Math 574: Topics in Logic and Foundations Spring 2005, MWF 9:05-9:55 AM, 101 Pond, Schedule 434329 Stephen G. Simpson, 321C Whitmore, 863-0775, t20@psu.edu The web page for this course is http://www.personal.psu.edu/t20/courses/math574/. This course is intended for graduate students in mathematical logic. I will carefully introduce a variety of topics which are important in contemporary mathematical logic, but not normally covered in our basic logic sequence, MATH 557-558. Among the topics are: - unsolvable problems in number theory (Hilbert's 10th Problem) - unsolvable problems in group theory (the Word Problem for groups, etc.) - unsolvable problems in geometry/topology - recursively enumerable sets and degrees - priority arguments - randomness and Kolmogorov complexity - models of arithmetic - independence results via nonstandard models