Analytic Geometry And Calculus I, Ii, & Iii (Dalton), 2018 Dalton State College

#### Analytic Geometry And Calculus I, Ii, & Iii (Dalton), Thomas Gonzalez, Michael Hilgemann, Jason Schmurr

*Mathematics Grants Collections*

This Grants Collection for Analytic Geometry and Calculus I, II, & III was created under a Round Six 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

Dalton State College Apex Calculus, 2018 Dalton State College

#### Dalton State College Apex Calculus, Thomas Gonzalez, Michael Hilgemann, Jason Schmurr

*Mathematics Open Textbooks*

This text for Analytic Geometry and Calculus I, II, and III is a Dalton State College remix of APEX Calculus 3.0. The text was created through a Round Six ALG Textbook Transformation Grant.

Topics covered in this text include:

- Limits
- Derivatives
- Integration
- Antidifferentiation
- Sequences
- Vectors

Files can also be downloaded on the Dalton State College GitHub:

https://github.com/DaltonStateCollege/calculus-text/blob/master/Calculus.pdf

Branching Matrices For The Automorphism Group Lattice Of A Riemann Surface, 2018 Rose-Hulman Institute of Technology

#### Branching Matrices For The Automorphism Group Lattice Of A Riemann Surface, Sean A. Broughton

*Mathematical Sciences Technical Reports (MSTR)*

Let *S* be a Riemann surface and *G* a large subgroup of* Aut(S)* (*Aut(S)* may be unknown). We are particularly interested in regular *n*-gonal surfaces, i.e., the quotient surface *S/G* (and hence *S/Aut(S)*) has genus zero. For various *H *the ramification information of the branched coverings *S/K -> S/H* may be captured in a matrix. The ramification information, in particular strong branching, may be then be used in analyzing the structure of *Aut(S)*. The ramification information is conjugation invariant so the matrix's rows and columns may be indexed by conjugacy ...

Lie Sphere Geometry And Dupin Hypersurfaces, 2018 College of the Holy Cross

#### Lie Sphere Geometry And Dupin Hypersurfaces, Thomas E. Cecil

*Mathematics Department Faculty Scholarship*

These notes were originally written for a short course held at the Institute of Mathematics and Statistics, University of São Paulo, S.P. Brazil, January 9–20, 2012. The notes are based on the author’s book [17], *Lie Sphere Geometry With Applications to Submanifolds*, Second Edition, published in 2008, and many passages are taken directly from that book. The notes have been updated from their original version to include some recent developments in the field.

A hypersurface *M ^{n}*

^{−1}in Euclidean space

**R**

^{n}is proper Dupin if the number of distinct principal curvatures is constant on

*M ...*

On The Notion Of Scalar Product For Finite-Dimensional Diffeological Vector Spaces, 2018 University of Pisa

#### On The Notion Of Scalar Product For Finite-Dimensional Diffeological Vector Spaces, Ekaterina Pervova

*Electronic Journal of Linear Algebra*

It is known that the only finite-dimensional diffeological vector space that admits a diffeologically smooth scalar product is the standard space of appropriate dimension. In this note, a way to dispense withthis issue is considered, by introducing a notion of pseudo-metric, which, said informally, is the least-degeneratesymmetric bilinear form on a given space. This notion is applied to make some observations on subspaces which split off as smooth direct summands (providing examples which illustrate that not all subspaces do), and then to show that the diffeological dual of a finite-dimensional diffeological vector space always has the standard diffeology and in ...

