Index Catalog // ScholarsArchive@OSU

A Statistical Analysis and Interpretation of the HyperLogLog Algorithm

Creator:: Chick, Alexander
Abstract:: The HyperLogLog (HLL) algorithm is used to estimate the cardinality of large sets. This thesis gives a novel analysis of the HyperLogLog algorithm by using techniques from statistics and probability. Initially, closed form bounds for the mean and variance of the max of n independent and identically distributed geometric random...
Resource Type:: Dissertation

Coordinatization Activated: How Students Understand and Apply Coordinate-Independent Integral Equations to Physics Situations

Creator:: Mulder, Gregory S.
Abstract:: Physics problems that require integration, such as finding the center of mass of an object or finding the electric field from a continuous distribution of charge, are one type of problem that is difficult for introductory physics students to solve. These problems require students to define a coordinate system in...
Resource Type:: Dissertation

Geometry of Locomotion

Creator:: Ramasamy, Suresh
Abstract:: Many animals and robots move through the world by coupling cyclical changes in shape called gaits to an interaction with the environment. Because mobility is an important aspect of such robots, a key metric when evaluating design and performance of mobile robots is the efficiency of their optimal gaits. The...
Resource Type:: Dissertation

Mathematics Graduate Student Instructors as a Complex System

Creator:: Gibbons, Claire J.
Abstract:: Mathematics Graduate Student Instructors (GSIs) have a significant impact on the teaching and learning of mathematics in post-secondary contexts through their work as instructors of record, tutors, graders, and recitation, laboratory, or discussion leaders for mathematics courses. Perhaps more importantly, GSIs are future teachers of mathematics: more than 60 percent...
Resource Type:: Dissertation

Variations of Mathematics in College Algebra Instruction : An Investigation Through the Lenses of Three Observation Protocols

Creator:: Gibbons, Claire J.
Abstract:: College Algebra is a prerequisite for calculus and is thus an important stepping stone in the careers of STEM-intending undergraduates. However, College Algebra has low pass rates across the United States, interrupting students’ pathways to success. To address this concern, a research-oriented university in the Northwest United States restructured its...
Resource Type:: Masters Thesis

Engagement in a community of learners as a mediating agent toward the construction of technological pedagogical content knowledge (TPACK) in an online Master's program

Creator:: Gillow-Wiles, Henry
Abstract:: This study investigates how teachers develop and extend their understanding and knowledge of teaching and learning with digital technologies in a primarily online Master of Science program. The investigation focuses on exploring the relationship between developing an online community of learners and the construction of technological pedagogical and content knowledge...
Resource Type:: Dissertation

Fundamental solution to the heat equation with a discontinuous diffusion coefficient with applications to Skew Brownian Motion and oceanography

Creator:: Harada, Sharon Julie
Abstract:: In this paper, we derive the fundamental solution to the heat equation with a discontinuous diffusion coefficient in the free space, with an absorbing boundary, and with a reflecting boundary. We use the fundamental solution with an absorbing boundary to make connections with the transition probability density of absorbed Skew...
Resource Type:: Masters Thesis

Learning classification rules by randomized iterative local search

Creator:: Chisholm, Michael (Michael Andrew), 1974-
Abstract:: Learning easily understandable decision rules from examples is one of the classic problems in machine learning. Most learning algorithms for this problem employ some variation of a greedy separate-and-conquer algorithm. In this paper, we describe a system called LERILS that learns highly accurate and comprehensible rules from examples using a...
Resource Type:: Masters Thesis

The cohomology rings of seven dimensional primitive cohomogeneity one manifolds

Creator:: Ultman, Shari K.
Abstract:: A striking feature in the study of Riemannian manifolds of positive sectional curvature is the narrowness of the collection of known examples. In this thesis, we examine the structure of the cohomology rings of three families of compact simply connected seven dimensional Riemannian manifolds that may contain new examples of...
Resource Type:: Dissertation

Triangular billiards surfaces and translation covers

Creator:: Schmurr, Jason Peter
Abstract:: 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.
Resource Type:: Dissertation

ScholarsArchive@OSU

A Statistical Analysis and Interpretation of the HyperLogLog Algorithm

Coordinatization Activated: How Students Understand and Apply Coordinate-Independent Integral Equations to Physics Situations

Geometry of Locomotion

Mathematics Graduate Student Instructors as a Complex System

Variations of Mathematics in College Algebra Instruction : An Investigation Through the Lenses of Three Observation Protocols

Engagement in a community of learners as a mediating agent toward the construction of technological pedagogical content knowledge (TPACK) in an online Master's program

Fundamental solution to the heat equation with a discontinuous diffusion coefficient with applications to Skew Brownian Motion and oceanography

Learning classification rules by randomized iterative local search

The cohomology rings of seven dimensional primitive cohomogeneity one manifolds

Triangular billiards surfaces and translation covers

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