Welcome! My name is Dana Ernst and I am an assistant professor in the Department of Mathematics and Statistics at Northern Arizona University in Flagstaff, AZ. This blog 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. 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. See my scholarship page for more information.
Furthermore, I am passionate about mathematics education. In particular, I am interested in inquiry-based learning (IBL) and the Moore method for teaching mathematics. This educational paradigm has transformed my teaching. 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.
I am also interested in utilizing technology to enhance the teaching and learning of mathematics. Specifically, I choose free and open-source software and technologies when appropriate. For example, I have been incorporating Sage and GeoGebra into my teaching. Sage is a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface. For examples of a few of the cool things you can do with Sage, check this page. According to their webpage, GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package. There are tons of awesome GeoGebra examples located here. For other examples of the software that I use for teaching and staying productive, check out my resources page.
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—and mathematics education—classroom. Our interest in and engagement with IBL color the column’s content.
Moreover, I am active on Google+ and post regularly about mathematics, teaching, and technology. You can find my G+ profile here. In addition, I frequently post about my cycling, trailing running, and rock climbing adventures on my Elevation Gain Blog.
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
Department of Mathematics & Statistics
Northern Arizona University
805 South Osborn Drive
PO Box 5717
Flagstaff, AZ 86011
Note: The views expressed on this blog are my own and are not necessarily shared by my employer Northern Arizona University.