Catherine Buell

Catherine Buell
Fitchburg State University · Department of Mathematics

Doctor of Philosophy

About

17
Publications
2,622
Reads
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18
Citations
Introduction
Ethics in mathematics, social justice mathematics. Algebraic group theory
Additional affiliations
September 2014 - present
Fitchburg State University
Position
  • Professor
August 2011 - June 2014
Bates College
Position
  • Professor (Assistant)
Education
August 2006 - May 2011
North Carolina State University
Field of study
  • Mathematics
August 2002 - May 2006
Springfield College
Field of study
  • Mathematics and Dance

Publications

Publications (17)
Article
In this paper we will discuss the orbits of the fixed-point group on the tori of the generalized symmetric spaces of SL2(k) where k is a finite field. Specifically, we will provide a characterization and classification of the maximal k-split and k-anisotropic tori.
Article
Full-text available
In this introduction to the PRIMUS Special Issue on Mathematics for Social Justice we provide a brief history of social justice in the context of undergraduate mathematics pedagogy and explain the purpose and motivation behind this movement in undergraduate education.
Chapter
Full-text available
We have created an open access online platform for using semantic workflows to analyze artistic style in paintings. We have implemented workflows for both standard computer vision image processing techniques and state-of-the-art methods such as convolutional neural networks to analyze images. These workflows can be used online by non-experts withou...
Article
As an interdisciplinary team, we set out to create an applied statistics course which would cover the traditional introductory statistics topics in a consistent framework of social justice. The goal was to motivate students to understand and learn math while deepening their understanding of the interplay at local and global levels of social and eco...
Conference Paper
Full-text available
In this paper, we present initial work towards creating an intelligent interface that can act as an open access laboratory for visual stylometry called WAIVS, Workflows for Analysis of Images and Visual Stylometry. WAIVS allows scholars, students, and other interested parties to explore the nature of artistic style using cutting-edge research metho...
Article
Full-text available
Using Intelligent Workflows to Analyze Artistic Style USC Information Sciences Institute (ISI) alumnus Ricky J. Sethi and his colleagues at Fitchburg State University in Massachusetts are using ISI's WINGS workflow system for art history in the WAIVS (Workflows for Analysis of Images and Visual Stylometry) project. WAIVS workflows were demonstrated...
Chapter
In this chapter, we determine the orbits of the fixed-point group on the unipotent elements in the generalized symmetric space for each involution of \({\mathrm{SL}}_2(\mathbb {F}_q)\) with \({\mathrm{char}}\left (\mathbb {F}_q \right ) \neq 2\). We discuss how the generalized symmetric spaces can be decomposed into semisimple elements and unipoten...
Article
In this paper we extend previous results regarding SL2(k) over any finite field k by investigating the structure of the symmetric spaces for the family of special linear groups SLn(k) for any integer n>2. Specifically, we discuss the generalized and extended symmetric spaces of SLn(k) for all conjugacy classes of involutions over a finite field of...
Article
Full-text available
Artistic style plays a critical role in our commerce with artworks. Artworks are artifacts that mediate a complex communicative exchange between artists and consumers, or more broadly among members of an artistic community. Artistic style is a perceptible quality of the appearance of an artwork that enables us to recognize it as belonging to one ca...
Article
In this paper we will discuss the generalized symmetric spaces for SL2(Fq) and GL2(Fq). Specifically we will characterize the structure of these spaces and prove that when the characteristic of Fq is not equal to two the extended generalized symmetric space is equal to the generalized symmetric space for SL2(Fq) and nearly equal for GL2(Fq) for all...
Article
Full-text available
It is widely accepted in the mathematics education community that pedagogies oriented toward inquiry are aligned with a constructivist theory of learning and that these pedagogies effectively support students’ learning of mathematics. In order to promote such an orientation, we first separate the idea of inquiry from its conception as a collection...
Article
Symmetric k-varieties have been a topic of interest in several fields of mathematics and physics since the 1980’s. For \( k\, =\,\mathbb{R} \), symmetric \( \mathbb{R} \)-varieties are commonly called real symmetric spaces; however, the generalization over other fields play a role in the study of arithmetic subgroups, geometry, singularity theory,...

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Cited By

Projects

Project (1)
Project
Visual Stylometry Team, including Bill Seeley, Wins NEH Digital Humanities Start-Up Grant Dr. Catherine Buell, PhD (Assistant Professor of Mathematics, Fitchburg State University), Dr. William Seeley, Ph.D. (Lecturer in Philosophy, Bates College), and Ricky Sethi (Associate Professor of Computer Science, Fitchburg State University) have received a National Endowment of the Humanities Digital Humanities Start-Up Grant for their project Scientific Workflows, Image Analysis, and Visual Stylometry in the Digital Analysis of Art. The goal of the grant is to develop a digital image analysis tool for studying paintings called WAIVS (Workflows for Analysis of Images and Visual Stylometry). WAIVS will be powerful enough to support advanced academic research in computer science, cognitive science, art history, and the philosophy of art while at the same time providing a user-friendly interface accessible to students and researchers with little or no computer science background. Dr. Buell’s and Dr. Seeley’s collaborative work on visual stylometry began in connection with a course on applied linear algebra taught by Dr. Buell while she was a Vising Assistant Professor in the Mathematics Department at Bates in Fall 2014. An interdisciplinary team of students worked with Dr. Buell and Dr. Seeley to program image analysis methods (Linnea Brotz ’15, Art and Visual Culture; Peter Cole ’15, Physics; Kathleen Morrill ’15, Biological Chemistry; Devon Brown ’14, Mathematics; and Brent Talbot ’14, Politics). Using entropy, foreground/background analysis, and discrete tonal features, the students were able to successfully train the computer to sort paintings by school (Impressionist from Hudson River School landscapes) and artist within each school (Monet from Renoir and Sisley). Based on this initial proof of concept, Dr. Sethi joined the collaboration, resulting in this new grant from the NEH.