Class:       Math 571  
                        Fall 2008 
                        Introduction to Mathematical Logic
                        MWF 8:50-9:40  
                        B223 Van Vleck

           Instructor:  A. Miller 
            office:     403 Van Vleck Hall 262-2925
            hours:      MW  1:10-3:30 
            email:      miller@math.wisc.edu
            web:        www.math.wisc.edu/~miller/m571


           Prerequisite: M340 or consent of instructor. However
           my experience is that it best if the student has
           already taken or is currently taking Math
           441 or 541 (abstract algebra - groups, rings, fields).

           Text: See my web page.

           Topics: The syntax and semantics of propositional and
           predicate logic. Formalization of the notions of
           first-order formula, proof, and model. The main goal
           of this course is to completely understand the
           following theorems of Godel and their proofs.


               Completeness Theorem: Given theory T and a
               sentence A, then if every model of T is a
               model of A, then T proves A.

               Incompleteness Theorem: For any true
               theory T which is strong enough to do
               some of elementary arithmetic and whose
               axioms can be effectively listed, there
               is a true sentence A of arithmetic such
               that T does not prove A.


           Grading:  Part of your grade will depend on attendance.
           There will be one midterm in the evening and the Final
           exam at the regular time.  There will be a daily
           assignment of 2 or 3 problems.  Homework solutions are
           due in lecture exactly one week from when they are
           assigned. Please put them on the desk in front of the
           room at the beginning or end of class.