Department of Mathematics and Statistics|
Grinnell, IA 50112-1690
Office: Noyce Science Center 2514
Math/Computer Science 208 - Discrete Structures
Math 444 - Senior Seminar: Ergodic Theory
Computability theory, reverse mathematics, set theory, Ramsey theory, and the interaction of mathematical logic with algebra and combinatorics.
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.
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 would like to see the current version.
I'm currently in the process of creating an online
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