Research

VanDieren's mathematics research is in Model Theory, a branch of Mathematical Logic.  Her specialization is in abstract elementary classes.  In her Ph.D. thesis she introduced the concept of tameness for abstract elementary classes and began the development for a classification theory for these classes. 

Two of VanDieren's papers have been consistently ranked among the top 20 most-cited articles of the Journal of Mathematical Logic.  Her paper, "Categoricity from one successor cardinal in tame abstract elementary classes," has appeared on the top of the JML most-cited list in 2017.  And her paper "Galois-stability of tame abstract elementary classes" has appeared at number 3 on this list.  Five of her papers each have been cited over 40 times, and her work has been cited over 350 times according to Google Scholar:



In addition to model theory research, VanDieren is interested in pedagogical research, particularly on interdisciplinary honors courses and on student understanding of multi-variable calculus concepts. 

A Pittsburgh Post Gazette article describes her research, outreach activities and how she finds beauty in mathematics.

Publications and Preprints

Rutgers, Fall 2005

VanDieren with Michael Morley, one 
of the pioneers of Model Theory

  1. R. Grossberg, A. Kolesnikov, I. Tomasic, M. VanDieren.  The equality S1=D=R.  Mathematical Logic Quarterly. 49 (2003) 115--128.
  2. M. VanDieren.  Categoricity in abstract elementary classes with no maximal models.  Annals of Pure and Applied Logic. 141 Issues 1-2, (2006) 108--147.
  3. R. Grossberg and M. VanDieren.  Shelah's Categoricity Conjecture from a successor for tame abstract elementary classes.  Journal of Symbolic Logic 71 Issue 2, (2006)  553--568.
  4. R. Grossberg and M. VanDieren.  Galois-stability of tame abstract elementary classes.  Journal of Mathematical Logic.  6  no. 1 (2006)  25--49.
  5. J. Baldwin, D. Kueker and M. VanDieren.  Stability transfer for tame abstract elementary classes.  Notre Dame Journal of Formal Logic.  4 no. 2 (2006)  291--298.
  6. R. Grossberg and M. VanDieren.  Categoricity from one successor cardinal in tame abstract elementary classes.  Journal of Mathematical Logic.  6  no. 2 (2006)  181--201.
  7. H. Pinson and M. VanDieren.  The Creative Process:  Risk-taking in an interdisciplinary honors course.  In R. Bosch, D. McKenna, R. Sarhangi (Eds.) Bridges: Mathematics, Music, Art, Architecture, and Culture, Tessellations Publishing, Phoenix, Arizona, USA, 2012  pp. 515--518.
  8. M. VanDieren.  Erratum to ``Categoricity in abstract elementary classes with no maximal models'' [Ann. Pure Appl. Logic 141 (2006) 108--147.]  Annals of Pure and Applied Logic. 164 (2013), pp. 131-133.  DOI 10.1016/jpal.2012.09.003.  Final version published online: 26-OCT-2012.
  9. H. Pinson and M. VanDieren.  The taxonomy of significant learning in a math, music, and art course.  In P. Hughes, J. Munoz, and M. Tanner (Eds.) Perspectives in Interdisciplinary and Integrative Studies, Texas Tech University Press, Lubbock TX, USA, 2015 pp. 150-167.
  10. R. Grossberg, A. Villaveces and M. VanDieren.  Uniqueness of limit models in classes with amalgamation.  Mathematical Logic Quarterly.  62 no. 4-5 (2016), pp 367-382. Preprint.  DOI 10.1002/malq.201500033.
  11. M. VanDieren. Visualizing and Estimating the Mass of a Solid Using Multi-colored Blocks.  In J. Libertini and J. Barnes (Eds).  Tactile Learning Activities in Undergraduate Mathematics: A Recipe Book for the Classroom.  To appear. Published by the MAA.
  12. M. VanDieren.  Effectiveness of Online Advising on Honors Student Retention and Engagement.  International Journal of Information and Communications Technology Education.  12 no. 2 (2016), pp 51-67.  10.4018/IJICTE.2016040105  Published version
