Faculty Employment Status and Student Characteristics as Predictors of Student Success in Modularized Developmental Mathematics

Approximately two-thirds of incoming community college students are considered academically unprepared for college-level work and lack adequate literacy and mathematical skills needed to learn at the postsecondary level. To address these realities, individual community colleges and state-wide systems have responded by redesigning developmental curricula and course structures into modularized programs that accelerate student progression through developmental sequences. Simultaneously, community colleges are hiring more adjunct faculty to meet the ever-growing demand to educate students in these programs. Data were collected for a study of the Virginia Community College System 2012 developmental math redesign to primarily examine the effects of adjunct faculty on student success in the modularized developmental math program. Secondary data analysis was conducted utilizing student characteristics. This study posed two research questions and 16 hypotheses. Logistic regression analysis was performed to examine the factors believed to have an impact on student pass rates in total and from grouped developmental pathways individually. Predictor variables used to measure the effect on achieving a passing grade were: faculty employment status, student race/ethnicity, gender, and age and institutional location— rural, urban, and suburban, were examined. This study examined secondary data of 48,765 first-time-in-college students who were enrolled in Virginia community colleges’ redesigned developmental math modules beginning in fall 2013, 2014 and 2015. Findings indicate the following: having an adjunct faculty increased the likelihood of students passing all nine modules but especially the earlier modules that make up 1-5; traditional-age students were more likely to be successful overall compared to non-traditional age students; student enrollment in urban and rural community colleges were negatively associated with achieving a passing grade. Black or African-American, Hispanic or Latino and male students had lower pass-rates than White and female students overall and in developmental pathway. Black or African-American students by comparison had considerably lower pass-rates across all developmental modules than their non-Black peers

Nenad Trinajstić – Pioneer of Chemical Graph Theory

We present a brief overview of many contributions of Nenad Trinajstić to Chemical Graph Theory, an important and fast developing branch of Theoretical Chemistry. In addition, we outline briefly the various activities of Trinajstić within the chemical community of Croatia. As can be seen, his scientific work has been very productive and has not abated despite the hostilities towards the Chemical Graph Theory in certain chemical circles over the past 30 years. On the contrary, Trinajstić continued, widened the areas of his research interest, which started with investigating the close relationship between Graph Theory and HMO, and demonstrated the importance of Chemical Graph theory for chemistry. In more than one way he has proven the opponents of Chemical Graph Theory wrong, though some continue to fail to recognize the importance of Graph Theory in Chemistry

Two essays in computational optimization: computing the clar number in fullerene graphs and distributing the errors in iterative interior point methods

Fullerene are cage-like hollow carbon molecules graph of pseudospherical sym- metry consisting of only pentagons and hexagons faces. It has been the object of interest for chemists and mathematicians due to its widespread application in various fields, namely including electronic and optic engineering, medical sci- ence and biotechnology. A Fullerene molecular, Γ n of n atoms has a multiplicity of isomers which increases as N iso ∼ O(n 9 ). For instance, Γ 180 has 79,538,751 isomers. The Fries and Clar numbers are stability predictors of a Fullerene molecule. These number can be computed by solving a (possibly N P -hard) combinatorial optimization problem. We propose several ILP formulation of such a problem each yielding a solution algorithm that provides the exact value of the Fries and Clar numbers. We compare the performances of the algorithm derived from the proposed ILP formulations. One of this algorithm is used to find the Clar isomers, i.e., those for which the Clar number is maximum among all isomers having a given size. We repeated this computational experiment for all sizes up to 204 atoms. In the course of the study a total of 2 649 413 774 isomers were analyzed.The second essay concerns developing an iterative primal dual infeasible path following (PDIPF) interior point (IP) algorithm for separable convex quadratic minimum cost flow network problem. In each iteration of PDIPF algorithm, the main computational effort is solving the underlying Newton search direction system. We concentrated on finding the solution of the corresponding linear system iteratively and inexactly. We assumed that all the involved inequalities can be solved inexactly and to this purpose, we focused on different approaches for distributing the error generated by iterative linear solvers such that the convergences of the PDIPF algorithm are guaranteed. As a result, we achieved theoretical bases that open the path to further interesting practical investiga- tion

