Mathematical Sciences
Permanent URI for this communityhttps://scholarworks.montana.edu/handle/1/48
Mathematical research at MSU is focused primarily on related topics in pure and applied mathematics. Research programs complement each other and are often applied to problems in science and engineering. Research in statistics encompasses a broad range of theoretical and applied topics. Because the statisticians are actively engaged in interdisciplinary work, much of the statistical research is directed toward practical problems. Mathematics education faculty are active in both qualitative and quantitative experimental research areas. These include teacher preparation, coaching and mentoring for in-service teachers, online learning and curriculum development.
Browse
95 results
Search Results
Item The Learning Difficulties Faced by Community College Algebra II Students in Understanding Algebraic and Symbolic Notation(Montana State University, 2017-04) Kong, AmyThis research project is aimed to find out students’ common errors and misconceptions regarding to the understanding of the algebraic and symbolic notation and what factors affecting them in their understanding. 18 students from a semester-long algebra II class from a community college were invited to participate in this study by taking a pre- and a post- diagnostics tests. Students’ answers on the tests were analyzed. 15 students were interviewed afterwards to explain their errors. Students’ answers on the tests and responses from the interviews have shown that students did have some misconceptions concerning learning of algebra. They generally had difficulty in recognizing the roles of the variables that were used in algebraic expressions or equations. They also ignored the order of operations. Most of them had difficulty in knowing the difference between algebraic expressions and equations. The other purpose of this research was to study the effectiveness of adopting collaboration as an instructional strategy on the students’ conceptual understanding of the algebraic and symbolic notation. A paired-samples t-test was conducted to compare the results between the pre- and the post-diagnostic tests in adopting collaboration as an instructional strategy. The results suggested that the collaboration did have an impact on the students’ learning in algebraic and symbolic notation. Specifically, the results suggested that adopting collaboration could help students’ conceptual understanding on the algebraic and symbolic notation. The teaching strategies that might help students combat misconceptions and overcome learning difficulties when learning basic algebra are also discussed in this research report.Item Lie Algebroids As L[infinity] Spaces(2018-02) Grady, Ryan; Gwilliam, OwenIn this paper, we relate Lie algebroids to Costello’s version of derived geometry. For instance, we show that each Lie algebroid – and the natural generalization to dg Lie algebroids – provides an (essentially unique) L infinity space. More precisely, we construct a faithful functor from the category of Lie algebroids to the category of L infinity spaces. Then we show that for each Lie algebroid L, there is a fully faithful functor from the category of representations up to homotopy of L to the category of vector bundles over the associated L infinity space. Indeed, this functor sends the adjoint complex of L to the tangent bundle of the L infinity space. Finally, we show that a shifted symplectic structure on a dg Lie algebroid produces a shifted symplectic structure on the associated L infinity space.Item Variable Selection and Parameter Tuning for BART Modeling in the Fragile Families Challenge(2019-09) Carnegie, Nicole B.; Wu, JamesOur goal for the Fragile Families Challenge was to develop a hands-off approach that could be applied in many settings to identify relationships that theory-based models might miss. Data processing was our first and most time-consuming task, particularly handling missing values. Our second task was to reduce the number of variables for modeling, and we compared several techniques for variable selection: least absolute selection and shrinkage operator, regression with a horseshoe prior, Bayesian generalized linear models, and Bayesian additive regression trees (BART). We found minimal differences in final performance based on the choice of variable selection method. We proceeded with BART for modeling because it requires minimal assumptions and permits great flexibility in fitting surfaces and based on previous success using BART in black-box modeling competitions. In addition, BART allows for probabilistic statements about the predictions and other inferences, which is an advantage over most machine learning algorithms. A drawback to BART, however, is that it