Date: August 23, 2013

 Subject: advertisement for MATH 557

 Dear Mathematics Graduate Students,

 This semester I am teaching MATH 557.  MATH 557 is an introductory
 course in mathematical logic.  It is suitable for all mathematics
 graduate students.

 Mathematical logic is an important branch of modern mathematics which
 grew out of profound investigations of Hilbert, Gödel, Turing, and
 others into the nature of mathematical reasoning.  An important goal
 of mathematical logic is to develop precise, mathematically rigorous
 answers to some of the most basic questions in the foundations of
 mathematics.  Some of the questions to be discussed and answered in
 this course are:

    What precisely is a mathematical theorem?

    What precisely is a mathematical definition?

    What precisely is a mathematical proof?

    What precisely is a computable function?

 Topics to be presented in the course include:

    - propositional calculus

    - predicate calculus

    - logical validity and consistency

    - the tableau method

    - the completeness theorem (Gödel)

    - the compactness theorem

    - explicit and implicit definability

    - predicate calculus with identity

    - many-sorted predicate calculus

    - proof systems

    - Beth's theorem on implicit definability

    - theories and models

    - mathematical theories (e.g., group theory)

    - foundational theories (e.g., axiomatic set theory)

    - undecidability of logical validity

    - incompleteness and undecidability

    - Gödel's Second Incompleteness Theorem 

 The course is meeting Tuesday-Thursday 9:45-11:00 in 315 McAllister.
 Chapters 1-5 of my lecture notes

 will serve as the textbook for much of the course.  The course web
 page is

 In case you decide to enroll, the Schedule Number is 178483.

 Best wishes,
 -- S. Simpson

 Stephen G. Simpson
 Department of Mathematics
 McAllister Building, Pollock Road
 Pennsylvania State University
 State College, PA 16802, USA

 office: 814-863-0775
 staff: 814-865-7527
 home: 814-238-2274
 fax: 814-865-3735