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 988819. Best wishes, -- S. Simpson Stephen G. Simpson Department of Mathematics McAllister Building, Pollock Road Pennsylvania State University State College, PA 16802, USA web: www.personal.psu.edu/t20/ email: t20@psu.edu office: 814-863-0775 staff: 814-865-7527 home: 814-238-2274 fax: 814-865-3735