## Spring 2002

## Math 570, MWF 11-12 DRL 3C8

## 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 and that, therefore, it is
uncertain that the basic axioms of arithmetic will not give
rise to contradictions. 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.

## Take-Home Midterm Due in Class on Friday, March 8

The following problems from Enderton, 2nd edition:

- p. 66: Exercises 10 ab, 11 ab, 12 abc.
- pp. 100-104: Exercises 16, 20 ab, 25 ab, 27, 28 abc.
- p. 146: Exercises 7 bc, 8, 9 abc.

This is a complete list of assignments due March 8, 2002.

## Take-Home Final Due in DRL 4E6 on Tuesday, April 30 at 12 noon

The following problems from Enderton, 2nd edition:

- p. 163: Exercises 4, 9, 10.
- pp. 223-224: Exercises 2, 4, 5, 6, 8, 9.
- p. 234: Exercises 1, 2.
**Optional problems for extra credit:** p. 245: Exercises 1, 2, 3.

This is a complete list of assignments due April 30, 2002.