(NEW: 2022) Artin’s First Article on the Artin L-Series (1924): Paraphrasis and Commentary. This is an expansive translation of Emil Artin's Über eine neue Art von L-Reihen (1924) with extensive commentary.
(2019) What are discrete valuation rings? What are Dedekind domains? A 69 page essay on discrete valuations rings, Dedekind domains, and related integral domains. Includes around 60 exercises.
(2003 - 2019) A quick introduction to Galois theory. Consists of an overview essay plus 16 one-page worksheets.
(2007-2019) (With L. Holt) Number systems: an axiomatic foundation for algebra, number theory, and analysis. A detailed introduction to the number systems from the natural numbers (Peano's axioms) to the complex numbers.
(2021) Report on Freely Representable Groups. This concerns groups that admit a linear representation acting freely on nonzero vectors.
(2020 - 2022) Commentary on Bourbaki's Chapter I, Description of Formal Mathematics. Describes in detail the formal logical system developed by Bourbaki in the 1950s.
(2011) (With F. Lemmermeyer) Counterexamples to the Hasse Principle.
(2003) (With J. Barrett) Computer Implication and Curry’s Paradox.