SYMBOLIC (a.k.a. MATHEMATICAL) LOGIC
PHI 421, Sec. 001: MW 1pm-2:15pm in CBC-C221
University of Nevada, Las Vegas
Spring 2008
Professor: James Woodbridge
email address:
Course Webpage: http://faculty.unlv.edu/jwood/unlv/Phil421a.htm
Office Hours: T 12pm-1:30pm, W 4pm-5pm, and by appointment
Office: CDC 426
Office Phone: 895-4051
Dept. Phone: 895-3433
This course has two main subjects: basic metalogic and computability theory. Through the study of these topics we will consider the scope and limits of formal theorizing. Metalogic is the study of facts about and properties of logical systems (as opposed to learning to use a particular logic system, e.g., to construct proofs). Topics in this area will include Truth-Functional Completeness, Models and Interpretations, the Soundness, Completeness, Compactness, and the Undecidability of First-Order Logic. Computability theory investigates what it is for a function to be computable, that is, when there is a mechanical procedure or algorithm for solving a particular mathematical problem. Specific elements of this study will include such topics as the relation between sets and functions; enumerable, denumerable, and non-denumerable sets; diagonalization; Turing Computability, Uncomputability, and the Halting Problem.
The book for the course is available at The UNLV Bookstore.
There will be additional handouts and on-line sources regarding computability theory, along with a free computer program for constructing and running simulations of Turing machines.
III. CLASS REQUIREMENTS AND GRADING SCHEME
Requirements
.............................................Percent of Final Grade
Participation................................................................10%
Homework...................................................................10%
First Quiz.....................................................................15%
Midterm Exam.............................................................25%
Second Quiz.................................................................15%
Final Exam...................................................................25%
Participation—This requirement is designed to take into account contributions during class (e.g., asking questions, suggesting moves for proofs done in class, etc.) and improvement throughout the term. To do well on this requirement it is vital that you keep up with the reading assignments.
Homework—This requirement covers completion of and performance on the homework assignments. The homework provides practice with the techniques presented in class, so it is crucial that you keep up with the assignments. There will be assignment due every week. No late assignments accepted.
The First Quiz—There will be a timed, in-class quiz in mid to late February. The quiz questions will consist of problems like those on the homework assignments and in the readings.
The Midterm Exam—There will be a timed, in-class test in mid March. The test questions will include problems and proofs like those on the homework assignments, as well as questions concerning definitions and concepts we have covered. Note: while I may not lecture on every element of the reading assignments, you are responsible on exams for all of the material covered in them.
The Second Quiz—There will be a second timed, in-class quiz in mid April. Again, the quiz questions will consist of problems like those on the homework assignments.
The Final Exam—There will be a timed, in-class final exam given during our scheduled exam time. The final will essentially be cumulative, but it will emphasize the material since the Midterm. The exam questions will include problems similar to the homework and some pertaining to concepts.
Note: All requirements must be satisfactorily completed in order to pass the course.The class will consist mostly of lectures, demonstrations of problem-solving techniques, and sample exercises. However, I want to encourage student participation throughout the class--both in the form of questions and suggestions about how to approach problems we are considering. Class meetings will typically consist of two different (not necessarily equal) parts: one in which I will lecture on the material you have read about for the day and work some sample problems, and one in which I will answer questions about problems from homework assignments that students would like to go over.