Dalton State College APEX Calculus

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 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/1016/thumbnail.jp

Analytic Geometry and Calculus I, II, & III (Dalton)

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 Reporthttps://oer.galileo.usg.edu/mathematics-collections/1024/thumbnail.jp

Cayley Graphs on Billiard Surfaces

In this article we discuss a connection between two famous constructions in mathematics: a Cayley graph of a group and a (rational) billiard surface. For each rational billiard surface, there is a natural way to draw a Cayley graph of a dihedral group on that surface. Both of these objects have the concept of "genus" attached to them. For the Cayley graph, the genus is defined to be the lowest genus amongst all surfaces that the graph can be drawn on without edge crossings. We prove that the genus of the Cayley graph associated to a billiard surface arising from a triangular billiard table is always zero or one. One reason this is interesting is that there exist triangular billiard surfaces of arbitrarily high genus , so the genus of the associated graph is usually much lower than the genus of the billiard surface.Comment: 10 pages, 9 figure

Triangular billiards surfaces and translation covers

We identify all translation covers among triangular billiards surfaces. Our main tools are the J-invariant of Kenyon and Smillie and a property of triangular billiards surfaces, which we call fingerprint type, that is invariant under balanced translation covers

Two Stories and Four Concepts: Searching for a Theory of Supply Chains

This paper suggests directions for developing a comprehensive theory of supply chains. It uses two vignettes, one on Henry Ford\u27s Fordlandia experiment, and the other a brief description of Wal-Mart\u27s supply chain. It starts the exploration of supply chain management by critiquing four widely published definitions and then proposes an alternative definition. It then goes on to look at supply chain management from the perspective of game theory and from the perspective of embeddedness. It concludes with suggests for further exploration to lead toward a comprehensive theory of supply chains

Monodromy Groups of Dessins d'Enfant on Rational Triangular Billiards Surfaces

A dessin d'enfant, or dessin, is a bicolored graph embedded into a Riemann surface, and the monodromy group is an algebraic invariant of the dessin generated by rotations of edges about black and white vertices. A rational billiards surface is a two dimensional surface that allows one to view the path of a billiards ball as a continuous path. In this paper, we classify the monodromy groups of dessins associated to rational triangular billiards surfaces