Personal information

Coxeter groups, Temperley-Lieb algebras, diagram algebras, heaps, inquiry-based learning, IBL, combinatorial game theory
United States

Biography

I am an associate professor in the Department of Mathematics and Statistics at Northern Arizona University in Flagstaff, AZ. My primary research interests are in the interplay between combinatorics and algebraic structures. More specifically, I study the combinatorics of Coxeter groups and their associated Hecke algebras, Kazhdan-Lusztig theory, generalized Temperley-Lieb algebras, diagram algebras, and heaps of pieces. By employing combinatorial tools such as diagram algebras and heaps of pieces, one can gain insight into algebraic structures associated to Coxeter groups, and, conversely, the corresponding structure theory can often lead to surprising combinatorial results. More recently, my research has expanded into combinatorial game theory. In particular, our research has focused on avoidance and achievement games involving finite groups. The combinatorial nature of my research naturally lends itself to collaborations with undergraduate students, and my goal is to incorporate undergraduates in my research as much as possible. My interests also include the scholarship of teaching and learning (SoTL) with a focus on inquiry-based learning (IBL) as an approach to teaching/exploring mathematics. I am currently a Special Projects Coordinator for the Academy of Inquiry-Based Learning and a mentor for several new IBL practitioners. Moreover, I actively give talks and organize workshops on the benefits of IBL as well as the nuts and bolts of how to implement this approach in the mathematics classroom.

Activities

Employment (10)

Northern Arizona University: Flagstaff, AZ, US

2017-08 to present | Associate Professor (Mathematics and Statistics)
Employment
Source: Self-asserted source
Dana C. Ernst

Northern Arizona University: Flagstaff, AZ, US

2012-08 to 2017-07 | Assistant Professor (Mathematics and Statistics)
Employment
Source: Self-asserted source
Dana C. Ernst

Plymouth State University: Plymouth, NH, US

2008-08 to 2012-05 | Assistant Professor (Mathematics)
Employment
Source: Self-asserted source
Dana C. Ernst

University of Colorado Boulder: Boulder, CO, US

2003-08 to 2008-05 | Graduate Teaching Assistant (Mathematics)
Employment
Source: Self-asserted source
Dana C. Ernst

University of Colorado Boulder: Boulder, CO, US

2006-08 to 2007-05 | Lead Graduate Teacher (Graduate Teacher Program)
Employment
Source: Self-asserted source
Dana C. Ernst

Front Range Community College - Boulder County Campus: Longmont, CO, US

2001-08 to 2003-05 | Faculty (Mathematics)
Employment
Source: Self-asserted source
Dana C. Ernst

Northern Arizona University: Flagstaff, AZ, US

2000-06 to 2001-05 | Instructor (Mathematics and Statistics)
Employment
Source: Self-asserted source
Dana C. Ernst

Northern Arizona University: Flagstaff, AZ, US

2000-01 to 2000-05 | Graduate Assistant (Northern Learning Assistance Center)
Employment
Source: Self-asserted source
Dana C. Ernst

Northern Arizona University: Flagstaff, AZ, US

1998-01 to 1999-12 | Graduate Teaching Assistant (Mathematics and Statistics)
Employment
Source: Self-asserted source
Dana C. Ernst

Northern Arizona University: Flagstaff, AZ, US

1997-08 to 1997-12 | Graduate Assistant (South Learning Assistance Center)
Employment
Source: Self-asserted source
Dana C. Ernst

Education and qualifications (3)

University of Colorado Boulder: Boulder, CO, US

2003-08 to 2008-05 | PhD Mathematics (Mathematics)
Education
Source: Self-asserted source
Dana C. Ernst

Northern Arizona University: Flagstaff, AZ, US

1997-08 to 2000-05 | MS Mathematics (Mathematics and Statistics)
Education
Source: Self-asserted source
Dana C. Ernst

George Mason University: Fairfax, VA, US

1993-08 to 1997-05 | BS Mathematics (Mathematics)
Education
Source: Self-asserted source
Dana C. Ernst

Funding (4)

An open problem library for mathematics

Grant
Faculty Grants Program at Northern Arizona University (Flagstaff, AZ, US)
Source: Self-asserted source
Dana C. Ernst

Applets for Calculus

Grant
Interns to Scholars Program at Northern Arizona University (Flagstaff, AZ, US)
Source: Self-asserted source
Dana C. Ernst

IBL course materials for group theory

Grant
Academy of Inquiry-Based Learning (San Luis Obispo, CA, US)
Source: Self-asserted source
Dana C. Ernst

Prime labelings of graphs

Grant
Center for Undergraduate Research in Mathematics (Provo, UT, US)
Source: Self-asserted source
Dana C. Ernst

Works (28)

