Mathematics Commons^™

Collaborating To Meet The Standards: Implications For Professional Development, Erik D. Jacobson, Laura M. Singletary

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Researchers from the University of Georgia interviewed 27 Mathematics 1 teachers about their experiences during the first year of the high school implementation of the Georgia Performance Standards (GPS). We report our findings about teachers’ experiences with Mathematics 1 professional development and describe features of professional development that teachers identified as most beneficial. Some teachers offered suggestions for professional development that differed from the professional development they had experienced. In addition, we found that many teachers used collaborative strategies to meet the demands of the new curriculum and the perceived inadequacies of resources and training. We discuss the various models …

Extending K-8 Mathematics Concepts In Alternate Bases, Dianna J. Spence

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

When learning to represent mathematics with manipulatives, many pre-service K-8 teachers rely on memorized rote procedures to perform the associated mathematical tasks; then they arrange the manipulatives to match their result, often with minimal understanding of underlying mathematical connections. In a Number and Operations course for K-8 pre-service teachers, a portion of the class was conducted in alternate bases: Base 6 and Base 8 Blocks were used to model operations with integers to facilitate deeper understanding of the number systems and arithmetic processes being represented. Fractions and decimals were later covered only in Base 10. On midterm and final exams, …

Basic Skills Testing In Math 2008, Susie M. Lanier, Sharon Taylor, Donna B. Saye

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Math 2008 is an Area F course for early childhood majors in the University System of Georgia. The course covers basic skills that pre-service teachers will most likely be teaching in their career. At Georgia Southern University, many students in the course do not possess or have forgotten these basic skills. In Fall 2009, a basic skills test was implemented for Math 2008. Students must earn a score of 90 or higher on the test in order to pass the course. The test not only serves to let students know their areas of weakness, but also informs the instructor’s teaching. …

Embracing The Vision: Our Work With Teachers Implementing Gps, Sarah Ledford, Wendy B. Sanchez

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Abstract: In 2005, three Kennesaw State University mathematics education faculty members began a series of workshops titled “Implementing the Georgia Performance Standards [GPS]: Embracing the Vision.” This workshop series has been underwritten by Georgia’s Teacher Quality Higher Education Program. The first series of workshops began with 6th grade teachers the first year the GPS was implemented and the project has been funded each subsequent year since its inception. Currently, we are working with Math III teachers as they implement the course for the first time. The initial focus for the project was on conceptual understanding versus procedural understanding, writing tasks …

Linear Stochastic State Space Theory In The White Noise Space Setting, Daniel Alpay, David Levanony, Ariel Pinhas

Mathematics, Physics, and Computer Science Faculty Articles and Research

We study state space equations within the white noise space setting. A commutative ring of power series in a countable number of variables plays an important role. Transfer functions are rational functions with coefficients in this commutative ring, and are characterized in a number of ways. A major feature in our approach is the observation that key characteristics of a linear, time invariant, stochastic system are determined by the corresponding characteristics associated with the deterministic part of the system, namely its average behavior.

Krein Systems And Canonical Systems On A Finite Interval: Accelerants With A Jump Discontinuity At The Origin And Continuous Potentials, Daniel Alpay, I. Gohberg, M. A. Kaashoek, L. Lerer, A. Sakhnovich

Mathematics, Physics, and Computer Science Faculty Articles and Research

This paper is devoted to connections between accelerants and potentials of Krein systems and of canonical systems of Dirac type, both on a finite interval. It is shown that a continuous potential is always generated by an accelerant, provided the latter is continuous with a possible jump discontinuity at the origin. Moreover, the generating accelerant is uniquely determined by the potential. The results are illustrated on pseudo-exponential potentials. The paper is a continuation of the earlier paper of the authors [1] dealing with the direct problem for Krein systems.

Regular Functions On The Space Of Cayley Numbers, Graziano Gentili, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we present a new definition of regularity on the space Ç of Cayley numbers (often referred to as octonions), based on a Gateaux-like notion of derivative. We study the main properties of regular functions, and we develop the basic elements of a function theory on Ç. Particular attention is given to the structure of the zero sets of such functions.

Meaningful Distributed Instruction— Conceptual Previews For Symbolic Procedures, Edward C. Rathmell

Faculty Work

Understanding a symbolic procedure means far more than “getting the right answer.” A mathematical symbolic procedure or written skill involves step-bystep thinking that leads from a computational problem to a solution. Memorizing this step-by-step procedure may enable a student to answer the problem, even answer it correctly. Yes, that is important, but understanding means much more.

Positive Solutions Of The (N-1, 1) Conjugate Boundary Value Problem, Bo Yang

Faculty Articles

We consider the (n - 1, 1) conjugate boundary value problem. Some upper estimates to positive solutions for the problem are obtained. We also establish some explicit sufficient conditions for the existence and nonexistence of positive solutions of the problem.

