Applications of fourier analysis to intersection bodies

The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.Title from title screen of research.pdf file (viewed on June 16, 2009)Vita.Includes bibliographical references.Thesis (Ph. D.) University of Missouri-Columbia 2008.Dissertations, Academic -- University of Missouri--Columbia -- Mathematics.The concept of an intersection body is central for the dual Brunn-Minkowski theory and has played an important role in the solution of the Busemann-Petty problem. A more general concept of [kappa]-intersection bodies is related to the generalization of the Busemann-Petty problem. We are interested in comparing classes of [kappa]-intersection bodies. In the first chapter we present the result that was published in J. Schlieper, A note on [kappa]-intersection bodies, Proceedings American. Mathematical Society,135 (2007), 2081-2088. The result examines the conjecture that the classes of [kappa]-intersection bodies increase with [kappa]. In particular, the result constructs a 4- intersection body that is not a 2-intersection body. The second chapter is concerned with the geometry of spaces of Lorentz type. We define a 1-homogeneous functional based on Lorentz type norms. Consider the family of norms [nearest integer function]x[nearest integer function][pi][alpha] = [alpha]i₁xq₁+ [alpha]inxqn₁/q where [alpha] = ([alpha]₁, . . . , [alpha]n) with [alpha]₁ [pi], . . . ,[pi] [alpha] [less than]0 and [pi]([alpha]) is [alpha] permutation of the vector [alpha]. Define a 1-homogeneous functional based on this family of norms as follows ... We examine the geometric properties of the space (Rn, [kappa].[kappa]k). First, we determine the conditions when the star body (Rn, [kappa].[kappa]) is a [kappa]-intersection body. Second, we find the extremal sections of the star body (Rn, [kappa].[kappa]). Throughout this work we use the Fourier Analytic methods that were recently developed

Armstrong Calculus

Authors\u27 Description: An open-source textbook for calculus. The text is mostly an adaptation of two other excellent open- source calculus textbooks: Active Calculus by Dr. Matt Boelkins of Grand Valley State University and Drs. Gregory Hartman, Brian Heinold, Troy Siemers, Dimplekumar Chalishajar, and Jennifer Bowen of the Virginia Military Institute and Mount Saint Mary\u27s University. Both of these texts can be found at http://aimath.org/textbooks/approved-textbooks/. The authors of this text have combined sections, examples, and exercises from the above two texts along with some of their own content to generate this text. The impetus for the creation of this text was to adopt an open-source textbook for Calculus while maintaining the typical schedule and content of the calculus sequence at our home institution. Accessible files with optical character recognition (OCR) and auto-tagging provided by the Center for Inclusive Design and Innovation.https://oer.galileo.usg.edu/mathematics-textbooks/1000/thumbnail.jp

Elementary Statistics

This Grants Collection for Elementary Statistics was created under a Round Four ALG Textbook Transformation Grant. Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process. Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials: Linked Syllabus Initial Proposal Final Reporthttps://oer.galileo.usg.edu/mathematics-collections/1003/thumbnail.jp

Proposal and Report for Grant 024: Calculus I, Calculus II, Calculus III

This proposal and final report are from the first ALG grants finishing between Spring 2015 and Spring 2016. They have been republished in the repository in order to move our first reports over from being hosted on the ALG website

Integrating Research into STEM Teacher Prep through Professional Learning Communities

Professional learning communities are commonplace in K-12 education as the avenue through which teachers engage in meaningful professional development. Armstrong MASTERS is an NSF Noyce scholarship program through which we have implemented a novel and replicable model for PLCs, called Future Teacher Professional Learning Communities. In these communities, our Noyce scholars are immersed in research on best-practices in STEM teaching, with an emphasis on active learning. They apply this research to the development and review of classroom materials, and engage in generating new results through classroom research projects with Noyce faculty. While our FTPLCs exhibit the essential characteristics of learning communities as documented in the literature, they are greatly strengthened by the breadth of their membership. Education and STEM faculty from Armstrong, teachers from local schools, and student scholars share experience and expertise. This composition of educators facilitates the integration of content knowledge, pedagogy, teacher practice knowledge, and research into the development of the Noyce scholars as teachers. In this session, we will describe our PLC model and its outcomes, including the impact on all members. Session participants will engage in and critique several learning community activities, including community building, lesson plan analysis, and production of a collective literature review

Meta-cognitive Enhancement of Cooperative Learning: Promoting Conceptual Understanding in Mathematics

There is a growing body of evidence suggesting that the use of research based models of cooperative learning as well as the promotion of metacognitive thinking strategies develop higher order thinking skills in students. Through a collaborative research learning community comprised of both faculty and undergraduate students we have developed and piloted a set of five cooperative learning modules that are focused on essential concepts in calculus, integrated into authentic tasks, and enhanced with meta-cognitive thinking strategies to promote the attainment of conceptual understanding. Student work samples and interview data collected during the pilot have provided preliminary evidence that higher levels of conceptual understanding are achieved through these experiences. The objectives of this session are to share and discuss an adaptable instructional model that integrates cooperative learning environments, authentic tasks, and metacognitive questioning strategies. Attendees will engage in cooperative learning groups to investigate the changing composition of the United States work-force using mathematical concepts which are accessible to all, regardless of discipline or expertise. Participants will have the opportunity to critique the cooperative learning activity, share experiences in this area, and discuss the potential value added by the metacognitive questioning strategies

Integrating Research into STEM Teacher Prep Through Professional Learning Communities

This presentation was given at the 9th Annual Scholarship of Teaching and Learning (SoTL) Commons Conference