I am no longer maintaining this wiki. Please see my web page located at http://oz.plymouth.edu/~dcernst.
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My name is Dana Ernst and I am an assistant professor in the Mathematics Department at Plymouth State University in Plymouth, NH. 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.
Furthermore, I am very passionate about mathematics education. Recently, I have become interested in inquiry-based learning and the Moore method for teaching mathematics. This educational paradigm has transformed my teaching.
I am interested in utilizing technology to enhance the learning of mathematics. In particular, I choose free and open-source software and technologies when appropriate. For example, I have been incorporating Sage and Lurch 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. Lurch is open-source mathematics validation software with the ability to check the steps of your work in many areas of mathematics, from calculus to logic. I also make use of wikis for some of my courses to enhance collaboration and to introduce students to LaTeX. For a recent example of one of my course wikis, go here.
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, go here.
I am also the co-organizer of the PSU Mathematics Seminars. If you are interested in giving a seminar, please contact me. Lastly, I am an avid cyclist and rock climber and also enjoy hikes with the family and drinking copious amounts of coffee.