The Convex Body Isoperimetric Conjecture In The Plane, 2018 Williams College

#### The Convex Body Isoperimetric Conjecture In The Plane, John Berry, Eliot Bongiovanni, Wyatt Boyer, Bryan Brown, Paul Gallagher, David Hu, Alyssa Loving, Zane Martin, Maggie Miller, Byron Perpetua, Sarah Tammen

*Rose-Hulman Undergraduate Mathematics Journal*

The Convex Body Isoperimetric Conjecture states that the least perimeter needed to enclose a volume within a ball is greater than the least perimeter needed to enclose the same volume within any other convex body of the same volume in *R ^{n}*. We focus on the conjecture in the plane and prove a new sharp lower bound for the isoperimetric profile of the disk in this case. We prove the conjecture in the case of regular polygons, and show that in a general planar convex body the conjecture holds for small areas.

Pythagorean Combinations For Lego Robot Building., 2018 Selected Works

#### Pythagorean Combinations For Lego Robot Building., Ronald I. Greenberg

*Ronald Greenberg*

This paper provides tips for LEGO robot construction involving bracing or gear meshing along a diagonal using standard Botball kits.

Pythagorean Approximations For Lego: Merging Educational Robot Construction With Programming And Data Analysis, 2018 Selected Works

#### Pythagorean Approximations For Lego: Merging Educational Robot Construction With Programming And Data Analysis, Ronald I. Greenberg

*Ronald Greenberg*

Abstract. This paper can be used in two ways. It can provide reference information for incorporating diagonal elements (for bracing or gear meshing) in educational robots built from standard LEGO kits. Alternatively, it can be used as the basis for an assignment for high school or college students to recreate this information; in the process, students will exercise skills in both computer programming and data analysis. Using the paper in the second way can be an excellent integrative experience to add to an existing course; for example, the Exploring Computer Science high school curriculum concludes with the units “Introduction to ...

From Convergence In Measure To Convergence Of Matrix-Sequences Through Concave Functions And Singular Values, 2017 Scuola Normale Superiore, Pisa, Italy

#### From Convergence In Measure To Convergence Of Matrix-Sequences Through Concave Functions And Singular Values, Giovanni Barbarino, Carlo Garoni

*Electronic Journal of Linear Algebra*

Sequences of matrices with increasing size naturally arise in several areas of science, such as, for example, the numerical discretization of differential and integral equations. An approximation theory for sequences of this kind has recently been developed, with the aim of providing tools for computing their asymptotic singular value and eigenvalue distributions. The cornerstone of this theory is the notion of approximating classes of sequences (a.c.s.), which is also fundamental to the theory of generalized locally Toeplitz (GLT) sequences, and hence to the spectral analysis of PDE discretization matrices. Drawing inspiration from measure theory, here it is introduced ...

Introduction To The Usu Library Of Solutions To The Einstein Field Equations, 2017 ian.anderson@usu.edu

#### Introduction To The Usu Library Of Solutions To The Einstein Field Equations, Ian M. Anderson, Charles G. Torre

*Tutorials on... in 1 hour or less*

This is a Maple worksheet providing an introduction to the USU Library of Solutions to the Einstein Field Equations. The library is part of the DifferentialGeometry software project and is a collection of symbolic data and metadata describing solutions to the Einstein equations.

Constructing A Square An Ancient Indian Way Activity, 2017 Pittsburg State University

#### Constructing A Square An Ancient Indian Way Activity, Cynthia J. Huffman Ph.D.

*Open Educational Resources - Math*

In this activity students use string to model one of the ways that was used in ancient India for constructing a square. The construction was used in building a temporary fire altar. The activity is based on a translation by Sen and Bag of the Baudhāyana-śulba-sūtra.

Euler Construction Activity, 2017 Pittsburg State University

#### Euler Construction Activity, Cynthia J. Huffman Ph.D.

*Open Educational Resources - Math*

Original sources of mathematics provide many opportunities for students to both do mathematics and to improve their problem solving skills. It is also interesting to explore original sources in new ways with the use of technology. In this activity, students can gain experience with dynamic geometry software and enhance their geometric intuition by working through a construction given by Euler in 1783.