is often difficult to identify or characterize individual predictors that have strong influences on the outcome variable.Item Evaluating and presenting uncertainty in model‐based unconstrained ordination(2019-12) Hoegh, Andrew; Roberts, David W.Variability in ecological community composition is often analyzed by recording the presence or abundance of taxa in sample units, calculating a symmetric matrix of pairwise distances or dissimilarities among sample units and then mapping the resulting matrix to a low‐dimensional representation through methods collectively called ordination. Unconstrained ordination only uses taxon composition data, without any environmental or experimental covariates, to infer latent compositional gradients associated with the sampling units. Commonly, such distance‐based methods have been used for ordination, but recently there has been a shift toward model‐based approaches. Model‐based unconstrained ordinations are commonly formulated using a Bayesian latent factor model that permits uncertainty assessment for parameters, including the latent factors that correspond to gradients in community composition. While model‐based methods have the additional benefit of addressing uncertainty in the estimated gradients, typically the current practice is to report point estimates without summarizing uncertainty. To demonstrate the uncertainty present in model‐based unconstrained ordination, the well‐known spider and dune data sets were analyzed and shown to have large uncertainty in the ordination projections. Hence to understand the factors that contribute to the uncertainty, simulation studies were conducted to assess the impact of additional sampling units or species to help inform future ordination studies that seek to minimize variability in the latent factors. Accurate reporting of uncertainty is an important part of transparency in the scientific process; thus, a model‐based approach that accounts for uncertainty is valuable. An R package, UncertainOrd, contains visualization tools that accurately represent estimates of the gradients in community composition in the presence of uncertainty.Item An Alternative to the Carnegie Classifications: Identifying Similar Institutions with Structural Equation Models and Clustering(2019-01) Harmon, Paul; McKnight, Sarah; Hildreth, Laura; Godwin, Ian; Greenwood, Mark C.The Carnegie Classification of Institutions of Higher Education is a commonly used framework for institutional classification that classifies doctoral-granting schools into three groups based on research productivity. Despite its wide use, the Carnegie methodology involves several shortcomings, including a lack of thorough documentation, subjectively placed thresholds between institutions, and a methodology that is not completely reproducible. We describe the methodology of the 2015 and 2018 updates to the classification and propose an alternative method of classification using the same data that relies on structural equation modeling (SEM) of latent factors rather than principal component-based indices of productivity. In contrast to the Carnegie methodology, we use SEM to obtain a single factor score for each school based on latent metrics of research productivity. Classifications are then made using a univariate model-based clustering algorithm as opposed to subjective thresholding, as is done in the Carnegie methodology. Finally, we present a Shiny web application that demonstrates sensitivity of both the Carnegie Classification and SEM-based classification of a selected university and generates a table of peer institutions in line with the stated goals of the Carnegie Classification.Item Characterization of synovial fluid metabolomic phenotypes of cartilage morphological changes associated with osteoarthritis(2019-08) Carlson, Alyssa K.; Rawle, Rachel A.; Wallace, Cameron W.; Brooks, Ellen G.; Adams, Erik; Greenwood, Mark C.; Olmer, Merissa; Lotz, Martin K.; Bothner, Brian; June, Ronald K."Objective Osteoarthritis (OA) is a multifactorial disease with etiological heterogeneity. The objective of this study was to classify OA subgroups by generating metabolomic phenotypes from human synovial fluid. Design: Post mortem synovial fluids (n = 75) were analyzed by high performance-liquid chromatography mass spectrometry (LC-MS) to measure changes in the global metabolome. Comparisons of healthy (grade 0), early OA (grades I-II), and late OA (grades III-IV) donor populations were considered to reveal phenotypes throughout disease progression. Results: Global metabolomic profiles in synovial fluid were distinct between healthy, early OA, and late OA donors. Pathways differentially activated among these groups included structural deterioration, glycerophospholipid metabolism, inflammation, central