A new mathematical and philosophical dictionary, comprising an explanation of terms and principles of pure and mixed mathematics, and such branches of natural philosophy as are susceptible of mathematical investigation. With historical sketches of the rise, progress and present state of the several departments of these sciences, and an account of the discoveries and writings of the most celebrated authors, both ancient and modern.

Mode of access: Internet.

A aprendizagem da Matemática no 1º ciclo através de atividades de investigação numa comunidade de aprendizagem

Dissertação apresentada para obtenção do grau de Mestre em Educação Matemática na Educação Pré-Escolar e nos 1º e 2º Ciclos do Ensino Básico na especialidade de Didática da Matemática

Computational Structure of Human Language

The central thesis of this report is that human language is NP-complete. That is, the process of comprehending and producing utterances is bounded above by the class NP, and below by NP-hardness. This constructive complexity thesis has two empirical consequences. The first is to predict that a linguistic theory outside NP is unnaturally powerful. The second is to predict that a linguistic theory easier than NP-hard is descriptively inadequate. To prove the lower bound, I show that the following three subproblems of language comprehension are all NP-hard: decide whether a given sound is possible sound of a given language; disambiguate a sequence of words; and compute the antecedents of pronouns. The proofs are based directly on the empirical facts of the language user's knowledge, under an appropriate idealization. Therefore, they are invariant across linguistic theories. (For this reason, no knowledge of linguistic theory is needed to understand the proofs, only knowledge of English.) To illustrate the usefulness of the upper bound, I show that two widely-accepted analyses of the language user's knowledge (of syntactic ellipsis and phonological dependencies) lead to complexity outside of NP (PSPACE-hard and Undecidable, respectively). Next, guided by the complexity proofs, I construct alternate linguisitic analyses that are strictly superior on descriptive grounds, as well as being less complex computationally (in NP). The report also presents a new framework for linguistic theorizing, that resolves important puzzles in generative linguistics, and guides the mathematical investigation of human language.

Narrativas no ensino de funções por meio de investigações matemáticas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Atividades exploratório-investigativas em sala de aula de cálculo I com uso de tecnologia

This study presents the results from a qualitative resource, based on research-action methodology, which examined the innovate teaching practices implementations in the Calculus I during 2011 year. The analysis of collected data from three used sources – an initial questionnaire, an exploratory-investigative classroom, and an interview with some students at the end of the second semester – reveals that the students had appropriated of the technological recourses, using it as a tool to look for the knowledge. The investigative activities with the use of information technologies made the use of multiple representations in solving mathematical tasks, making the transition of numerical, algebraic and geometrical results possible for the students when they have looking for validation of their hypotheses and conjectures during mathematical problems solving. This works helped in the insertion of new practices in the discipline, and their results validate the proposal presented by the teacher, which is the discipline of Calculus use, whose character is strongly linked to the training content of the student, as a discipline whose can contributed to the pedagogical formation of the graduation student, leading him to know the Mathematical Education possibilities, specially the Mathematical Investigation - Solving Problems, in the outlook of dialogued classes where the teacher assumes the facilitator role and where the students become actives in their pursuit of knowledge

As mudanças procedimentais de alunos do ensino médio durante o trabalho com investigação matemática em sala de aula

The paper that if presents, tells a research carried through next to students of the High School, in which activities of mathematical investigation from questions of some examinations of federal and state public universities had been elaborated; later applied to these students in a state school of the inside of São Paulo and with data obtained from their productions, we search to analyze which procedures had been used for them and which procedural changes had occurred. It is intended with this, to collaborate for the mathematical formation of the students of High School aiming at a more significant learning of the mathematical concepts and the procedures involved when working with this type of activity.

A geometria do compasso (1797) de Mascheroni (1750 – 1800) em atividades com o GeoGebra

