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Department of Mathematics 6188 Kemeny Hall Dartmouth College Hanover, NH 03755
Office: 308 Kemeny |
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Department of Mathematics 6188 Kemeny Hall Dartmouth College Hanover, NH 03755
Office: 308 Kemeny |
Computability theory, reverse mathematics, set theory, Ramsey theory, and the general interaction of mathematical logic with algebra and combinatorics.
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.
The recursion theorem (or how I learned to stop worrying and love the recursion theorem), in preparation.
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.
Spring 2009: Discrete Probability
Spring 2009: Graph Theory
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