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

Teaching

Math/Computer Science 208 - Discrete Structures

Math 444 - Senior Seminar: Ergodic Theory

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, *Computability
and Complexity* (2017), edited by Adam Day, Michael Fellows, Noam
Greenberg, Bakhadyr Khoussainov, Alexander Melnikov, and Frances Rosamond, Lecture Notes in Computer Science, Springer.

The complexity of primes in computable UFDs (with
D. Dzhafarov), pdf, to appear
in *Notre Dame Journal of Formal Logic*.

On uniform relationships between combinatorial problems (with F. Dorais,
D. Dzhafarov, J. Hirst, and
P. Shafer), pdf, *Transactions of the
American Mathematical Society*, 368 (2016), no. 2, 1321-1359.

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