Publications of Shira Viel
%% Papers Published
@article{fds337148,
Author = {Gilbert, S and Tymoczko, J and Viel, S},
Title = {Generalized splines on arbitrary graphs},
Journal = {Pacific Journal of Mathematics},
Volume = {281},
Number = {2},
Pages = {333-364},
Publisher = {Mathematical Sciences Publishers},
Year = {2016},
Month = {January},
Abstract = {Let G be a graph whose edges are labeled by ideals of a
commutative ring. We introduce a generalized spline, which
is a vertex labeling of G by elements of the ring so that
the difference between the labels of any two adjacent
vertices lies in the corresponding edge ideal. Generalized
splines arise naturally in combinatorics (algebraic splines
of Billera and others) and in algebraic topology (certain
equivariant cohomology rings, described by Goresky,
Kottwitz, and MacPherson, among others). The central
question of this paper asks when an arbitrary edge-labeled
graph has nontrivial generalized splines. The answer is
"always", and we prove the stronger result that the module
of generalized splines contains a free submodule whose rank
is the number of vertices in G. We describe the module of
generalized splines when G is a tree, and give several ways
to describe the ring of generalized splines as an
intersection of generalized splines for simpler subgraphs of
G. We also present a new tool which we call the GKM matrix,
an analogue of the incidence matrix of a graph, and end with
open questions.},
Doi = {10.2140/pjm.2016.281.333},
Key = {fds337148}
}
@article{fds337147,
Author = {Barnard, E and Meehan, E and Reading, N and Viel,
S},
Title = {Universal Geometric Coefficients for the Four-Punctured
Sphere},
Journal = {Annals of Combinatorics},
Volume = {22},
Number = {1},
Pages = {1-44},
Publisher = {Springer Nature},
Year = {2018},
Month = {March},
Abstract = {We construct universal geometric coefficients for the
cluster algebra associated to the four-punctured sphere and
obtain, as a by-product, the g-vectors of cluster variables.
We also construct the rational part of the mutation fan.
These constructions rely on a classification of the
allowable curves (the curves which can appear in
quasi-laminations). The classification allows us to prove
the Null Tangle Property for the four-punctured sphere, thus
adding this surface to a short list of surfaces for which
this property is known. The Null Tangle Property then
implies that the shear coordinates of allowable curves are
the universal coefficients. We compute shear coordinates
explicitly to obtain universal geometric
coefficients.},
Doi = {10.1007/s00026-018-0378-0},
Key = {fds337147}
}
@article{fds353793,
Author = {Akin, V and Viel, S},
Title = {Interpreting Student Evaluations of Teaching},
Editor = {Maki, D and Bookman, J and Jacobson, M and Speer, N and Murphy,
TJ},
Year = {2019},
Key = {fds353793}
}
@article{fds350520,
Author = {Barcelo, H and Bernstein, M and Bockting-Conrad, S and McNicholas, E and Nyman, K and Viel, S},
Title = {Algebraic voting theory & representations of
Sm≀Sn},
Journal = {Advances in Applied Mathematics},
Volume = {120},
Year = {2020},
Month = {September},
Abstract = {We consider the problem of selecting an n-member committee
made up of one of m candidates from each of n distinct
departments. Using an algebraic approach, we analyze
positional voting procedures, including the Borda count, as
QSm≀Sn-module homomorphisms. In particular, we decompose
the spaces of voter preferences and election results into
simple QSm≀Sn-submodules and apply Schur's Lemma to
determine the structure of the information lost in the
voting process. We conclude with a voting paradox result,
showing that for sufficiently different weighting vectors,
applying the associated positional voting procedures to the
same set of votes can yield vastly different election
outcomes.},
Doi = {10.1016/j.aam.2020.102077},
Key = {fds350520}
}
@article{fds367542,
Author = {Spencer, D and Fenn, M and Willis, C and Shen, Y and Viel,
S},
Title = {Utilizing a Blended + Flipped Learning Approach in a
Calculus for Life and Management Sciences
Classroom},
Journal = {PRIMUS},
Publisher = {Taylor and Francis},
Year = {2022},
Month = {November},
Doi = {10.1080/10511970.2022.2122645},
Key = {fds367542}
}
@article{fds369772,
Author = {Tackett, M and Viel, S and Manturuk, K},
Title = {A validation of the short-form classroom community scale for
undergraduate mathematics and statistics
students},
Journal = {Journal of University Teaching and Learning
Practice},
Volume = {20},
Number = {1},
Pages = {1-17},
Year = {2023},
Month = {January},
Abstract = {This study examines Cho & Demmans Epp’s short-form
adaptation of Rovai’s well-known Classroom Community Scale
(CCS-SF) as a measure of classroom community among
introductory undergraduate math and statistics students. A
series of statistical analyses were conducted to investigate
the validity of the CCS-SF for this new population. Data
were collected from 351 students enrolled in 21 online
classes, offered for credit in Fall 2020 and Spring 2021 at
a private university in the United States. Further
confirmatory analysis was conducted with data from 128
undergraduates enrolled in 13 in-person and hybrid classes,
offered for credit in Fall 2021 at the same institution.
Following Rovai’s original 20-item CCS, the 8-item CCS-SF
yields two interpretable factors, connectedness and
learning. This study confirms the two-factor structure of
the CCS-SF, and concludes that it is a valid measure of
classroom community among undergraduate students enrolled in
remote, hybrid, and in-person introductory mathematics and
statistics courses. Practitioner Notes 1. Cho & Demmans
Epp's 2019 Classroom Community Scale Short Form (CCS-SF) is
a promising but relatively new instrument for measuring
students’ sense of community, previously validated only
for graduate online courses. This research article validates
the instrument's use for undergraduate students in online,
hybrid, and in-person courses. 2. According to Rovai’s
original Classroom Community Scale from which the CCS-SF is
adapted, students’ sense of community can be understood by
two subscales, connectedness and learning. These subscales
measure how students relate to their peers and their
perception of being in a supportive learning environment. 3.
Through exploratory factor analysis, we have shown more
nuanced views of the subscales demonstrating the multiple
facets in which students evaluate belongingness among their
peers and perception of having shared learning goals. 4.
With this validation article, instructors can now administer
the CCS-SF instrument in undergraduate courses to assess the
classroom community, as well as using the instrument for
research on undergraduate students. 5. With this validation
article, educational researchers can use the CCS-SF to
better understand situational factors and pedagogies
associated with students’ sense of community and how these
associations vary for students with different
identities.},
Doi = {10.53761/1.20.01.08},
Key = {fds369772}
}
@article{fds374307,
Author = {Hunt, S and Daily, SB and Viel, S and Boyd-Sinkler,
K},
Title = {Examining the Impact of Introductory Mathematics Courses on
Undergraduate Students' Desire to Pursue a STEM
Major},
Journal = {ASEE Annual Conference and Exposition, Conference
Proceedings},
Year = {2023},
Month = {June},
Key = {fds374307}
}
@article{fds374501,
Author = {Akin, V and Viel, S},
Title = {Equity in Grading Systems: Moving Away From “Fair”
Towards Transparency and Inclusion in Coordinated Calculus
Courses},
Volume = {96},
Booktitle = {Justice through the lens of calculus: Framing new
possibilities for diversity, equity, and
inclusion.},
Publisher = {MAA Press},
Editor = {Voigt, M and Hagaman, J and Gehrtz, J and Ratliff, B and Alexander, N and Levy, R},
Year = {2023},
Month = {September},
Key = {fds374501}
}