Physical Sciences and Mathematics Commons^™

A Collection And Analysis Of Local Middle Grade Math Projects For The Common Core, Lynnette Checketts

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

The State of Utah has changed the mathematics core curriculum several times over the past decade. The latest change was the adoption of the Common Core State Standards introducing both grade level content standards and standards of mathematical practice that emphasize how students are to study and reason with mathematics at all grade levels. According to state officials, these standards require more mathematical reasoning, problem solving, and deeper understanding than previous core curriculum documents. One way to address this change is for teachers to educate using projects during their instruction as unit starters, daily lessons, and for evaluation purposes. Yet …

Black-Scholes And Extended Black-Scholes Models: A Comparative Statistical Analysis, Bradley Thomas Bush

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

Much research has been done on options pricing. Black and Scholes [12] set the benchmark in 1973 with their model for arbitrage-free, risk-neutral options valuation. Arbitrage-free refers to a market environment where prices are such that trading opportunities with no risk do not exist and risk-neutral commodities earn a risk free interest rate. Since then the literature has seen a multitude of models improving the fit of the traditional Black -Scholes (BS) model. A brief overview of options and these models is given. A derivation and discussion of BS is followed by a derivation and discussion of the Extended Black-Scholes …

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 …

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.

Analysis Of A Non-Replicated Split-Split Plot Experiment, Emily Simmons Sim

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

A major obstacle in the analysis of experimental data, in many situations, is the lack of "true" or "complete" replication. In some disciplines, researchers are very aware of the importance of replication and the methods for correctly replicating an experiment. In other subject areas, however, researchers are less aware of what it means to properly replicate an experiment. Due to this lack of awareness, many non-replicated experiments are carried out every year. For many of these non-replicated experiments, there is no satisfactory statistical analysis.

The subject of this report is the analysis of two non-replicated experiments in environmental engineering. First, …

Program Development For Computer Simulation And Analysis For Multiplex Chromatography, Barbara Pawliszyn

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

In this report, the programs developed for the analysis of simulated data in multiplex chromatography are written in the ASYST language. The integration of the program modules into a menu-driven, user-friendly prototype program is outlined. The program is developed to allow for flexibility and easy upgrading of the code.

This report examines the calculation procedures potentially useful in multiplex chromatography. Analysis of the mutliplex chromatograms is done by three mathematical methods, Cross-Correlation, Hadamard Transform and Fast Fourier Transform. The effects of experimental length/chromatogram length and decision sequences on correlation noise present in a single chromatogram, are discussed. As the number …

Linear Comparisons In Multivariate Analysis Of Variance, Hsin-Ming Tzeng

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

The analysis of variance was created by Ronald Fisher in 1923. It is most widely used and basically useful approach to study differences among treatment averages.

Principal Component Factor Analysis, Kuang-Ming Chu

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

The principal-factor solution is probably the most widely used technique in factor analysis and a relatively straight forward method to determine the minimum number of independent dimensions needed to account for most of the variance in the original set of variables.

The principal components approach to parsimony was first proposed by Karl Pearson (1901) who studied the problem for the case of nonstochastic variables, and in a different context. Hotelling provided the full development of the method (1933) and Thomson (1947) was the first to apply it to the principal factor analysis.

This method was first developed to deal with …

Functional Analysis Techniques In Numerical Analysis, Kenneth D. Schoenfeld

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

In this paper we will consider the problem of selecting the best, or optimal, numerical method of solution to a given mathematical problem. The admissible numerical methods will be a clearly defined set for each problem. Obviously, in order to find the best method in this set, we must have a clear mathematical formulation of just what "best" means; this will be the intent of Theorem 0.1. Intuitively, the best method will be understood to be the one which minimizes the maximum possible error where this error will be measured in terms of the norm of a given Hilbert space. …

Computer Analysis Of Consumer Attitude And Consumption Data For Fluid Milk Products, James Reed Fisher

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

The American public, with a per capita disposable income currently at an all time high, has become a source of vital concern to dairy market researchers. The unique socio-economic structure of the present generation causes the dairy industry to be concerned with how the consumer view its products. Effective education and advertising programs must be developed to attract the taste and meet the demands of the consumer.

Two factors which greatly influence market research and advertising programs are the attitude of the consumer toward a given product and the relationship of attitude to the degree of actual milk consumption. To …