Constructing A Square Indian Fire Altar Activity, 2017 Pittsburg State University

#### Constructing A Square Indian Fire Altar Activity, Cynthia J. Huffman Ph.D.

*Open Educational Resources - Math*

In this activity, we will model constructing a square fire altar with a method similar to one used by people in ancient India. The fire altars, which were made of bricks, had various shapes. Instructions for building the altars were in Vedic texts called *Śulba-sūtras*. We will follow instructions for constructing a square *gārhapatya *fire altar* *from the *Baudhāyana-śulba-sūtra*, which was written during the Middle Vedic period, about 800-500 BC.

Generalizations Of Coarse Properties In Large Scale Spaces, 2017 University of Tennessee, Knoxville

#### Generalizations Of Coarse Properties In Large Scale Spaces, Kevin Michael Sinclair

*Doctoral Dissertations*

Many results in large scale geometry are proven for a metric space. However, there exists many large scale spaces that are not metrizable. We generalize several concepts to general large scale spaces and prove relationships between them. First we look into the concept of coarse amenability and other variations of amenability on large scale spaces. This leads into the definition of coarse sparsification and connections with coarse amenability. From there, we look into an equivalence of Sako's definition of property A on uniformly locally finite spaces and prove that finite coarse asymptotic definition implies it. As well, we define ...

Localization Of Large Scale Structures, 2017 University of Tennessee, Knoxville

#### Localization Of Large Scale Structures, Ryan James Jensen

*Doctoral Dissertations*

We begin by giving the definition of coarse structures by John Roe, but quickly move to the equivalent concept of large scale geometry given by Jerzy Dydak. Next we present some basic but often used concepts and results in large scale geometry. We then state and prove the equivalence of various definitions of asymptotic dimension for arbitrary large scale spaces. Some of these are generalizations of asymptotic dimension for metric spaces, and many of the proofs are new. Particularly useful in proving the equivalences of the various definitions is the notion of partitions of unity, originally set forth by Jerzy ...

Mathematical Description And Mechanistic Reasoning: A Pathway Toward Stem Integration, 2017 Oakland University

#### Mathematical Description And Mechanistic Reasoning: A Pathway Toward Stem Integration, Paul J. Weinberg

*Journal of Pre-College Engineering Education Research (J-PEER)*

Because reasoning about mechanism is critical to disciplined inquiry in science, technology, engineering, and mathematics (STEM) domains, this study focuses on ways to support the development of this form of reasoning. This study attends to how mechanistic reasoning is constituted through mathematical description. This study draws upon Smith’s (2007) characterization of mathematical description of scientific phenomena as ‘‘bootstrapping,’’ where negotiating the relationship between target phenomena and represented relations is fundamental to learning. In addition, the development of mathematical representation presents a viable pathway towards STEM integration. In this study, participants responded to an assessment of mechanistic reasoning while cognitive ...

The Closure Operation As The Foundation Of Topology, 2017 Ursinus College

#### The Closure Operation As The Foundation Of Topology, Nicholas A. Scoville

*Topology*

No abstract provided.

A Compact Introduction To A Generalized Extreme Value Theorem, 2017 Ursinus College

#### A Compact Introduction To A Generalized Extreme Value Theorem, Nicholas A. Scoville

*Topology*

In a short paper published just one year prior to his thesis, Maurice Frechet gives a simple generalization one what we might today call the Extreme value theorem. This generalization is a simple matter of coming up with ``the right" definitions in order to make this work. In this mini PSP, we work through Frechet's entire 1.5 page paper to give an extreme value theorem in more general topological spaces, ones which, to use Frechet's newly coined term, are compact.

An Introduction To Topology For The High School Student, 2017 John Carroll University

#### An Introduction To Topology For The High School Student, Nathaniel Ferron

*Masters Essays*

No abstract provided.

Conference Program, 2017 University of Dayton

#### Conference Program, University Of Dayton

*Summer Conference on Topology and Its Applications*

Document provides a list of the sessions, speakers, workshops, and committees of the 32nd Summer Conference on Topology and Its Applications.