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.