Fostering Mathematical Creativity While Impacting Beliefs And Anxiety In Mathematics,
2020
University of Central Arkansas
Fostering Mathematical Creativity While Impacting Beliefs And Anxiety In Mathematics, James M. Fetterly
Journal of Humanistic Mathematics
This quantitative study examined the notion of mathematical creativity and its relationship to epistemological beliefs of the nature of mathematics and mathematical anxiety. A counterbalanced design was employed, randomizing a class of elementary pre-service teachers into two groups and giving a pre- and post-test to determine if significant differences exist in the participants who are exposed to problem posing, divergent thought, and invented strategies, that is, a punctuated, intentional experience with mathematical creativity. This difference in mathematical anxiety, beliefs, and creativity was also gauged using repeated measures during the study. Furthermore, beliefs and anxiety were correlated with mathematical creativity employing …
Everyday Examples In Linear Algebra: Individual And Collective Creativity,
2020
The University of Arizona
Everyday Examples In Linear Algebra: Individual And Collective Creativity, Aditya P. Adiredja, Michelle Zandieh
Journal of Humanistic Mathematics
This paper investigates creativity in students’ constructions of everyday examples about basis in Linear Algebra. We analyze semi-structured interview data with 18 students from the U.S. and Germany with diverse academic and social backgrounds. Our analysis of creativity in students’ everyday examples is organized into two parts. First, we analyze the range of students’ creative products by investigating the mathematical variability in the more commonly mentioned examples. Second, we unpack some of the collective processes in the construction of students’ examples. We examine how creativity was distributed through the interactions among the student, the interviewers, and other artifacts and ideas. …
Special Issue -- Creativity In Mathematics: Foreword,
2020
University of La Verne
Special Issue -- Creativity In Mathematics: Foreword, Emily Cilli-Turner, Houssein El Turkey, Gulden Karakok, Milos Savic, Gail Tang
Journal of Humanistic Mathematics
No abstract provided.
A World Of Creativity,
2020
Claremont McKenna College
A World Of Creativity, Mark Huber, Gizem Karaali
Journal of Humanistic Mathematics
No abstract provided.
Front Matter,
2020
Claremont Colleges
Integrating Data Science Ethics Into An Undergraduate Major,
2020
Smith College
Integrating Data Science Ethics Into An Undergraduate Major, Benjamin Baumer, Randi L. Garcia, Albert Y. Kim, Katherine M. Kinnaird, Miles Q. Ott
Statistical and Data Sciences: Faculty Publications
We present a programmatic approach to incorporating ethics into an undergraduate major in statistical and data sciences. We discuss departmental-level initiatives designed to meet the National Academy of Sciences recommendation for weaving ethics into the curriculum from top-to-bottom as our majors progress from our introductory courses to our senior capstone course, as well as from side-to-side through co-curricular programming. We also provide six examples of data science ethics modules used in five different courses at our liberal arts college, each focusing on a different ethical consideration. The modules are designed to be portable such that they can be flexibly incorporated …
De Branges Spaces On Compact Riemann Surfaces And A Beurling-Lax Type Theorem,
2020
Chapman University
De Branges Spaces On Compact Riemann Surfaces And A Beurling-Lax Type Theorem, Daniel Alpay, Ariel Pinhas, Victor Vinnikov
Mathematics, Physics, and Computer Science Faculty Articles and Research
Using the notion of commutative operator vessels, this work investigates de Branges-Rovnyak spaces whose elements are sections of a line bundle of multiplicative half-order differentials on a compact real Riemann surface. As a special case, we obtain a Beurling-Lax type theorem in the setting of the corresponding Hardy space on a finite bordered Riemann surface.
Uniform Random Variate Generation With The Linear Congruential Method,
2020
University of North Florida
Uniform Random Variate Generation With The Linear Congruential Method, Joseph Free
PANDION: The Osprey Journal of Research and Ideas
This report considers the issue of using a specific linear congruential generator (LCG) to create random variates from the uniform(0,1) distribution. The LCG is used to generate multiple samples of pseudo-random numbers and statistical computation techniques are used to assess whether those samples could have resulted from a uniform(0,1) distribution. Source code is included with this report in the appendix along with annotations.
