Publications

Publications in refereed professional journals:

  • From Circle to Hyperbola in Taxicab Geometry, NCTM, Mathematics Teacher, publication date: October 2015. An older version of the manuscript is available.
  • Parabolas in Taxicab Geometry, NCTM, online supplement to the above. A more detailed version is available.
  • Green Jello World and Escher’s World, College Mathematics Journal Vol.45 No.1 (2014) p.50-53. Access to this publication is available online. An older, more detailed, version of the manuscript is available.
    Abstract: Summary Introducing models of hyperbolic geometry informally in the setting of different worlds lets students naturally come up with the idea that lines (shortest paths) can look like parts of Euclidean circles. By learning to think like inhabitants of these worlds, students are able to abandon their totally Euclidean view of lines and take ownership of hyperbolic geometry.
  • Hidden Group Structure, Mathematics Magazine Vol.78 No.1 (February 2005)  p.45-48. Available online.
    (This article is listed as one of the suggested readings for chapter 3 of  Gallian’s “Contemporary Abstract Algebra” textbook)

    Abstract: Starting with U(n) new groups can be constructed that have a non-obvious identity element, forcing students to think carefully about the identifying features of elements they are looking for.
  • Discovering  Abstract Algebra with ISETL, Innovations in Teaching Abstract Algebra, MAA Notes Vol. 60. (2002) p.55-62.
    Abstract: 
    ISETL stands for Interactive SET Language. It is a mathematical programming language whose syntax resembles standard mathematical notation. In this paper I describe how I use ISETL in my abstract algebra class at Luther College. Many examples of ISETL programming code are included, so interested instructors can easily evaluate the usefulness of this tool for their classes.
  • Ideal Class Groups, some computations, Journal of Number Theory Vol.50 No.2 (1995) p.251-260. Available online.
    Abstract: Starting from a base field with properties similar to those of the rational numbers, the structure of the ideal class group of a biquadratic dicyclic extension is examined. Class number relations and structural connections between the ideal class groups of the intermediate fields allow the determination of this structure in some cases. Explicit computations are performed for some number fields of degree 8.
  • Hasse's Class Number Product Formula for generalized Dirichlet Fields and other Types of Number Fields,  Manuscripta Mathematica  Vol.76 (1992) p.397-406. Available online.
    Abstract: In the 1950's Hasse gave a formula that relates the class number of a biquadratic dicyclic number field to the class numbers of its, three quadratic subfields. Similar formulas are derived here for biquadratic dicyclic extensions of more general base fields, in cases where the base fields retain several properties of ℚ.
  • Regular fields: normic criteria, joint paper with G. Gras,  Publ. Math. Fac. Sci. Besancon (1991/92) p.1-4.
  • Class Number Parity and Unit Signature, Archiv der Mathematik, Vol.59 (1992) p.427-435.
  • The Kernel of  C(N)->C(N(sqrt(-1)) and the 4-Rank of K_2(O), Canadian Bulletin of Mathematics, Vol.35 No.3 (1992) p.295-302.   
  • Quadratic Extensions with Elementary Abelian K_2(O), Journal of Algebra Vol.142 No.2 (1991) p.394-404.
  • Quadratic Extensions of Number Fields with Elementary Abelian 2-prim K_2(O_F) of smallest Rank,  Journal of Number Theory  Vol.34 No.3 (1990) p.284-292;  with addendum in Journal of Number Theory Vol.37 (1991) p.122.

Other contributions:

  • Co-author in chapter 3 of “Cooperative learning in Undergraduate Mathematics”, MAA notes #55 (2001). Available online.
  • Book review for the MAA publication “Oval Track and other permutation puzzles”, available online.         
  • I collaborated with Reg Laursen on writing a solution manual for Addison Wesley Publishers for the text book “Calculus, an integrated approach to Functions and their Rates of Change” by Gottlieb, which we were using in our integrated calculus sequence at Luther at the time.