Numerical calculations for electronic transport through molecular systems

Thema der vorliegenden Arbeit ist die Beschreibung von Ladungstransporteigenschaften molekularer Systeme, wenn diese das Verbindungsstück zweier Elektroden bilden. Einen technologischen Meilenstein setzte auf diesem Gebiet die Rastertunnelmikroskopie, welche ursprünglich für die Abbildung von Oberflächen mit atomarer Auflösung entwickelt wurde (Binnig et al., 1981). Heute ermöglicht sie die gezielte Untersuchung von Transporteigenschaften einzelner, auf Oberflächen adsorbierter Moleküle. Parallel dazu hat der immense Fortschritt in der Miniaturisierung klassischer elektronischer Bauteile in jüngster Zeit ermöglicht, Zuleitungsstrukturen auf der Nanometerskala zu bauen, und diese mit einzelnen oder wenigen Molekülen zu überbrücken (Reed et al., 1997). Es besteht die Hoffnung, mit solchen Systemen Schaltungselemente zu realisieren, die heutigen elektronischen Bauteilen in Hinblick auf ihre Effizienz und den Grad ihrer Miniaturisierung deutlich überlegen sind. Experimente mit diesen molekularelektronischen Apparaten werfen die Frage auf, wie sich die chemische Natur eines Moleküls sowie seine Kopplung an die Oberfläche der Elektroden auf die Leitungseigenschaften auswirkt. Eine theoretische Beantwortung dieser Frage erzwingt eine quantenmechanische Beschreibung des Systems. Ein genaues Verständnis dieser Zusammenhänge würde ein gezieltes Entwerfen molekuarelektronischer Bauteile ermöglichen. Trotz bedeutender experimenteller wie theoretischer Fortschritte besteht zwischen den Ergebnissen bisher allerdings nur beschränkt Übereinstimmung. Diese Arbeit beginnt mit einem Überblick über die gängigen Methoden zur theoretischen Beschreibung von Ladungstransport durch molekulare Systeme und charakterisiert sie hinsichtlich der ihnen zugrundeliegenden Annahmen und Näherungen. Dabei findet eine Unterteilung in störungstheoretische sowie streutheoretische Verfahren statt. Anschließend werden Methoden der Quantenchemie behandelt, da diese in nahezu allen Ansätzen zur Beschreibung von elektronischem Transport durch molekulare Systeme Anwendung finden. Wir liefern eine Zusammenstellung der wichtigsten unter den auf diesem Gebiet in immenser Anzahl entwickelten Methoden und der ihnen zugrundeliegenden Näherungen. Auf diese allgemeinen Darstellungen folgt eine detaillierte Beschreibung des numerischen Verfahrens, das im Rahmen dieser Dissertation zur Berechnung von Stromtransport durch Molekülstrukturen implementiert worden ist. Mit der vorliegenden Arbeit wird eine Verallgemeinerung eingeführt, die eine vormalige Einschränkung der ursprünglichen Methode bezüglich der betrachtbaren Systeme beseitigt. Diese so erhaltene Methode wird dann verwendet, um der durch Experimente von Dupraz et al. (2003) aufgekommenen Frage nachzugehen, welchen Einfluß die verschiedenen geometrischen Anordnungen einer Gruppe von identischen Molekülen auf die Leitfähigkeitseigenschaften eines molekularelektronischen Apparats ausüben. Unsere Untersuchungen zeigen, daß sich die Transporteigenschaften nur bei Bildung von Molekülgruppierungen mit bedeutender intermolekularer Wechselwirkung wesentlich von denen einzelner Moleküle unterscheiden. Damit lassen sich Konsequenzen aus der Stabilität von Molekül-Elektroden Verbindungen für die Reproduzierbarkeit von gewonnenen Meßdaten ableiten. Abschließend befassen wir uns mit der Berechnung von Rastertunnelmikroskop-Bildern. Dabei geben wir zuerst einen Überblick über bisherige Anwendungen von Modellrechnungen zur Erklärung experimenteller Daten. Dann präsentieren wir eigene Berechnungen, die im Rahmen einer Kooperation mit Constable et al. (2004) dazu beitragen sollen, durch Vergleich mit deren experimentellen Bildern verschiedene Konformationen eines auf Graphit adsorbierten Moleküls identifizieren zu können. Die enorme Größe des Moleküls führt zu Gesamtsystemgrößen, die eine numerische Durchführung in der Praxis bisher scheitern ließen. Durch eine neuartige Zerlegung des Eigenwertproblems, das die praktische Durchführung der von uns verwendeten Methode bisher verhinderte, sind wir in der Lage, erstmalig Berechnungen für weitaus größere als die bisher betrachtbaren Systeme durchzuführen

Advances in Quantum Theory

The quantum theory is the first theoretical approach that helps one to successfully understand the atomic and sub-atomic worlds which are too far from the cognition based on the common intuition or the experience of the daily-life. This is a very coherent theory in which a good system of hypotheses and appropriate mathematical methods allow one to describe exactly the dynamics of the quantum systems whose measurements are systematically affected by objective uncertainties. Thanks to the quantum theory we are able now to use and control new quantum devices and technologies in quantum optics and lasers, quantum electronics and quantum computing or in the modern field of nano-technologies

A Self-regulated Learning Intervention for Developmental Mathematics Students at a Community College: Effects of Study Journals on Achievement and Study Habits

Self-regulated learners continually monitor and adjust the learning process through a recursive loop of forethought, learning enactment, and reflection. The literature review for this study used a systematic approach with defined criteria to evaluate the effects of self-regulated learning interventions for college students. The review revealed a shortage of rigorous achievement-based research in authentic settings. This study evaluated a study-journaling intervention for developmental mathematics students at a large urban community college. Two weekly study journal worksheets were designed, based on self-regulated learning theory. In each of nine pairs of intact classes, one class was randomly assigned to the treatment (study journal) condition and the other to control. The mixed methods research design had two strands: a confirmatory strand that evaluated the intervention’s effect, and an exploratory strand that sought information about the students’ study habits. The statistical analysis had two phases: propensity score matching to strategically trim the groups so they had similar distributions of starting characteristics, and logistic regression to estimate the intervention’s effect on binary variables representing course success and final exam success. Departing students were counted among the unsuccessful. Due to implementation shortcomings, the original sample (117 treatment, 140 control) was replaced by a modified sample (60 treatment, 77 control). Propensity score matching trimmed this sample further (54 treatment, 54 control). Control students experienced significantly higher course success rates and slightly higher final exam success rates. Treatment students were significantly more likely to leave the class than control students (odds ratio 2.94). However, qualitative data from focus groups and surveys indicated the study journals may have positively affected study habits. Taken together, the qualitative and quantitative results suggest the intervention increased students’ awareness of study habit inadequacies and time constraints. This position was supported by qualitative analysis of the study journal entries. This study shows that study journals have potential to improve achievement. However, caution is advised, as the journals may also influence students to leave the class due to increased awareness of problems. Research recommendations include combining study journals with training, feedback or peer support; and collecting subsequent-semester data and data on students’ reasons for departure