Teaching

I am the Director of Graduate Studes in Philosophy at Carnegie Mellon.

Since 2006, I have been directing the Carnegie Mellon Summer School in Logic and Formal Epistemology. I taught a week-long workshop on Logic and Formal Verification in 2007 and 2008.

In the spring of 2007, I taught a seminar on practical decision procedures with Ed Clarke.

Reed Solomon and I organized a special session on effective aspects of measure theory and analysis for the ASL meeting in Montreal in Spring 2006.

In the summer of 2005, I taught a short course on proof theory with Henry Towsner.

In the fall of 2002, I taught a seminar on mathematical structuralism with Ken Manders (Department of Philosophy, University of Pittsburgh). We taught another seminar on algebraic methods in mathematics in the fall of 2005.

Here are some of the courses I teach regularly at Carnegie Mellon:

• The Nature of Reason (80-150)
  A survey of philosophical views on the nature of reason, including deductive logic, inductive logic, the philosophy of mind, and computation.
• Logic and Computation (80-310/610)
  The syntax and semantics of first-order logic, completeness, compactness, and other topics.
  Lecture notes (version: January 2002, 120 pages): pdf.
• Computability and Incompleteness (80-311/611)
  Formal models of computation, unsolvability, and Gödel's incompleteness theorems.
  Lecture notes (version: January 2007, 128 pages): pdf.
  David Gray's Wall of Logic: jpg.
  Notes on the incompleteness theorems, and the halting problem: pdf.
  Doug Perkins's Turing machine simulation: java applet.
• Proof Theory (80-411/711)
  An introduction to proof theory

Here are some notes on classical and constructive logic: pdf.

When I was in graduate school, I taught a summer course for high school students called "An intuitive approach to higher mathematics," with the Academic Talent Development Program.