Physical Sciences and Mathematics Commons^™

Analytic Geometry And Calculus I, Shaun V. Ault, Sudhir Goel

Mathematics Grants Collections

This Grants Collection for Analytic Geometry and Calculus I was created under a Round Two 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 Report

Comparison Of Experimental And Theoretical Electron-Impact-Ionization Triple-Differential Cross Sections For Ethane, Esam Ali, Kate Nixon, Andrw Murray, Chuangang Ning, James Colgan, Don H. Madison

Physics Faculty Research & Creative Works

We have recently examined electron-impact ionization of molecules that have one large atom at the center, surrounded by H nuclei (H₂O, NH₃, CH₄). All of these molecules have ten electrons; however, they vary in their molecular symmetry. We found that the triple-differential cross sections (TDCSs) for the highest occupied molecular orbitals (HOMOs) were similar, as was the character of the HOMO orbitals which had a p-type "peanut" shape. In this work, we examine ethane (C₂H₆) which is a molecule that has two large atoms surrounded by H nuclei, so that …

Coplanar Asymmetric Angles And Symmetric Energy Sharing Triple Differential Cross Sections For 200 Ev Electron-Impact Ionization Of Ar (3p), Zehra Nur Ozer, Sadek M. Amami, Onur Varol, Murat Yavuz, Mevlut Dogan, Don H. Madison

Physics Faculty Research & Creative Works

We have measured triple differential cross sections (TDCSs) for electron-impact ionization of the 3p shell of Ar at 200 eV incident electron energy. The experiments have been performed in coplanar asymmetric energy sharing geometry. The experimental results are compared with the theoretical models of three body distorted wave (3DW) and distorted wave Born approximation (DWBA).

Quantization Of Two Types Of Multisymplectic Manifolds, Baran Serajelahi

Electronic Thesis and Dissertation Repository

This thesis is concerned with quantization of two types of multisymplectic manifolds that have multisymplectic forms coming from a Kahler form. In chapter 2 we show that in both cases they can be quantized using Berezin-Toeplitz quantization and that the quantizations have reasonable semiclassical properties.

In the last chapter of this work, we obtain two additional results. The first concerns the deformation quantization of the (2n-1)-plectic structure that we examine in chapter 2, we make the first step toward the definition of a star product on the Nambu-Poisson algebra (C^{\infty}(M),{.,...,.}). The second result concerns the algebraic properties of the generalized …

Differential Geometry: Curvature And Holonomy, Austin Christian

Math Theses

We develop the basic language of differential geometry, including smooth manifolds, bundles, and differential forms. Once this background is established, we explore parallelism in smooth manifolds -- in particular, in Riemannian manifolds -- and conclude by presenting a proof of the Ambrose-Singer theorem, which relates parallelism (holonomy) to curvature in principal bundles.

Schwarzschild Spacetime And Friedmann-Lemaitre-Robertson-Walker Cosmology, Zachary Cohen

Honors Scholar Theses

The advent of General Relativity via Einstein's field equations revolutionized our understanding of gravity in our solar system and universe. The idea of General Relativity posits that gravity is entirely due to the geometry of the universe -- that is, the mass distribution throughout the universe results in the "curving" of spacetime, which gives us the physics we see on a large scale. In the framework of General Relativity, we find that the universe behaves differently than was predicted in the model of gravitation developed by Newton. We will derive the general relativistic model for a simple system near a …

Geometry: Drawing From The Islamic Tradition, Carol Bier

Carol Bier

Getting students involved in careful observation and analysis and encouraging their exploration of cultural forms of expression is an excellent means of introducing mathematical ideas. Geometric patterns abound in Islamic art and architecture. Exhibiting great ingenuity over the centuries, Muslim artists and craftsmen created beautiful patterns to adorn architectural monuments and exquisite objects. The Alhambra in Spain and the Taj Mahal in India offer the most famous examples of extraordinary patterns using brick and glazed tile, or carved and inlaid marble. Other examples of patterns are made using metal, wood, and fiber. Students may gain conceptual and theoretical understanding of …

Probleme De Geometrie Și Trigonometrie, Compilate Și Rezolvate, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

255 Compiled And Solved Problems In Geometry And Trigonometry, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Identifying Similar Polygons: Comparing Prospective Teachers’ Routines With A Mathematician’S, Sasha Wang

Mathematics Faculty Publications and Presentations

This paper reports two prospective teachers' and a mathematician's ways of identifying similar triangle and hexagons through the analysis of routines, a characteristic of geometric discourse. The findings show that visual recognition was a common approach for the mathematician as wells as the two prospective teachers. However, when asked for justification, their routines of identifying similar polygons diverged. The paper also discusses the implication of classroom discourse practices to enhance prospective teachers' communication and reasoning skills while learning geometric concepts such as similarity.

A Critique Of A Student-Centered Learning Approach Used In A Geometry Classroom, Alana Blackwell Day

LSU Master's Theses

This thesis offers a framework for identifying effective classroom materials to support student-centered learning. Based on a review of published studies on effective classroom activities, as well as theses by Louisiana Math and Science Teachers Institute (LaMSTI) graduates, we identify promising characteristics. We employed these in five lessons, refined them into questions, and offer in final form for use.

Writing In The Geometry Classroom, Amy Lynn Rome

LSU Master's Theses

This study sought a time-efficient way to implement writing in ninth-grade Geometry. Students wrote responses to five expository writing prompts spread out over the spring semester of the 2014-2015 school year. Students’ first attempts were graded and returned to them along with feedback in the form of a teacher-written exemplar. Students rewrote assignments to improve their grades. All first and second attempts were collected and evaluated. We found that students were more successful after seeing the exemplar. Moreover, on assignments occurring later in the semester, more students were able to score in the top categories of the writing assignments on …