### Dana Ernst

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Dana Ernst

Works at Northern Arizona University

Attended George Mason University

Lives in Flagstaff, AZ

36,519 followers|605,627 views

AboutPostsReviews

I'm having a serious case of imposter syndrome.

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Vincent Knight

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Congrats!

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We saw this beautiful horny toad on our family hike today. One of biggest I've ever seen.

http://en.wikipedia.org/wiki/Horned_lizard

http://en.wikipedia.org/wiki/Horned_lizard

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Debra Vercammen

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I haven't seen one of these in forever! used to catch them all the time when I was a kid. They're so cute.

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Double bonus day!

First, my grad student, Kirsten Davis successfully defended her MS thesis titled "A cellular quotient of the Temperley-Lieb algebra of type D." I'm really proud of Kirsten and what she has produced. This is my first grad student, so I'm extra stoked! Thanks to Janet McShane and +Michael Falk for serving on the committee. I'll have a another student defending in a couple weeks.

Second, +Ellie Blair Kennedy, Brian Beaudrie, Roy St. Laurent, and I submitted a paper today on a study involving "flipping" second semester calculus.

Boom.

First, my grad student, Kirsten Davis successfully defended her MS thesis titled "A cellular quotient of the Temperley-Lieb algebra of type D." I'm really proud of Kirsten and what she has produced. This is my first grad student, so I'm extra stoked! Thanks to Janet McShane and +Michael Falk for serving on the committee. I'll have a another student defending in a couple weeks.

Second, +Ellie Blair Kennedy, Brian Beaudrie, Roy St. Laurent, and I submitted a paper today on a study involving "flipping" second semester calculus.

Boom.

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Dana Ernst

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+Richard Green, yep!

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Oh, man, I love this. +Robert Jacobson, may I repost this someplace on my webpage?

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Richard Green

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I love this too, +Dana Ernst!

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Via Jean Spencer on Facebook.

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Joanne Hopper

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No - its not for the stupid materialistic shit - its for the big stuff that changes peoples lives.....

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In his circles

981 people

For our Easter Hike, the Ernst Tribe did some exploring off the AZ Trail near our home. We explored some native American ruins that are unknown to the general public. We found lots of pottery and saw some cool wildlife. I don't think the obsidian on the right in my hand is an arrowhead, but it's likely something of interest since obsidian is not naturally occurring in the immediate area.

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A regular octagon has sixteen distance preserving symmetries. Eight of the symmetries are rotations, and the other eight are reflections.

This graphic by

The top row of eight octagons shows the result of rotating the standard STOP sign anticlockwise (=counterclockwise) by multiples of 45°. The leftmost octagon in the second row is obtained from the standard STOP sign by reflecting in the horizontal axis. (It may be helpful to imagine that the sign is transparent, so that the word can be read from either side.) The rest of the second row is obtained by rotating the reflected version of the sign anticlockwise by multiples of 45°. This collection of sixteen signs illustrates all the symmetries of a regular octagon.

The inverted versions of the sign in the second row can all be obtained from the standard STOP sign by using a single reflection, rather than a combination of reflections and rotations. This is because as well as reflecting a regular octagon about the horizontal axis, one can reflect it (a) about any axis joining the midpoints of two opposite sides of the octagon or (b) about any axis joining two opposite corners of the octagon. There are four ways to do (a), and four ways to do (b), and applying these eight reflections to the standard STOP sign will produce the eight inverted signs in the second row.

The transformations

The four stop signs at the bottom of the graphic show that the net effect of applying

Picture credit:

The top part of this graphic appears on the Wikipedia entry on the dihedral group (http://en.wikipedia.org/wiki/Dihedral_group). The bottom part of the graphic is also on Wikipedia but is not currently used in an article there.

#mathematics #scienceeveryday

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My brother Brandt C. Ernst was born on April 17, 1971. He passed away from leukemia at age 11. He would be 43 years old today. In his honor, my family celebrates Brothers Day each year on his birthday.

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Dayal Purohit

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Happy birthday Brandt Ernst in heaven. May you continue to smile upon the success of your brother Dana Ernst.

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Brian Nelson

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Just to be a little cynical... Not starting some things until you have finished others is not infrequently better than not starting. :-P

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This would have come in handy a couple days ago. #LaTeX

Building a tool like this into +writeLaTeX would be cool.

Building a tool like this into +writeLaTeX would be cool.

Thank goodness.

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People

In his circles

981 people

Work

Occupation

Assistant Professor of Mathematics

Employment

- Northern Arizona UniversityAssistant Professor, 2012 - present
- University of Colorado at BoulderGraduate Student/Teaching Assistant, 2003 - 2008
- Front Range Community CollegeMath Faculty, 2001 - 2003
- Northern Arizona UniversityGraduate Student/Instructor, 1997 - 2001
- Plymouth State UniversityAssistant Professor, 2008 - 2012

Places

Currently

Flagstaff, AZ

Previously

Williamsville, NY - Fairfax, VA - Flagstaff, AZ - Boulder, CO - Plymouth, NH

Links

YouTube

Contributor to

- Dana's Blog (current)
- Math Ed Matters (current)

Story

Tagline

Father of two boys, husband, mathematician, cyclist, trail runner, rock climber, and coffee drinker.

Introduction

My name is Dana Ernst and I am an assistant professor in the Department of Mathematics and Statisticsat 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. 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.

In addition to using free and open-source software, I am inspired by the recent open-source textbookmovement and I strongly believe that educators should choose free, open-source, or low cost textbooks when a viable alternative exists. For a list of open-source textbooks, go here and here.

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.

I also maintain a personal blog, which is part of the Booles' Rings network of academic home pages/blogs. On my blog, I typically write about topics related to mathematics, education, and technology. In addition, I occasionally 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.

Education

- George Mason UniversityBS, Mathematics, 1993 - 1997
- Northern Arizona UniversityMS, Mathematics, 1997 - 2000
- University of Colorado at BoulderPhD, Mathematics, 2003 - 2008

Basic Information

Gender

Male

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