Automatic subsemigroups of free products

AbstractWe consider the automaticity of subsemigroups of free products of semigroups, proving that subsemigroups of free products, with all generators having length greater than one in the free product, are automatic. As a corollary, we show that if S is a free product of semigroups that are either finite or free, then any finitely generated subsemigroup of S is automatic. In particular, any finitely generated subsemigroup of a free product of finite or monogenic semigroups is automatic

On the injectivity of the Leibniz operator

The class of weakly algebrizable logics is defined as the class of logics having monotonic and injective Leibniz operator. We show that \monotonicity" can- not be discarded on this definition, by presenting an example of a system with injective and non monotonic Leibniz operator. We also show that the non injectivity of the non protoalgebraic inf-sup fragment of the Classic Propositional Calculus, CPC_{inf,sup}, holds only from the fact that the empty set is a CPC_{inf,sup}-filter.FCT via UIM

Comparing learning objects for effective learning in Mathematics

The too high number of students per class, situation typically found in higher education in Portugal, makes it difficult to adopt an approach were the student work is taken as the center of the learning process. The use of digital contents in this context is helpful for the students to build their own appropriate environment outside the classroom, using all support and learning material built up for that purpose. A fundamental problem we have in Mathematics is that many students are not well prepared in previous concepts. We have been developing and using several kinds of learning objects (LO) for calculus in the recent years, some of them dedicated to recall previous concepts. Among all kinds of contents, students valorize more learning objects that simultaneously challenge them and give them useful feedback. In this paper, we compare the usefulness of different kinds of LO, using computers, in a calculus course for students from several sciences and engineering, with a population of 290 students, based on a survey answered by 40% of them. The learning objects include multiple-choice questions with detailed solutions, quizzes, formative tests, short videos, and others. We present a quantitative analysis comparing different kinds of LO, considering students of several study areas. Together with the quantitative analysis, we add some qualitative considerations based on student’s answers to open questions concerning the learning methodology adopted.publishe

Generalized Green'S Equivalences on the Subsemigroups of the Bicyclic Monoid

We study generalized Green's equivalences on all subsemigroups of the bicyclic monoid B and determine the abundant (and adequate) subsemigroups of B. © 2010 Copyright Taylor and Francis Group, LLC

Automatic structures for semigroup constructions

We survey results concerning automatic structures for semigroup constructions, providing references and describing the corresponding automatic structures. The constructions we consider are: free products, direct products, Rees matrix semigroups, Bruck-Reilly extensions and wreath products.Comment: 22 page

Science Competitions: Do They Foster Learning

Many studies have shown positive effects of gamification and serious games on teaching and learning. From 1989, we have been organizing National Science Competitions in Portugal, with participants from schools from all over the Country. In this work, we assess the impact of these competitions on student’s motivation and performance in the school. The study is mainly based on surveys done on the years 2015 and 2017. Both, students and their teachers, have participated in the surveys. We also present some data about usage of the computer system used in the competitions during the event and for practicing to the event. Based on teacher’s opinions we conclude the events have some positive influence on student’s motivation.publishe

Motivating Study Before Classes on Flipped Learning

For the flipped learning environment to be effective, it is essential that students use the learning materials before the classes, where they are supposed to practice, collaborating with colleagues with the help and guidance of the teacher. Students can easily get lost and unmotivated if the teacher simply gives them the learning material for studying before the classes. There is a need for some level of guidance and orientation in this autonomous learning for many students or they will go to the classes without having done the previous work required. We have developed a computer system with the main goal of motivating and guiding students to do this work before the classes. The computer system implements a Bayesian student model together with a learning trajectories model and makes use of a parameterized question generator, without any limitations on the parameterization we have also helped to develop. In practice, the computer system for learning presents the materials in an appealing and appropriate way, individually according to each student progress, including videos and other materials. Students can answer some of the many existing questions, generated among many parameterized templates, see detailed solutions of questions, also generated, and finally obtain a feedback about their progress in the learning contents required to next class. In the first semester of academic year 2017/2018, we have used our computer system with students in some of the topics of a course about calculus with several variables. The system keeps track of all activity and allows us to investigate student behaviour during the semester. We present an analysis of the system usage data on the topics in the experience comparing to those on traditional teaching, and relate with the results in final assessment, with the main goal of investigating the effectiveness of the use of this kind of computer systems in a flipped learning environment for motivating and guiding autonomous work before the classes.publishe