My name is Dana Ernst and I am an associate professor in the Department of Mathematics and Statistics at Northern Arizona University in Flagstaff, AZ. This site is part of the Booles’ Rings network of academic home pages/blogs.
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 (joint with Nandor Sieben and Bret Benesh). In particular, our research has focused on avoidance and achievement games involving finite groups. See my scholarship page for more information.
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. Check out my undergraduate research page for examples of recent projects.
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.
In addition to using free and open-source software, I am inspired by the recent open-source textbook movement and I strongly believe that educators should choose free, open-source, or low cost textbooks when a viable alternative exists. For a selection of free and/or open-source textbooks, see my list located here. Also, take a peek at Rob Beezer’s selection on this page. Moreover, the American Institute of Mathematics maintains a list of approved open-source textbooks. If you find one of the books list on any of the above links more helpful than another, please let me know.
Angie Hodge and I are coauthors for Math Ed Matters, which is a (roughly) monthly column sponsored by the Mathematical Association of America. The column explores topics and current events related to undergraduate mathematics education. Posts aim to inspire, provoke deep thought, and provide ideas for the mathematics classroom. Our interest in and engagement with IBL color the column’s content.
Besides blogging here and for Math Ed Matters, I am also an editor for Mathblogging.org, which is a site devoted to aggregating the multitude of math-related blogs and news sources across the Internet. My job as editor is to select a blog posts to be included in the Editors’ Picks List.
Lastly, I am a husband and a father of two incredible sons. Oh, I enjoy drinking copious amounts of coffee, too.Dana C. Ernst, PhD
Mathematics & Teaching
Unless stated otherwise, content on this site is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.
The views expressed on this site are my own and are not necessarily shared by my employer Northern Arizona University.
The source code is on GitHub.