Joe Mileti

John Wesley Young Research Instructor

Department of Mathematics
6188 Kemeny Hall
Dartmouth College
Hanover, NH 03755

Office: 308 Kemeny
Phone: 603-646-9837
Email: joseph.r.mileti ~at~ dartmouth.edu


Professional Information

Curriculum Vitae


Research Interests

Computability theory, reverse mathematics, set theory, Ramsey theory, and the general interaction of mathematical logic with algebra and combinatorics.


Research Papers

A Note on Reverse Mathematics and Partitions of Trees (with J. Corduan and M. Groszek), submitted.

The strength of the rainbow Ramsey theorem (with B. Csima), pdf, To appear in Journal of Symbolic Logic.

The canonical Ramsey theorem and computability theory, pdf, Transactions of the American Math Society, 360 (2008), 1309-1340.

Ideals in computable rings (with R. Downey and S. Lempp), pdf, Journal of Algebra, 314 (2007), no. 2, 872-887.

Subspaces of computable vector spaces (with R. Downey, D. Hirschfeldt, A. Kach, S. Lempp, and A. Montalbán), pdf, Journal of Algebra, 314 (2007), no. 2, 888-894.

Partition theorems and computability theory, pdf ps, dissertation at UIUC. Thesis Advisor: Carl Jockusch.

Partition theorems and computability theory, Bulletin of Symbolic Logic, vol. 11 #3 (2005), 411--427.

Ramsey degrees, in preparation.


Expository Papers

The recursion theorem (or how I learned to stop worrying and love the recursion theorem), in preparation.


Books

Building on course notes from my experiences teaching mathematical logic over the past few years, I am currently writing a book tentatively titled Mathematical Logic for Mathematicians. Please contact me if you like to see the current version.


Teaching

Spring 2009: Discrete Probability
Spring 2009: Graph Theory


Mathematics Museum

I'm currently in the process of creating an online Mathematics Museum that discusses, at an elementary yet honest level, the basics of the mathematician's craft. I've only written a few pages so far, but I hope to work on it during my spare time.

The Different Sizes of Infinity
Ramsey's Theorem
Abstract Algebra