  13. M. VanDieren.   Symmetry and the Union of Saturated Models in Superstable Abstract Elementary Classes.  Annals of Pure and Applied Logic. 167 (2016), pp 395-407.  DOI 10.1016/j.apal.2015.12.007.  Final version.
  14. M. VanDieren.  Superstability and Symmetry. Annals of Pure and Applied Logic.  167 no.12 (2016), pp 1171-1183. DOI 10.1016/j.apal.2016.05.004.  Final version. 
  15. M. VanDieren and S. Vasey.   Symmetry in Abstract Elementary Classes with Amalgamation. Archive for Mathematical Logic56 no. 17 (2017), pp 423-452.  Preprint.
  16. W. Boney, R. Grossberg, M. VanDieren, and S. Vasey.  Superstability from Categoricity in Abstract Elementary Classes.  Annals of Pure and Applied Logic.168 no. 7 (2017), pp 1383-1395. http://doi.org/10.1016/j.apal.2017.01.005 Preprint.  Final Version.
  17. M. VanDieren, D. Moore-Russo, J. Wilsey, and P. Seeburger.  Students' Understanding of Vectors and Cross Products: Results from a Series of Visualization Tasks.  To appear in Proceedings of the 20th Annual Conference on Research on Undergraduate Mathematics Education.
  18. D. Moore-Russo, M. VanDieren, J. Wilsey, and P. Seeburger.  Developing a Conceptual Framework for Students' Understanding of Cross Product.  To appear.
  19. W. Boney and M. VanDieren.  Limit Models in Strictly Stable Abstract Elementary Classes.  First posted August 19, 2015. Under review.  Preprint.
Funding
  • NSF Division of Undergraduate Education Grant: "Collaborative Research: Improving Conceptual Understanding of Multivariable Calculus Through Visualization Using CalcPlot3D."  Co-PI.  Sept 2015-August 2018.  $134,601. 
  • Amazon Web Services in Education Grant to house a WeBWorK server for RMU students.  2015-2016.  $6000.
  • AWM-NSF Mentoring Travel Grant: "Developing a Tool to Measure Student Understanding of Multivariable Calculus Concepts."  Spring 2015. $1500.
  • Amazon Web Services in Education Grant to house a WeBWorK server for RMU students.  2014-2015.  $6000.
  • Professional Experience Program (PREP) Grant to fund an undergraduate mathematics and computer science research assistant to aid in converting CalcPlot3D exploratory labs into WeBWorK using the Perl programming language.  2014-15 academic year.  
  • NSF Division of Mathematical Sciences Grant 0801313:  ``RUI: Model Theory of Abstract Elementary Classes."  PI.  May 2008-April 2013.  $111,000.
  • NCHC Portz Grant: ``Intersections: A Multi-University, Hybrid Undergraduate Research Conference."  Co-PI.  2009-2010.  $1000.
  • NSF Division of Undergraduate Education Grant:  "Robert Morris University S-STEM Scholar Program."  Senior Faculty and Co-PI on a previous submission.  August 2008-July 2013.  $562,220.
  • US-Colombian Research Group ``Establilidad en Clases No Elementales [Stability in Non-Elementary Classes]."  Associate Researcher.
  • American Institute of Mathematics Workshop on Non-elementary Model Theory.  Co-PI.  July 2006.
  • Rackham Faculty Fellowship.  PI.  Summer 2005.
Dissertation Committees
  • Outside Reviewer for the Ph.D. dissertation defense of Sebastien Vasey at Carnegie Mellon University, 2017.
  • Outside Reviewer for the Ph.D. dissertation defense of William Boney at Carnegie Mellon University, 2014.
  • Outside Reviewer for the Ph.D. dissertation defense of Fred Drueck at the University of Illinois at Chicago, 2012.
  • Outside Reviewer for the Ph.D. dissertation defense of Pedro Zambrano at the National University of Colombia in Bogotá, 2011.
  • The Opponent for the Ph.D. dissertation defense of Meeri Kesälä at the University of Helsinki, 2006.
  • Committee Member for the Ph.D. dissertation defense of Bart Kastermans at the University of Michigan, 2006.
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