Impartial geodetic building games on graphs

International Journal of Game Theory
2024-12 | Journal article
Contributors: Bret J. Benesh; Dana C. Ernst; Marie Meyer; Sarah K. Salmon; Nándor Sieben
Source: check_circle
Crossref

Using the Spin 3 × 3 Virtual Manipulative to Introduce Group Theory

PRIMUS
2024-07-02 | Journal article
Contributors: Dana C. Ernst; Jeffrey Slye
Source: check_circle
Crossref

Impartial achievement games for generating nilpotent groups

J. Group Theory
2019 | Journal article
Source: Self-asserted source
Dana C. Ernst

Diagram calculus for a type affine C Temperley--Lieb algebra, II

J. Pure Appl. Alg.
2018-12 | Journal article
Source: Self-asserted source
Dana C. Ernst

Doceamus: What Is Inquiry-Based Learning?

Notices of the AMS
2017 | Journal article
Source: Self-asserted source
Dana C. Ernst

Factorization of Temperley--Lieb diagrams

Involve
2017 | Journal article
Source: Self-asserted source
Dana C. Ernst

Impartial achievement games for generating generalized dihedral groups

Australas. J. Combin.
2017 | Journal article
Source: Self-asserted source
Dana C. Ernst

Impartial achievement and avoidance games for generating finite groups

Int. J. Game Theory
2017-12-07 | Journal article
Source: Self-asserted source
Dana C. Ernst

Bringing Inquiry to the First Two Years of College Mathematics

PRIMUS
2017-08-09 | Journal article
Contributors: Dana C. Ernst; Theron Hitchman; Angie Hodge
Source: check_circle
Crossref

Impartial avoidance and achievement games for generating symmetric and alternating groups

Int. Electron. J. Algebr.
2016 | Journal article
Source: Self-asserted source
Dana C. Ernst

Impartial avoidance games for generating finite groups

North-W. Eur. J. Math.
2016 | Journal article
Source: Self-asserted source
Dana C. Ernst

On the number of commutation classes of the longest element in the symmetric group

Open Problems in Mathematics
2016 | Journal article
Source: Self-asserted source
Dana C. Ernst

Prime vertex labelings of several families of graphs

Involve
2016 | Journal article
Source: Self-asserted source
Dana C. Ernst

Within ε of Independence: An Attempt to Produce Independent Proof Writers via IBL

Beyond Lect. Tech. to Improv. Student Proof-Writing Across Curric.
2016 | Book chapter
Source: Self-asserted source
Dana C. Ernst

An Inquiry-Based Approach to Abstract Algebra

Source: Self-asserted source
Dana C. Ernst

An Introduction to Proof via Inquiry-Based Learning

Source: Self-asserted source
Dana C. Ernst

Enhancing Proof Writing via Cross-Institutional Peer Review

PRIMUS
2015 | Journal article
Source: Self-asserted source
Dana C. Ernst

Inquiry-Based Learning and the Flipped Classroom Model

PRIMUS
2015 | Journal article
Source: Self-asserted source
Dana C. Ernst

Inverted Pedagogy in Second Semester Calculus

PRIMUS
2015 | Journal article
Source: Self-asserted source
Dana C. Ernst

The many faces of IBL

Handbook of Research on Pedagogical Practice in STEM Education
2015 | Book chapter
Source: Self-asserted source
Dana C. Ernst

To friend or not to friend? Facebook for professional educators

MAA Focus
2015 | Magazine article
Source: Self-asserted source
Dana C. Ernst

First Semester Experiences in Implementing a Mathematics Emporium Model

Proceedings of Society for Information Technology & Teacher Education International Conference
2013 | Journal article
Contributors: Dana C. Ernst
Source: Self-asserted source
Dana C. Ernst

Redesigning an Algebra for Precalculus Course.

Proceedings of World Conference on E-Learning in Corporate, Government, Healthcare, and Higher Education
2013 | Journal article
Contributors: Dana C. Ernst
Source: Self-asserted source
Dana C. Ernst

Diagram calculus for a type affine C Temperley--Lieb algebra, I

J. Pure Appl. Alg.
2012 | Journal article
Source: Self-asserted source
Dana C. Ernst

On the cyclically fully commutative elements of Coxeter groups

J. Algebr. Comb.
2012 | Journal article
Source: Self-asserted source
Dana C. Ernst

Non-cancellable elements in type affine C Coxeter groups

Int. Electron. J. Algebr.
2010 | Journal article
Source: Self-asserted source
Dana C. Ernst

A diagrammatic representation of an affine C Temperley--Lieb algebra

PhD Thesis
2008 | Dissertation or Thesis
Source: Self-asserted source
Dana C. Ernst

Cell Complexes for Arrangements with Group Actions

MS Thesis
2000 | Dissertation or Thesis
Contributors: Dana C. Ernst
Source: Self-asserted source
Dana C. Ernst