Date: November 15, 2012

  Subject: advertisement for MATH 559

  Dear Mathematics Graduate Students,

  Next semester I will teach MATH 559.  This course is an introduction
  to the branch of mathematics which grew out of Turing's celebrated
  1936 theory of computability and unsolvability.  The subject is now
  known as Computability Theory or Recursion Theory; these are two names
  for the same subject.  In the 1950's and 1960's it was discovered that
  algorithmically unsolvable problems exist in virtually every branch of
  mathematics, so our subject may be considered as essential background
  knowledge for virtually every mathematician.

  I plan to begin at the beginning, with a complete discussion of
  computable functions, unsolvability of the Halting Problem, and Turing
  oracles.  After that I will present some advanced topics, including:

   - computable analysis

   - computable algebra

   - algorithmic randomness

   - Kolmogorov complexity

   - degrees of unsolvability

   - the arithmetical hierarchy

   - hyperarithmeticity

   - effective descriptive set theory

  The course will meet Monday-Wednesday-Friday 10:10-11:00 in 106
  McAllister.  In case you decide to enroll, the Schedule Number is

  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