Differential Calculus: From Practice to Theory

Differential Calculus: From Practice to Theory covers all of the topics in a typical first course in differential calculus. Initially it focuses on using calculus as a problem solving tool (in conjunction with analytic geometry and trigonometry) by exploiting an informal understanding of differentials (infinitesimals). As much as possible large, interesting, and important historical problems (the motion of falling bodies and trajectories, the shape of hanging chains, the Witch of Agnesi) are used to develop key ideas. Only after skill with the computational tools of calculus has been developed is the question of rigor seriously broached. At that point, the foundational ideas (limits, continuity) are developed to replace infinitesimals, first intuitively then rigorously. This approach is more historically accurate than the usual development of calculus and, more importantly, it is pedagogically sound. The text also incorporates curated activities from the TRansforming Instruction in Undergraduate Mathematics Instruction via Primary Historical Sources (TRIUMPHS) project to provide students with ample opportunities to develop relevant competencies.https://knightscholar.geneseo.edu/oer-ost/1031/thumbnail.jp

Polymers and Composite Materials

This text serves to cover in more detail polymer physics concepts and specifically how polymers respond from the atomistic to meter length scale. This text spans topics from polymerization chemistry, chain models, Flory-Huggins theory, viscosity, characterization techniques, self assembly, polymer dynamics, viscoelasticity, and mechanics of polymer and composite materials. This work is licensed under a Creative Commons Attribution-NonCommerical-No Derivative Works 4.0 License.https://scholarlycommons.pacific.edu/open-textbooks/1017/thumbnail.jp

1945-02-22 Rowan County News

Rowan County News published on February 22, 1945

An experimental study of the effects of autocratic, student-centered and laissez-faire group leadership on college orientation classes

Thesis (Ed.M.)--Boston UniversityThe purpose of this study is to attempt to determine the effect of different types of leadership for freshman orientation groups at Boston University School of Educatio

A guide to the methodology

Corpora are widely used in linguistics, but not always wisely. This book attempts to frame corpus linguistics systematically as a variant of the observational method. The first part introduces the reader to the general methodological discussions surrounding corpus data as well as the practice of doing corpus linguistics, including issues such as the scientific research cycle, research design, extraction of corpus data and statistical evaluation. The second part consists of a number of case studies from the main areas of corpus linguistics (lexical associations, morphology, grammar, text and metaphor), surveying the range of issues studied in corpus linguistics while at the same time showing how they fit into the methodology outlined in the first part

Relationships between implicit and explicit uncertainty monitoring and mindreading: Evidence from autism spectrum disorder

We examined performance on implicit (non-verbal) and explicit (verbal) uncertaintymonitoring tasks among neurotypical participants and participants with autism, while also testing mindreading abilities in both groups. We found that: (i) performance of autistic participants was unimpaired on the implicit uncertainty-monitoring task, while being significantly impaired on the explicit task; (ii) performance on the explicit task was correlated with performance on mindreading tasks in both groups, whereas performance on the implicit uncertainty-monitoring task was not; and (iii) performance on implicit and explicit uncertainty-monitoring tasks was not correlated. The results support the view that (a) explicit uncertainty-monitoring draws on the same cognitive faculty as mindreading whereas (b) implicit uncertainty-monitoring only test first-order decision making. These findings support the theory that metacognition and mindreading are underpinned by the same meta-representational faculty/resources, and that the implicit uncertainty-monitoring tasks that are frequently used with nonhuman animals fail to demonstrate the presence of metacognitive abilities

Renormalized Perturbation Theory And Its Optimization By The Principle Of Minimal Sensitivity

The results of renormalized perturbation theory, in QCD and other quantum field theories, are ambiguous at any finite order, due to renormalization-scheme dependence. The perturbative results depend upon extraneous scheme variables, including the renormalization scale, that the exact result cannot depend on. Such 'non-invariant approximations' occur in many other areas of physics, too. The sensible strategy is to find where the approximant is stationary under small variations of the extraneous variables. This general principle is explained and illustrated with various examples. Also dimensional transmutation, RG equations, the essence of renormalization and the origin of its ambiguities are explained in simple terms, assuming little or no background in quantum field theory. The minimal-sensitivity approach leads to 'optimized perturbation theory,' which is developed in detail. Applications to Re⁺e⁻, the infrared limit, and to the optimization of factorized quantities, are also discussed thoroughly

The State Space of Complex Systems

In dieser Arbeit wird eine Beschreibung von Monte-Carlo-Verfahren zur Lösung komplexer Optimierungsaufgaben mit Hilfe von Markov-Ketten durchgeführt. Nach einer kurzen Einführung werden Lösungsmenge solcher Aufgaben und der physikalische Zustandsraum komplexer Systeme identifiziert. Zunächst wird die Dynamik von Zufallswanderern im Zustandsraum mit Hilfe von Master-Gleichungen modelliert. Durch Einführung von Performanzkriterien können verschiedene Optimierungsstrategien quantitativ miteinander verglichen werden. Insbesondere wird das Verfahren Extremal Optimization vorgestellt, dass ebenfalls als Markov-Prozess verstanden werden kann. Es wird bewiesen, dass eine im Sinne der genannten Kriterien beste Implementierung existiert. Da diese von einem sogenannten Fitness Schedule abhängt, wird dieser für kleine Beispielsysteme explizit berechnet. Daran anschließend wird die Zustandsdichte komplexer Systeme betrachtet. Nach einem kurzen Überblick über vorhandene Methoden folgt eine detaillierte Untersuchung des Verfahrens von Wang und Landau. Numerische und analytische Hinweise werden gegeben, nach denen dieser Algorithmus innerhalb seiner Klasse wahrscheinlich der Optimale ist. Eine neue Methode zur Approximation der Zustandsdichte wird vorgestellt, die insbesondere für die Untersuchung komplexer Systeme geeignet ist. Abschließend wird ein Ausblick auf zukünftige Arbeiten gegeben

Corpus linguistics

Corpora are widely used in linguistics, but not always wisely. This book attempts to frame corpus linguistics systematically as a variant of the observational method. The first part introduces the reader to the general methodological discussions surrounding corpus data as well as the practice of doing corpus linguistics, including issues such as the scientific research cycle, research design, extraction of corpus data and statistical evaluation. The second part consists of a number of case studies from the main areas of corpus linguistics (lexical associations, morphology, grammar, text and metaphor), surveying the range of issues studied in corpus linguistics while at the same time showing how they fit into the methodology outlined in the first part