Morphing Of Triangular Meshes In Shape Space, Stefanie Wuhrer, Prosenjit Bose, Chang Shu, Joseph O'Rourke, Alan Brunton

Computer Science: Faculty Publications

We present a novel approach to morph between two isometric poses of the same non-rigid object given as triangular meshes. We model the morphs as linear interpolations in a suitable shape space S. For triangulated 3D polygons, we prove that interpolating linearly in this shape space corresponds to the most isometric morph in R³ . We then extend this shape space to arbitrary triangulations in 3D using a heuristic approach and show the practical use of the approach using experiments. Furthermore, we discuss a modified shape space that is useful for isometric skeleton morphing. All of the newly presented …

Support Varieties And Representation Type Of Small Quantum Groups, Jorg Feldvoss, Sarah Witherspoon

University Faculty and Staff Publications

In this paper, we provide a wildness criterion for any finite dimensional Hopf algebra with finitely generated cohomology. This generalizes a result of Farnsteiner to not necessarily cocommutative Hopf algebras over ground fields of arbitrary characteristic. Our proof uses the theory of support varieties for modules, one of the crucial ingredients being a tensor product property for some special modules. As an application, we prove a conjecture of Cibils stating that small quantum groups of rank at least two are wild.

Statistical Analysis Of Wastewater Remediation And Bio-Fuels Production Of Algae, Jay D. Jones

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The Logan city wastewater treatment system consists of a series of seven large aerated ponds (460 acres) that biologically treats 15 million gallons per day of wastewater from Logan city and six other communities. Tighter regulations of allowed phosphorus levels in the effluent have recently been implemented due to environmental concerns of a downstream reservoir. The Biological Engineering program at Utah State University, the Bio-fuels Center, the Utah Water Research Laboratory (UWRL) and the city of Logan are working together to remediate the wastewater treatment system using microalgae. Algal growth requires the uptake of phosphorus. Thus, phosphorus in the effluent …

A Comparison Of Prediction Methods Of Functional Autoregressive Time Series, Devin Didericksen

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Functional data analysis (FDA) is a relatively new branch of statistics that has seen a lot of expansion recently. With the advent of computer processing power and more efficient software packages we have entered the beginning stages of applying FDA methodology and techniques to data. Part of this undertaking should include an empirical assessment of the effectiveness of some of the tools of FDA, which are sound on theoretical grounds. In a small way, this project helps advance this objective.

This work begins by introducing FDA, scalar prediction techniques, and the functional autoregressive model of order one - FAR(1). Two …

Assessing The Precision And Accuracy In A Small Sample Of Actical Devices, Peter Sherick

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Actigraphy is an increasingly popular approach in medicine to assess patient activity levels in a variety of scenarios. The devices are essentially accelerometers encased in a write-watch type assembly. This project sought to determine the device precision and accuracy for the Actical model. In a sample of four Acticals, it was found that intra-device variability was minimal. However, one device was found to be statistically biased in comparison to the other three. This bias could have adverse effects on aggregated or magnitude dependent data analysis. Also, inter-device comparisons may be problematic.

Bass’ Nk Groups And Cd H-Fibrant Hochschild Homology, G. Cortiñas, C. Haesemeyer, Mark E. Walker, C. Weibel

Department of Mathematics: Faculty Publications

The K-theory of a polynomial ring R[t ] contains the K-theory of R as a summand. For R commutative and containing Q, we describe K∗(R[t ])/K∗(R) in terms of Hochschild homology and the cohomology of Kähler differentials for the cdh topology.

We use this to address Bass’ question, whether K_n(R) = K_n(R[t ]) implies K_n(R) = K_n(R[t₁, t₂]). The answer to this question is affirmative when R is essentially of …

Generalized Fourier-Feynman Transforms, Convolution Products, And First Variations On Function Space, Seung Jun Chang, Jae Gil Choi, David Skough

Department of Mathematics: Faculty Publications

In this paper we examine the various relationships that exist among the first variation, the convolution product and the Fourier-Feynman transform for functionals of the form F(x) = f((α₁, x), . . . , (α_n, x)) with x in a very general function space C_a,b[0,T].

Review: Pythagoras’ Revenge: A Mathematical Mystery; The Housekeeper And The Professor, Susan Jane Colley

Faculty & Staff Scholarship

No abstract provided.

Book Review: Visual Motion Of Curves And Surfaces, Andrei Ludu

Publications

This is Dr. Ludu's review of the book Visual Motion of Curves and Surfaces by Roberto Cipolla and Peter Giblin. Published by Cambridge University Press in 2009. ISBN: 978-0-521-63251-5.

Discrete-Time Multi-Scale Systems, Daniel Alpay, Mamadou Mboup

Mathematics, Physics, and Computer Science Faculty Articles and Research

We introduce multi-scale filtering by the way of certain double convolution systems. We prove stability theorems for these systems and make connections with function theory in the poly-disc. Finally, we compare the framework developed here with the white noise space framework, within which a similar class of double convolution systems has been defined earlier.

Fusion Of Imprecise Qualitative Information, Florentin Smarandache, Xinde Li, Xianzhong Dai, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we present a new 2-tuple linguistic representation model, i.e. Distribution Function Model (DFM), for combining imprecise qualitative information using fusion rules drawn from Dezert-Smarandache Theory (DSmT) framework. Such new approach allows to preserve the precision and efficiency of the combination of linguistic information in the case of either equidistant or unbalanced label model. Some basic operators on imprecise 2-tuple labels are presented together with their extensions for imprecise 2-tuple labels. We also give simple examples to show how precise and imprecise qualitative information can be combined for reasoning under uncertainty. It is concluded that DSmT can deal …