Department of Mathematics and Statistics Grinnell College Grinnell, IA 50112-1690
Office: Noyce Science Center 2514 |

Teaching

Math 218 - Combinatorics

Math 321 - Foundations of Abstract Algebra

Professional Information

Research Interests

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

Research Papers

Irreducibles and primes in computable integral domains (with L. Evron and E. Ratliff-Crain), pdf, submitted.

The complexity of primes in computable UFDs (with D. Dzhafarov), pdf, submitted.

On uniform relationships between combinatorial problems (with F. Dorais,
D. Dzhafarov, J. Hirst, and
P. Shafer), pdf, to appear
in *Transactions of the American Mathematical Society*.

Reverse mathematics and Ramsey's property for trees (with J. Corduan and
M. Groszek), *Journal of Symbolic Logic*, 75 (2010), no. 3, 945-954.

The strength of the rainbow Ramsey theorem (with B. Csima),
pdf, *Journal of Symbolic Logic*,
74 (2009), no. 4, 1310-1324.

The canonical Ramsey theorem and computability theory,
pdf,
*Transactions of the American Mathematical 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.

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 would like to see the current version.

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