Joint Lattice Of Reconstructability Analysis And Bayesian Network General Graphs,
2020
Portland State University
Joint Lattice Of Reconstructability Analysis And Bayesian Network General Graphs, Marcus Harris, Martin Zwick
Complex Systems Faculty Publications and Presentations
This paper integrates the structures considered in Reconstructability Analysis (RA) and those considered in Bayesian Networks (BN) into a joint lattice of probabilistic graphical models. This integration and associated lattice visualizations are done in this paper for four variables, but the approach can easily be expanded to more variables. The work builds on the RA work of Klir (1985), Krippendorff (1986), and Zwick (2001), and the BN work of Pearl (1985, 1987, 1988, 2000), Verma (1990), Heckerman (1994), Chickering (1995), Andersson (1997), and others. The RA four variable lattice and the BN four variable lattice partially overlap: there are ten …
Reconstructability Analysis And Its Occam Implementation,
2020
Portland State University
Reconstructability Analysis And Its Occam Implementation, Martin Zwick
Complex Systems Faculty Publications and Presentations
This talk will describe Reconstructability Analysis (RA), a probabilistic graphical modeling methodology deriving from the 1960s work of Ross Ashby and developed in the systems community in the 1980s and afterwards. RA, based on information theory and graph theory, resembles and partially overlaps Bayesian networks (BN) and log-linear techniques, but also has some unique capabilities. (A paper explaining the relationship between RA and BN will be given in this special session.) RA is designed for exploratory modeling although it can also be used for confirmatory hypothesis testing. In RA modeling, one either predicts some DV from a set of IVs …
Decomposition Of Certain Complete Graphs And Complete Multipartite Graphs Into Almost-Bipartite Graphs And Bipartite Graphs,
2020
Anna University, Chennai
Decomposition Of Certain Complete Graphs And Complete Multipartite Graphs Into Almost-Bipartite Graphs And Bipartite Graphs, G. Sethuraman, M. Sujasree
Theory & Applications of Graphs
In his classical paper [14], Rosa introduced a hierarchical series of labelings called ρ, σ, β and α labeling as a tool to settle Ringel’s Conjecture which states that if T is any tree with m edges then the complete graph K2m+1 can be decomposed into 2m + 1 copies of T . Inspired by the result of Rosa [14] many researchers significantly contributed to the theory of graph decomposition using graph labeling. In this direction, in 2004, Blinco et al. [6] introduced γ-labeling as a stronger version of ρ-labeling. A function g defined on the vertex set …
Image Dehazing From The Perspective Of Environmental Illumination.,
2020
Indian Statistical Institute
Image Dehazing From The Perspective Of Environmental Illumination., Sanchayan Santra Dr.
Doctoral Theses
Haze and fog are atmospheric phenomena where the particles suspended in the air obscure visibility by scattering the light propagating through the atmosphere. As a result only a part of the reflected light reaches the observer. So, the apparent intensity of the objects get reduced. Apart from that, the in-scatter of the atmospheric light creates a translucent veil, which is a common sight during haze. Image dehazing methods try to recover a haze-free version of a given image by removing the effects of haze.Although attempts have been made to accurately estimate the scene transmittance, the estimation of environmental illumination has …
Lattice Of Maximal-Primary Ideals In Quadratic Orders,
2020
University of new mexico
Lattice Of Maximal-Primary Ideals In Quadratic Orders, Ryan Bridges
Mathematics & Statistics ETDs
An order is a subring of the ring of integers of an algebraic extension, Peruginelli and Zanardo classified the lattices of orders with prime index inside te ring of integers of quadratic extensions of the rational numbers. The lattices are quite striking and have different layered structure depending on whether the prime is inert, split, or ramified. This thesis considers the orders which have prime power index inside the Gaussian integers. This is a nice generalization of the work of Peruginelli and Zanardo, and succeeds in a few classifications of specific instances of orders derived from inert primes.
