Physical Sciences and Mathematics Commons^™

Mathematical Functions: An Interactive Emodule, Sarah Jean Moody

Undergraduate Honors Capstone Projects

The National Library of Virtual Manipulatives (NLVM, http://nlvm.usu.edu/) is a widely used and highly praised teaching/learning resource for school mathematics. The NLVM is the result of a four-year USU project, funded primarily by the National Science Foundation, Award #9819107, to create a web-based, freely accessible, library of interactive virtual manipulatives to help students learn basic mathematics concepts. During a typical school day, the NLVM server receives more than 3 million hits.

Wavelet Factorization Via A Homogenization Analogy For Solutions Of Linear Systems, Andrea Van Sickle

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

A system of linear equations can be solved using a factorization method that produces a wavelet structure and is akin to a homogenization process used in determining the solution of differential equations. The method is dependant on the particular structure of Hadamard matrices and their implementation in a similarity transform. This paper details the development of such a method for systems of size 2n x 2n, including establishing the theoretical underpinnings necessary to define an orthogonal transform. Also, we present the development of an algorithm to implement the method for a simple 2 x 2 system, which will then be …

Simulation Study Of Estimation And Inference In Factor Analysis: Normal And Non-Normal Noise Distributions, Ping Zhang

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

Objective: To study the estimation and inference m factor analyses when the data have normal or non-normal noise distributions.

Methods: Population data were created in package R with a specified number of factors, factor structure and observable variables with known loadings. Then, repeated simple random samples (SRS's) were taken from the population, independently. The maximum likelihood method with varimax rotation was used to perform factor analysis and inference on each sampled dataset. Factor loadings were estimated to determine if the estimation of the loadings was (approximately) unbiased and/or efficient for each specified population and chi-square x2-statistics were obtained to test …

Special Classification Models For Lichens In The Pacific Northwest, Janeen Ardito

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

A common problem in ecological studies is that of determining where to look for rare species. This paper shows how statistical models, such as classification trees, may be used to assist in the design of probability-based surveys for rare species using information on more abundant species that are associated with the rare species. This model assisted approach to survey design involves first building models for the more abundant species. The models are then used to determine stratifications for the rare species that are associated with the more abundant species. The goal of this approach is to increase the number of …

Hand-Held Calculators And Mathematics Achievement: What The 1996 National Assessment Of Educational Progress Eighth-Grade Mathematics Exam Scores Tell Us, Kenneth L. Wareham

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this study was to analyze the 1996 National Assessment of Educational Progress data to identify the relationship between calculator use and student performance on the National Assessment of Educational Progress Mathematics Assessment. This general purpose includes several sub issues. In addition to being interested in the overall relationship between use and National Assessment of Educational Progress achievement (including the effort to control for spurious factors), this study examined the contextual factors that moderate the impact of calculator use. Similarly, it analyzed the relationship between calculator use and student performance on calculator-allowed and calculator-restricted items, as well as …

Using Wavelets As A Computational And Theoretical Tool For Homogenization, Laura Lee Watkins

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Since the cost of petroleum fluctuates widely, it is advisable to optimize extraction of oil and other hydrocarbon products form existing oil reserves. Because of the costs involved in recovering oil from a reservoir, predicting reservoir performance can be a useful tool for determining whether continued extraction might be profitable. This can be done using computer simulations of the physical processes involved such as pressure/head, fluid velocities, and so forth. Fluid flow within a reservoir occurs at a very small scale relative to the size of the reservoir. This size difference makes performing simulations at the physically appropriate scale unfeasible. …

Wavelet Analysis Of Magnetometer Data, Inga Maslova

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

The wavelet analysis of the ground-based magnetograms' records is performed in this project. We explore the records from low, medium and high latitude stations during a calm period and a stormy one. Different methods for detecting and estimating the tail index of heavy-tailed distributions are compared. A detailed analysis of the properties of the distributions of the discrete wavelet transform coefficients of magnetometer data is presented. Conclusions on the tail index estimation techniques and the distribution of the discrete wavelet transform coefficients are made.

Estimation, Testing, And Monitoring Of Generalized Autoregressive Conditionally Heteroskedastic Time Series, Aonan Zhang

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We study in this dissertation Generalized Autoregressive Conditionally Heteroskedastic (GARCH) time series. The research focuses on squared GARCH sequences. Our main results are as follows:

1. We compare three methods of constructing confidence intervals for sample autocorrelations of squared returns modeled by models from the GARCH family. We compare the residual bootstrap, block bootstrap and subsampling methods. The residual bootstrap based on the standard GARCH(l,1) model is seen to perform best. Confidence intervals for cross-correlations of a bivariate GARCH model are also studied.

2. We study a test to discriminate between long memory and volatility changes in financial returns data. …

Exterior Differential Systems With Symmetry, Ian M. Anderson, Mark E. Fels

Mathematics and Statistics Faculty Publications

We use the theory of reduction of exterior differential systems with symmetry to study the problem of using a symmetry group of a differential equation to find noninvariant solutions.

Coffee To Go! Modeling Thermoclines In Multivariable Calculus, Andrea Bruder, Brynja R. Kohler

Mathematics and Statistics Faculty Publications

While mathematical modeling is an integral process in applied mathematics, students rarely encounter genuine modeling opportunities in their calculus courses. Here we introduce a laboratory experience as a natural starting point for calculus students to investigate multivariable functions. A layered system of coffee and milk serves as a physical model for temperature gradients in lakes or the atmosphere, where temperature depends on both a temporal and spatial variable. Students create, observe, and collect temperature data of their own, graph the data, and develop mathematical models to fit the data. We require students to write a report about their findings. This …