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.
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
- R. Grossberg, A. Kolesnikov, I. Tomasic, M. VanDieren. The equality S1=D=R. Mathematical Logic Quarterly. 49 (2003) 115--128.
- M. VanDieren. Categoricity in abstract elementary classes with no maximal models. Annals of Pure and Applied Logic. 141 Issues 1-2, (2006) 108--147.
- 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.
- R. Grossberg and M. VanDieren. Galois-stability of tame abstract elementary classes. Journal of Mathematical Logic. 6 no. 1 (2006) 25--49.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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. Chapter accepted for publication by the editors. Book to be reviewed by the MAA.
- 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.
- 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.
- 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.
- M. VanDieren. A Characterization of Uniqueness of Limit Models in Categorical Abstract Elementary Classes. To appear in Beyond First Order Model Theory (José Iovino ed.), CRC Press. Preprint.
- 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.
- M. VanDieren and S. Vasey. Symmetry in Abstract Elementary Classes with Amalgamation. First posted August 13, 2015. Under review. Preprint.
- W. Boney and M. VanDieren. Limit Models in Strictly Stable Abstract Elementary Classes. First posted August 19, 2015. Under review. Preprint.
- W. Boney, R. Grossberg, M. VanDieren, and S. Vasey. Superstability from Categoricity in Abstract Elementary Classes. Under review. Preprint.
- W. Boney, M. VanDieren, and S. Vasey. Shelah-Villaveces Revisited. Under review. Preprint.
- 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.
- 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.