Maintaining Rich Dialogic Interactions In The Transition To Synchronous Online Learning,
2020
Marquette University
Maintaining Rich Dialogic Interactions In The Transition To Synchronous Online Learning, Hyunyi Jung, Corey Brady
Mathematical and Statistical Science Faculty Research and Publications
A central premise across a variety of educational research and policy documents is that students learn with greater understanding in classrooms where they engage in exploring, reasoning, and communicating about their thinking (Hiebert and Wearne, 1993; National Council of Teachers of English, 2016; National Council of Teachers of Mathematics, 2000). With the recent emergency transition to remote online instruction in higher education, opportunities for rich synchronous learning have been diminished in many courses. Most instructors have had to adapt rapidly from in-person classroom settings to online environments without sufficient time and training. Accordingly, college students have shared concerns about the …
Expected Resurgence Of Ideals Defining Gorenstein
Rings,
2020
University of California, Riverside
Expected Resurgence Of Ideals Defining Gorenstein Rings, Eloísa Grifo, Craig Huneke, Vivek Mukundan
Department of Mathematics: Faculty Publications
Building on previous work by the same authors, we show that certain ideals defining Gorenstein rings have expected resurgence, and thus satisfy the stable Harbourne Conjecture. In prime characteristic, we can take any radical ideal defining a Gorenstein ring in a regular ring, provided its symbolic powers are given by saturations with the maximal ideal. While this property is not suitable for reduction to characteristic p, we show that a similar result holds in equicharacteristic 0 under the additional hypothesis that the symbolic Rees algebra of I is noetherian.
Guided Reinvention As A Context For Investigating Students' Thinking About Mathematical Language And For Supporting Students In Gaining Fluency,
2020
Portland State University
Guided Reinvention As A Context For Investigating Students' Thinking About Mathematical Language And For Supporting Students In Gaining Fluency, Kristen Vroom
Dissertations and Theses
Fluency with mathematical language is important for students' engagement in many disciplinary practices such as defining, conjecturing, and proving; yet, there is growing evidence that mathematical language is challenging for undergraduate students. This dissertation study draws on two design experiments with pairs of students who were supported to encode their mathematical meanings with more formal language. I aimed to investigate the teaching and learning of mathematical language, and particularly the language in statements with multiple quantifiers, by engaging students in this type of activity. In the first paper, I investigated the complex ways in which the students in my study …
Exact And Strongly Exact Filters,
2020
Chapman University
Exact And Strongly Exact Filters, M. A. Moshier, A. Pultr, A. L. Suarez
Mathematics, Physics, and Computer Science Faculty Articles and Research
A meet in a frame is exact if it join-distributes with every element, it is strongly exact if it is preserved by every frame homomorphism. Hence, finite meets are (strongly) exact which leads to the concept of an exact resp. strongly exact filter, a filter closed under exact resp. strongly exact meets. It is known that the exact filters constitute a frame FiltE(L) somewhat surprisingly isomorphic to the frame of joins of closed sublocales. In this paper we present a characteristic of the coframe of meets of open sublocales as the dual to the frame of strongly exact filters FiltsE(L).
On Pseudo-Spectral Factorization Over The Complex Numbers And Quaternions,
2020
Chapman University
On Pseudo-Spectral Factorization Over The Complex Numbers And Quaternions, Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
This paper is a continuation of the research of our previous work[5] and considers quaternionic generalized Carathéodory functions and the related family of generalized positive functions. It is addressed to a wide audience which includes researchers in complex and hypercomplex analysis, in the theory of linear systems, but also electric engineers. For this reason it includes some results on generalized Carathéodory functions and their factorization in the classic complex case which might be of independent interest. An important new result is a pseudo-spectral factorization and we also discuss some interpolation problems in the class of quaternionic generalized positive functions.
Geometry Aided Sonification,
2020
Ursinus College
Geometry Aided Sonification, Michael Tecce
Computer Science Summer Fellows
Sonification is the process of deriving an audio representation of a time series which conveys important information about that time series. Otology and vision science have established that humans process audio information more quickly than visual information, and sonification can convey data to the visually impaired. In our work, we implement pipelines using Python/Numpy, and we handle both ordinary 1D time series and multivariate time series. For 1D time series, we find that using data to modulate the pitch or timing of preselected sounds (such as sine waves) simply and effectively captures repeating patterns and anomalies/outliers within the data. To …
Geometry Aided Sonification,
2020
Ursinus College
Geometry Aided Sonification, Michael Tecce
Mathematics, Computer Science & Statistics Presentations
Sonification is the process of deriving an audio representation of a time series which conveys important information about that time series. Otology and vision science have established that humans process audio information more quickly than visual information, and sonification can convey data to the visually impaired. In our work, we implement pipelines using Python/Numpy, and we handle both ordinary 1D time series and multivariate time series. For 1D time series, we find that using data to modulate the pitch or timing of preselected sounds (such as sine waves) simply and effectively captures repeating patterns and anomalies/outliers within the data. To …
