Search results for "Mathematical logic"
showing 10 items of 394 documents
Do Dogs Know Related Rates Rather than Optimization?
2006
(2006). Do Dogs Know Related Rates Rather than Optimization? The College Mathematics Journal: Vol. 37, No. 1, pp. 16-19.
Leon Henkin the Reviewer
2014
In this chapter, we intend to look at Henkin’s reviews, a total of forty-six. The books and papers reviewed deal with a large variety of subjects that range from the algebraic treatment of logical systems to issues concerning the philosophy of mathematics and, not surprisingly—given his active work in mathematical education—one on the teaching of this subject. Most of them were published in The Journal of Symbolic Logic and only one in the Bulletin of the American Mathematical Society. We will start by sorting these works into subjects and continue by providing a brief summary of each of them in order to point out those aspects that are originally from Henkin, and what we take to be mistake…
Associative and reflective connections between the limit of the difference quotient and limiting process
2006
Abstract This paper reports a study of how students may connect the limiting process inherent in the derivative to the limit of the difference quotient (LDQ) when solving problems. The data was collected mainly through task-based interviews with five eleventh grade students. It was found that the students used various kinds of limiting processes and connected them in different ways to LDQ. Some of them changed between these two representations, and some students explained one with the other. The two kinds of connections were, respectively, named as associative and reflective connections. One of the students, who made the associative connection, used LDQ skillfully. On the contrary, a studen…
Representable states on quasilocal quasi *-algebras
2011
Continuing a previous analysis originally motivated by physics, we consider representable states on quasi-local quasi *-algebras, starting with examining the possibility for a {\em compatible} family of {\em local} states to give rise to a {\em global} state. Some properties of {\em local modifications} of representable states and some aspects of their asymptotic behavior are also considered.
A BASIC MODEL OF INTERACTING SUBJECTS
1980
Abstract In studying the problem of interaction between subjects, an approach which allows us to define in an unambiguous way the concepts of symmetrical, complementary and parallel interaction is proposed. This approach makes use of a point of view within which it is possible to develop a rational model based only on some fundamental elements of set theory and mathematical logic The model allows us to develop a probabilistic theory of change, the representation basis of which is furnished by the 16 basic set functions. The functions represent operations on two partially overlapping sets, which will be called the “worlds”, of interacting subjects.. Both an interaction test that allows a “me…
Fundamentals of the design and the operation of an intelligent tutoring system for the learning of the arithmetical and algebraic way of solving word…
2013
Designers of interactive learning environments with a focus on word problem solving usually have to compromise between the amount of resolution paths that a user is allowed to follow and the quality of the feedback provided. We have built an intelligent tutoring system (ITS) that is able to both track the user's actions and provide adequate supervision during the resolution. This is done without imposing any restriction on the resolution paths that are allowed. Instead, the system attempts to enforce metacognitive learning by requiring an appropriate definition of quantities before they are used. The program (a) supports both the arithmetical and algebraic way of solving problems; (b) allow…
Chemical logic challenge.
2004
Does complexity explain the structure of trade?
2013
This paper analyzes whether complexity, measured by the number of skilled tasks that are performed in production, explains countries commodity trade structure. We modify the Romalis ( ) model to incorporate advantage differences in complexity across commodities together with differences in the number of mistakes made by workers in the production process in developed and developing countries as a source of comparative advantage. Our model predicts that the share of developed countries in world trade increases with products complexity. Empirical tests confirm this prediction. Moreover, we find that complexity complements the explanation provided by skillintensity on countries commodity trade …
Non-Hierarchical Clustering as a method to analyse an open-ended questionnaire on algebraic thinking
2016
The problem of taking a data set and separating it into subgroups, where the members of each subgroup are more similar to each other than they are to members outside the subgroup, has been extensively studied in science and mathematics education research. Student responses to written questions and multiple-choice tests have been characterised and studied using several qualitative and/or quantitative analysis methods. However, there are inherent difficulties in the categorisation of student responses in the case of open-ended questionnaires. Very often, researcher bias means that the categories picked out tend to find the groups of students that the researcher is seeking out. In this paper, …
Introduction to Nuclear-Reaction Theory
2019
These notes summarise the lectures I gave during the summer school "International Scientific Meeting on Nuclear Physics" at La R\'abida in Spain in June 2018. They offer an introduction to nuclear-reaction theory, starting with the basics in quantum scattering theory followed by the main models used to describe breakup reactions: the Continuum Discretised Coupled Channel method (CDCC),the Time-Dependent approach (TD) and the eikonal approximation. These models are illustrated on the study of the exotic structure of halo nuclei.