The present work aims to show a possible relationship between the use of the History of Mathematics and Information and Communication Technologies (TIC) in teaching Mathematics through activities that use geometric constructions of the “Geometry of the Compass” (1797) by Lorenzo Mascheroni (1750-1800). For this, it was performed a qualitative research characterized by an historical exploration of bibliographical character followed by an empirical intervention based on use of the History of Mathematics combined with TIC through Mathematical Investigation. Thus, studies were performed in papers dealing with the topic, as well as a survey to highlight problems and /or episodes of the history of mathematics that can be solved with the help of TIC, allowing the production of a notebook of activities addressing the resolution of historical problems in a computer environment. In this search, we came across the problems of geometry that are presented by Mascheroni stated previously in the work that we propose solutions and investigations using GeoGebra software. The research resulted in the elaboration of an educational product, a notebook of activities, which was structure to allow during its implementation, students can conduct historical and/or Mathematics research, therefore, we present the procedures for realization of each construction, followed at some moments by original solution of the work. At the same time, we encourage students to investigate/reflect its construction (GeoGebra), in addition to making comparisons with the solution Mascheroni. This notebook was applied to two classes of the course of Didactics of Mathematics I (MAT0367) Course in Mathematics UFRN in 2014. Knowing the existence of some unfavorable arguments regarding the use of history of mathematics, such as loss of time, it was found that this factor can be mitigated with the aid of computational resource, because we can make checks using only the dynamism of and software without repeating the construction. It is noteworthy that the minimized time does not mean loss of reflection or maturation of ideas, when we adopted the process of historical and/or Mathematics Investigation

Closed-loop investigation of the dynamical properties of cardiomyocyte electrophysiology by means of Dynamic clamp and Mathematical modelling

The research field of my PhD concerns mathematical modeling and numerical simulation, applied to the cardiac electrophysiology analysis at a single cell level. This is possible thanks to the development of mathematical descriptions of single cellular components, ionic channels, pumps, exchangers and subcellular compartments. Due to the difficulties of vivo experiments on human cells, most of the measurements are acquired in vitro using animal models (e.g. guinea pig, dog, rabbit). Moreover, to study the cardiac action potential and all its features, it is necessary to acquire more specific knowledge about single ionic currents that contribute to the cardiac activity. Electrophysiological models of the heart have become very accurate in recent years giving rise to extremely complicated systems of differential equations. Although describing the behavior of cardiac cells quite well, the models are computationally demanding for numerical simulations and are very difficult to analyze from a mathematical (dynamical-systems) viewpoint. Simplified mathematical models that capture the underlying dynamics to a certain extent are therefore frequently used. The results presented in this thesis have confirmed that a close integration of computational modeling and experimental recordings in real myocytes, as performed by dynamic clamp, is a useful tool in enhancing our understanding of various components of normal cardiac electrophysiology, but also arrhythmogenic mechanisms in a pathological condition, especially when fully integrated with experimental data.

An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities.

Mode of access: Internet.

An investigation of the laws of thought, on which are founded mathematical theories of logic and probabilities.

Mode of access: Internet.

An investigation into the tension arising between natural language and mathematical language experienced by mechanical engineering students

This investigation is grounded within the concept of embodied cognition where the mind is considered to be part of a biological system. A first year undergraduate Mechanical Engineering cohort of students was tasked with explaining the behaviour of three balls of different masses being rolled down a ramp. The explanations given by the students highlighted the cognitive conflict between the everyday interpretation of the word energy and its mathematical use. The results showed that even after many years of schooling, students found it challenging to interpret the mathematics they had learned and relied upon pseudo-scientific notions to account for the behaviour of the balls.

Monte Carlo investigation of the critical behavior of Stavskaya's probabilistic cellular automaton

Stavskaya's model is a one-dimensional probabilistic cellular automaton (PCA) introduced in the end of the 1960s as an example of a model displaying a nonequilibrium phase transition. Although its absorbing state phase transition is well understood nowadays, the model never received a full numerical treatment to investigate its critical behavior. In this Brief Report we characterize the critical behavior of Stavskaya's PCA by means of Monte Carlo simulations and finite-size scaling analysis. The critical exponents of the model are calculated and indicate that its phase transition belongs to the directed percolation universality class of critical behavior, as would be expected on the basis of the directed percolation conjecture. We also explicitly establish the relationship of the model with the Domany-Kinzel PCA on its directed site percolation line, a connection that seems to have gone unnoticed in the literature so far.

Investigation of Cationic Polymerization of beta-Pinene Using Calorimetric Measurements

An experimental investigation of the kinetics of cationic polymerization of beta-pinene was performed using two different initiator systems under two different operating conditions (shot additions of initiator, and continuous feeding of monomer). The experiments were done using calorimetric measurements under isoperibolic conditions. The heat of polymerization of beta-pinene was found to be -30.6 kcal . mol(-1). A simple kinetic model was tentatively proposed, and the model fit reasonably well to the different experimental runs. Different values of the fitting parameters were obtained for runs carried out under different conditions, which can probably be ascribed to the presence of adventitious impurities in the commercial-grade monomer used.