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

Dana Ernst's posts

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The 2016 Nebraska Conference for Undergraduate Women in Mathematics (NCUWM) took place this weekend at the University of Nebraska-Lincoln. This was the 18th annual conference. Cool!

I wasn't there, but I had some students present stuff.

Joni Hazelman and Parker Montfort presented the following poster.

Title: Explorations of Conway’s Sylver Coinage Game

Abstract: Sylver Coinage is a game in which two players, A and B, alternately name positive integers that are not the sum of nonnegative multiples of previously named integers. The person who names 1 is the loser! This seemingly innocent looking game is the subject of one of John Conway's open problems with monetary rewards. One such open problem is: If player A names 16 to start, and both players play optimally thereafter, then who wins? In this talk, we will discuss a simplified version of the game in which a fixed positive integer n (greater than 2) is agreed upon in advance. Then A and B alternately name positive integers from the set {1,2,...,n} that are not linear combinations with positive coefficients of previously named numbers. As in the original game, the person who is forced to name 1 is the loser. We will investigate who wins under optimal play for given values of n and determine the Nim-values for the simplified game under certain conditions. Joint work with Robert Voinescu and Ryan Wood.


+Hannah Paige Prawzinsky gave the following presentation.

Title: New coprime vertex labelings

Abstract: A coprime vertex labeling is an injective assignment of the labels {1, 2, . . . , n} to the vertices of an n-vertex simple connected graph such that adjacent vertices receive relatively prime labels. I will present new labelings for several infinite families of graphs. No prior knowledge of graph theory will be assumed. Joint work with Nathan Diefenderfer, Michael Hastings, Levi Heath, Briahna Preston, Emily White, and Alyssa Whittemore. This research was supported by the National Science Foundation grant #DMS-1148695 through the Center for Undergraduate Research (CURM).


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+Hugh Denoncourt, Dustin Story, and I recently wrote up a 4-page paper that summarizes an interesting open problem involving the longest element of the symmetric group. The paper is available as a free download from "Open Problems in Mathematics." Here are some details.

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

Original proposers of the open problem: Donald E. Knuth
The year when the open problem was proposed: 1992
Sponsor of the submission: Richard M. Green - University of Colorado Boulder
AMS Subject classification: 05
Status of the problem: Open

Abstract: Using the standard Coxeter presentation for the symmetric group S_n, two reduced expressions for the same group element are said to be commutation equivalent if we can obtain one expression from the other by applying a finite sequence of commutations. The resulting equivalence classes of reduced expressions are called commutation classes. How many commutation classes are there for the longest element in S_n?

Thanks to +Richard Green for being our sponsor. Potentially of interest to +Drew Armstrong and +Christopher Hanusa.

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I enjoyed this.

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On Friday last week, I gave a talk titled "The mathematics of Boggle logic puzzles" in our Friday Afternoon Mathematics Undergraduate Seminar (FAMUS). The talk was inspired by +Richard Green's post on Google+ about the topic:

In the second half of FAMUS, I discussed my path from hating mathematics as a child to falling in love with mathematics to eventually earning my PhD and becoming a professor of mathematics. I also shared a bit about what I love about mathematics, as well as the joys and struggles of teaching. The students seemed to really enjoy this.

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+Albert Schueller just posted about a new open-source abstract algebra text over on "Open Mathbook". I've also added it to my list of open-source math textbooks located at

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My undergraduate abstract algebra students had a great conversation about productive failure on the first day of the semester while we were doing my "Setting the Stage" activity. During our discussion, I mentioned that skateboarders likely attempt and fail at doing a kick flip hundreds of times before getting it. Well, I just had an awesome conversation with a group of skateboarders on campus about this. These skateboarders were pretty darn awesome by the way. I walked up and asked them how many times they tried a kick flip before getting it. Every one of them guessed it was in the thousands! One kid said he tried it roughly a hundred times everyday for six months. These kids had a lot of insight about productive failure and persistence. We can learn a thing or two from the skaters.

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"A major obstacle for some students, in my opinion, is the misperception that mistakes are "bad," which is one of the unfortunate side effects afflicting many of our students, who have come up through a very rote memorization education. When mistakes are viewed as something to be avoided, then students holding this view are severely limited. Curiosity and the adventurous spirit of an explorer are sacrificed for the sake of not ever making a mistake. Productive failure is part of the set of topics within the general area of growth mindset."
IBL Calculus and "Learn by Doing" Assignments
This past fall I had the pleasure of teaching Calculus 1 to freshmen.  It was a blast!  I enjoyed every minute of it, and it's truly a privilege to be able to be one of the first professors that students see in college.  Not only is it a great experience fo...

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New at Math Ed Matters: +Angie Hodge discusses the use of a math autobiography assignment.

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