College of Letters & Science
Permanent URI for this communityhttps://scholarworks.montana.edu/handle/1/37
The College of Letters and Science, the largest center for learning, teaching and research at Montana State University, offers students an excellent liberal arts and sciences education in nearly 50 majors, 25 minors and over 25 graduate degrees within the four areas of the humanities, natural sciences, mathematics and social sciences.
Browse
4 results
Search Results
Item Functional Analysis of Variance for Association Studies(Public Library of Science, 2014) Greenwood, Mark C.; Vsevolozhskaya, Olga; Zaykin, Dmitri; Wei, Changshuai; Lu, QingWhile progress has been made in identifying common genetic variants associated with human diseases, for most of common complex diseases, the identified genetic variants only account for a small proportion of heritability. Challenges remain in finding additional unknown genetic variants predisposing to complex diseases. With the advance in next-generation sequencing technologies, sequencing studies have become commonplace in genetic research. The ongoing exome-sequencing and whole-genome-sequencing studies generate a massive amount of sequencing variants and allow researchers to comprehensively investigate their role in human diseases. The discovery of new disease-associated variants can be enhanced by utilizing powerful and computationally efficient statistical methods. In this paper, we propose a functional analysis of variance (FANOVA) method for testing an association of sequence variants in a genomic region with a qualitative trait. The FANOVA has a number of advantages: (1) it tests for a joint effect of gene variants, including both common and rare; (2) it fully utilizes linkage disequilibrium and genetic position information; and (3) allows for either protective or risk-increasing causal variants. Through simulations, we show that FANOVA outperform two popularly used methods – SKAT and a previously proposed method based on functional linear models (FLM), – especially if a sample size of a study is small and/or sequence variants have low to moderate effects. We conduct an empirical study by applying three methods (FANOVA, SKAT and FLM) to sequencing data from Dallas Heart Study. While SKAT and FLM respectively detected ANGPTL 4 and ANGPTL 3 associated with obesity, FANOVA was able to identify both genes associated with obesity.Item Intermediate Statistics with R(2014-01) Greenwood, Mark C.Introductory statistics courses prepare students to think statistically but cover relatively few statistical methods. Building on the basic statistical thinking emphasized in an introductory course, a second course in statistics at the undergraduate level can explore a large number of statistical methods. This text covers more advanced graphical summaries, One-Way ANOVA with pair-wise comparisons, Two-Way ANOVA, Chi-square testing, and simple and multiple linear regression models. Models with interactions are discussed in the Two-Way ANOVA and multiple linear regression setting with categorical explanatory variables. Randomization-based inferences are used to introduce new parametric distributions and to enhance understanding of what evidence against the null hypothesis “looks like”. Throughout, the use of the statistical software R via Rstudio is emphasized with all useful code and data sets provided within the text. This is Version 3.1 of the book.Item Robert Grosseteste, and the History of the Actual Infinite(2013-09) Hylwa, SamThe problems with the notion of infinity that plagued pre-modern philosophers and mathematicians ever since the introduction of Zeno’s paradoxes are thought to see their first solution in the original and singular accomplishments of the late-19th century German mathematician Georg Cantor. In this paper I argue that a select few Medieval philosophers advanced the concept of the actual infinite from its largely Aristotelian conception to a stage that foreshadowed Cantor’s accomplishments. I emphasize, in particular, the contributions of the 13th century scholastic philosopher Robert Grosseteste, whose work in this arena seems especially under-recognized and deserving of tribute.Item Teachers' beliefs regarding effective teaching strategies for American Indian students in mathematics(Montana State University - Bozeman, College of Letters & Science, 2008) Vallines Mira, Raquel; Chairperson, Graduate Committee: Maurice J. BurkeExtensive research has been conducted on teaching strategies that are effective for American Indians in mathematics. Despite the variety of cultural, linguistic, socioeconomic, and geographic factors influencing student learning within and among American Indian communities, common characteristics of learning styles and effective teaching practices have been identified. Though the wording in each definition varies, research based on a variety of theoretical frameworks and using a variety of methodologies and instruments suggests that among American Indian students, there is a tendency to learn better when the following three strategies are used: contextualization, modeling and demonstration, and joint productive activity. Despite the general agreement in education research that the beliefs that teachers hold about mathematics teaching and learning greatly impact their instructional decisions in the classroom, few, if any, of those studies have examined teachers' beliefs regarding effective strategies for American Indians in mathematics. The main purpose of this study was to add the voices of four teachers to the research community conversation about effective teaching strategies for American Indians in mathematics. Two elementary and two high school teachers from two schools in Montana were selected for this study for their experience with and commitment to the mathematics education of American Indian students. Two are American Indians and two are White. Using a combination of classroom observations and a modification of videoclip interviews, the beliefs of the four teachers were identified with particular focus on the three teaching strategies mentioned above. The study shows that teachers' definitions of research-based strategies often differ from those intended by the research. Teachers' views about these strategies seemed to be idiosyncratic to individual teachers and appeared to be shaped by multiple lenses. In this study, some of those lenses emerged including, among others, school structures and teachers' cultural backgrounds. In light of the results of the study, future efforts for constructive bi-directional communication between the research community and practitioners are recommended.