Commutative Algebra is area of mathematics that has its origin in number theory, algebraic geometry and invariant theory. My research is focused on the study of prime ideals in certain commutative rings.  A main goal of my research program is to classify the prime spectra of various polynomial/power series rings.  Prime ideals are important as they are the building blocks of the ideal structure for the ring. For instance in some rings every ideal can be written as a product of prime ideals.

My Mathematics Education research focuses on efforts to improve the mathematical content knowledge of both pre-service and in-service teachers.  In particular, how to strengthen the mathematical practices and mathematical habits of mind of teachers.

I have also led undergraduate research projects on topics related to Graph Theory and Coding Theory.  In particular, I have led student projects where we have looked at and developed list decoding algorithms for Reed-Solomon codes.  In the area of Graph Theory, I have led projects that examine interlace polynomials of various simple graphs related to the wheel graph.

Here is a list of my publications.

C. Eubanks-Turner, P. Beaulieu, N. Pal, A. Vatsala, Smooth Transition for Advancement to Graduate Education (STAGE) for Underrepresented Groups in Mathematical Sciences Pilot Project: The Benets and Challenges of Mentoring (accepted, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies).

B. Baker Swart, K. Beck, S. Crook,  C. Eubanks-Turner, H. Grundman, M. Mei, L. Zack, Augmented Generalized Happy Functions (accepted, Rocky Mountain Journal of Mathematics, arxiv.org/abs/1410.0297).

A. Kreide,  C. Eubanks-Turner, A. Tomlinson, Preservice teachers’ development of questioning skills through Common Core aligned exemplar videotaped math lessons, Proceedings of the Hawaii University International Conferences, (2015), 13 pages, http://www.huichawaii.org/steam2015p.html

C. Eubanks-Turner, M. Lennon, E. Reynoso, B. Thibodeaux, A. Urquiza, A. Wheatley, D. Young, Using the Division Algorithm to Decode Reed-Solomon Codes, Journalof Shanghai Normal University (Natural Sciences) (2015), 44:3, 262-269. ** Work originating from an undergraduate research project.

C. Eubanks-Turner, N. Hajj, Mardi Gras Math, Mathematics Teaching in the Middle School (2015), 20:8, 492-498.

C. Eubanks-Turner, A. Li, Graphical Properties of the Bipartite Graph of Spec(Z[x])\{0}, Journal of Algebra Combinatorics, Discrete Structures and Applications (2015), 2:1, 65-73.

E. Celikbas,  C. Eubanks-Turner, S. Wiegand, Prime Ideals in Power Series Rings and Polynomial Rings over Noetherian Domains, Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions, Springer (2014), 55-82.

C. Eubanks-Turner, The W.I.P.E. Rubric: Assessing Student Presentations of Mathematical Proofs, Proceedings of the Lilly Conference on College and University Teaching and Learning,(2014), 10-14.

C. Eubanks-Turner, M. Luckas, and S. Saydam, Prime ideals in Birational Extensions of Two-Dimensional Power Series Rings, Communications in Algebra (2013), 41: 2, 703-735.

E. Celikbas,  C. Eubanks-Turner, The Projective Line Over the Integers, Progress in Commutative Algebra 2, De Gruyter (2012), 221-240.