rigidly logical mathematical
system there are propositions (or questions) that cannot be proved or
disproved on the basis of the axioms within that system; that is, such a
system cannot be proved simultaneously to be complete and consistent.
This proof has become a hallmark of 20th-century mathematics, and its
repercussions continue to be felt and debated.

## Textbook

## Topics

Chapters 0 - 3 from Enderton:

- Propositional Logic: Propositions and Connectives, Semantics, Natural
Deduction, Completeness.
- Predicate Logic: Quantifiers, Structures, Semantics, Natural Deduction,
The Completeness Theorem, Compactness and Skolem-Löwenheim Theorems,
Skolem Functions.
- Undecidability and Incompleteness: Turing Machines, Undecidability of
Predicate Logic, Gödel's First and Second Incompleteness Theorems.

## Homework Due in Class on Wednesday, September 24

The following problems from Enderton, 2-nd edition:

- p. 27: Exercises 1, 2ab, 3ab, 5ab
- p. 29: Exercise 15.
- p. 65: Exercise 2.

This is the complete list of assignments due September 24, 2008.

## Homework Due in Class on Monday, October 6

The following problems from Enderton, 2-nd edition:

- p. 52: Exercise 2.
- p. 53: Exercise 9b.
- p. 66: Exercises 8, 11ab.

In addition, also prove the following:
- There are no integers
*k* and *n*, with *n* not equal to
*0*, such that 2 * (*n*^2) = *k*^2. That is, square root
of 2 is not a fraction.

This is the complete list of assignments due October 6, 2008.

## Take-Home Midterm Due in Class on Wednesday, October 29

The following problems from Enderton, 2-nd edition:

- p. 66: Exercise 12abc.
- pp. 101-104: Exercises 16, 25ab, 27, 28abc.
- p. 146: Exercises 7bc, 8, 9abc.

This is the complete list of take-home midterm assignments
due in class on Wednesday, October 29, 2008.

## Take-Home Final Exam Due in DRL 4E6 at 11 am on Monday, December 15

The following problems from Enderton, 2-nd edition:

- pp. 223-224: Exercises 2, 4, 5.
- p. 234: Exercises 1, 2.
**Optional problems for extra credit: ** p. 245: Exercises 1, 2, 3.

This is the complete list of take-home final exam assignments
due in DRL 4E6 at 11 am on Monday, December 15.