Fall, 2015

** Announcements **

Chapter's I and II in ** Logical Foundations of Proof Complexity **
by Cook and Nguyen

(available on line through the U of T library)
closely follows pp 1 - 52 in the Notes.

** Lectures: ** MW 4 in SS 1085

** Tutorial: ** F12 in SS 1085

** Tutor: **

** Instructor: **
Stephen Cook
,
email: sacook@cs,
Office: Sandford Fleming 2303C, 416-978-5183

Office Hours: MW 5:15 - 6:00
Or make an appointment, or drop in.

QUESTIONS VIA EMAIL ARE WELCOME.

** Text: ** None. See Lecture Notes below.

** Marking Scheme: **

- 4 assignments worth 15% each (Due at beginning of tutorial Oct 2, Oct 23, Nov 20, Monday Lecture Dec 7.)
- 1 closed-book test worth 10%: Oct 30
- final exam worth 30%

** Reference Link: **
Handbook of Proof Theory, Chapters I and II
by Sam Buss

** Other References: **

- Herbert Enderton:
**A Mathematical Introduction to Logic**. Academic Press, 1972. - E. Mendelson:
**Introduction to Mathematical Logic**. Wadsworth & Brooks/Cole, 1987 - Pavel Pudlak:
**Logical Foundations of Mathematics and Computational Complexity**`A Gentle Introduction.'

This is a new book, full of interesting historical notes and philosophical comments.

Michael Sipser:

** Lecture Notes **

Please send corrections and comments to the instructor.

- Notes pp1-18: Propositional Calculus (slightly revised)
- Notes pp1-17: Propositional Calculus
- Notes pp18-30: Predicate Calculus (page 21, 3) clarified
- Notes pp31-38: Completeness of LK
- Notes pp39-53: Herbrand Theorem, Equality and Compactness
- Notes pp54-70: Computability Theory
- Notes pp71-82: Recursive and Recursively Enumerable Sets
- Notes pp83-95: Incompleteness and Undecidability Part I.
- Notes pp96-108: Peano Arithmetic
- Notes pp109-112: Godel's Incompleteness Theorems

** Problem Sets ** (.pdf files)