energy metabolism, oxidative stress, and vitamin metabolism. Within disease states (early and late OA), subgroups of donors revealed distinct phenotypes. Synovial fluid metabolomic phenotypes exhibited increased inflammation (early and late OA), oxidative stress (late OA), or structural deterioration (early and late OA) in the synovial fluid. Conclusion: These results revealed distinct metabolic phenotypes in human synovial fluid, provide insight into pathogenesis, represent novel biomarkers, and can move toward developing personalized interventions for subgroups of OA patients.Item Coliform Contamination in private well water on the Crow Reservation(2018-10) Powell, MichaelaEmery Three Irons is a master’s level graduate student in the Department of Land Resources and Environmental Sciences (LRES) at Montana State University (MSU). Advised by Scott Powell, Ph.D., who is an Associate Professor in the Department of LRES at MSU, Emery is working on his master’s thesis which explores coliform contamination in private well water on the Crow Reservation. He has requested the assistance of the Statistical Consulting and Research Services in deciding on an appropriate analysis for the data he collected.Item Impact of an automated hand hygiene monitoring system and additional promotional activities on hand hygiene performance rates and healthcare-associated infections(2019-07) Boyce, John M.; Laughman, Jennifer A.; Ader, Michael H.; Wagner, Pamela T.; Parker, Albert E.; Arbogast, James W.Objective: Determine the impact of an automated hand hygiene monitoring system (AHHMS) plus complementary strategies on hand hygiene performance rates and healthcare-associated infections (HAIs). Design: Retrospective, nonrandomized, observational, quasi-experimental study. Setting: Single, 93-bed nonprofit hospital. Methods: Hand hygiene compliance rates were estimated using direct observations. An AHHMS, installed on 4 nursing units in a sequential manner, determined hand hygiene performance rates, expressed as the number of hand hygiene events performed upon entering and exiting patient rooms divided by the number of room entries and exits. Additional strategies implemented to improve hand hygiene included goal setting, hospital leadership support, feeding AHHMS data back to healthcare personnel, and use of Toyota Kata performance improvement methods. HAIs were defined using National Healthcare Safety Network criteria. Results: Hand hygiene compliance rates generated by direct observation were substantially higher than performance rates generated by the AHHMS. Installation of the AHHMS without supplementary activities did not yield sustained improvement in hand hygiene performance rates. Implementing several supplementary strategies resulted in a statistically significant 85% increase in hand hygiene performance rates (P < .0001). The incidence density of non–Clostridioies difficile HAIs decreased by 56% (P = .0841), while C. difficile infections increased by 60% (P = .0533) driven by 2 of the 4 study units. Conclusion: Implementation of an AHHMS, when combined with several supplementary strategies as part of a multimodal program, resulted in significantly improved hand hygiene performance rates. Reductions in non–C. difficile HAIs occurred but were not statistically significant.Item Randomized controlled trial evaluating the antimicrobial efficacy of chlorhexidine gluconate and para-chloro-meta-xylenol handwash formulations in real-world doses(2019-06) Arbogast, James W.; Bowersock, Lisa B.; Parker, Albert E.; Macinga, D. R.Chlorhexidine gluconate-based soaps have become the gold standard for handwashing in critical care settings and para-chloro-meta-xylenol is an effective alternative antibacterial active ingredient. This study benchmarked 2 novel foaming handwashes, compared to a bland soap for antimicrobial effectiveness using the health care personnel handwash method at realistic soap doses (0.9 mL and 2.0 mL). To our knowledge, this is the first published efficacy study on realistic soap doses. Both soaps met Food and Drug Administration success criteria.Item Who goes in and out of patient rooms? An observational study of room entries and exits in the acute care setting(2019-05) Arbogast, James W.; Moore, Lori; Clark, Tracy; Thompson, MariaThe objective of this study is to determine what percentage of patient room entries and exits (opportunities) are attributed to health care personnel (HCP) and non-HCP. A total of 14,876 opportunities were observed by clinicians in 29 units of 16 hospitals. HCP accounted for 83.6%; 95% confidence interval, 81.3%-87.6%. This finding provides hospitals an initial baseline for HCP room traffic when implementing community-based automated hand hygiene monitoring and compliance improvement efforts.