Linear algebra: selected problems

Linear Algebra—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Linear Algebra. Vector spaces are presented first, and linear transformations are reviewed secondly. Matrices and Linear systems are presented. Determinants and Basic geometry are presented in the last two chapters. The solutions for proposed excises are listed for readers to references.

Deciding Kleene Algebra Terms Equivalence in Coq

This paper presents a mechanically verified implementation of an algorithm for deciding the equivalence of Kleene algebra terms within the Coq proof assistant. The algorithm decides equivalence of two given regular expressions through an iterated process of testing the equivalence of their partial derivatives and does not require the construction of the corresponding automata. Recent theoretical and experimental research provides evidence that this method is, on average, more efficient than the classical methods based on automata. We present some performance tests, comparisons with similar approaches, and also introduce a generalization of the algorithm to decide the equivalence of terms of Kleene algebra with tests. The motivation for the work presented in this paper is that of using the libraries developed as trusted frameworks for carrying out certified program verification.

Lanczos algorithm on the grassmann manifold

5th. European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) 8th. World Congress on Computational Mechanics (WCCM8)

Teaching and learning mathematics using moodle

This paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the student understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. We also use the Excel and the mathematical open source software wxMaxima. To supplement our theoretical and practical classes we have developed a project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students, encourage them to overcome theirs difficulties through an auto-study giving them more confidence. In the MatActiva project the students have a big collection of information about the way of the subject works, which includes the objectives, the program, recommended bibliography, evaluation method and summaries. It works as material support for the practical and theoretical classes, the slides of the theoretical classes are available, the sheets with exercises for the students to do in the classroom and complementary exercises, as well as the exams of previous years. Students can also do diagnostic tests and evaluation tests online. Our approach is a reflexive one, based on the professional experience of the teachers that explore and incorporate new tools of Moodle with their students and coordinate the project MatActiva.

The active mathematics project at ISCAP

This paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the students understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. To supplement our theoretical and practical classes we have developed an active mathematics project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). In the last versions of Moodle, it is possible use the TeX language to create math questions. Using this tool we created a set of interactive materials. With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students, encourage them to overcome theirs difficulties through an auto-study, giving them more confidence and the opportunity to seeing others perspectives of the mathematics subjects. In the MatActiva project the students have a big collection of information about the way of the subject works, which includes the objectives, the program, recommended bibliography, evaluation method and summaries. It works as material support for the practical and theoretical classes, the slides of the theoretical classes are available, the sheets with exercises for the students to do in the classroom and complementary exercises, as well as the exams of previous years. Students can also do diagnostic tests and evaluation tests online. Our approach is a reflexive one, based on the professional experience of the teachers that explore and incorporate new tools of Moodle with their students and coordinate the project MatActiva.

Auditoria energética à indústria têxtil do Ave

A Indústria Têxtil do Ave S.A. (ITA) dedica-se, desde 1948, à produção de componentes têxteis para pneus em forma de fio torcido (corda) e tela. Estes componentes são quimicamente activados e impregnados em estufas, possibilitando assim a posterior adesão ao pneu. A máquina de impregnar corda Single End é composta pelos grupos de estiragem, por um recipiente contendo a solução química e por 4 estufas em série. A máquina de impregnar tela Zell é composta pelos grupos de estiragem, pelos acumuladores de saída e entrada, pelos recipientes com as soluções químicas e por um grupo de 7 estufas em série. O aquecimento das estufas é feito através da queima de gás natural. O presente trabalho teve como objectivo a realização de uma auditoria energética à ITA com um especial destaque às máquinas de impregnar corda (Single End) e tela (Zell). As correntes de entrada que contribuem para a potência térmica de impregnação são a combustão do gás natural, o ar de combustão, o ar fresco, o artigo em verde e as soluções químicas. As correntes de saída correspondem aos gases de combustão e exaustão, ao artigo impregnado e às perdas térmicas. A auditoria à máquina Single End mostrou que a potência térmica de impregnação é de 413,1 kW. Dessa potência térmica, 77,2% correspondem à combustão do gás natural, 6,7% ao ar de combustão, 15% ao ar fresco, 0,7% às cordas em verde e 0,4% à solução química. Da potência térmica de saída, 88,4% correspondem aos gases de combustão e exaustão, 3,2% às cordas impregnadas e 8,4% às perdas térmicas. Da auditoria à máquina Zell observou-se que a potência térmica de impregnação é de 5630,7 kW. Dessa potência, 73,3% corresponde à combustão do gás natural, 1,6% ao ar de combustão, 24,5% ao ar fresco, 0,3% à tela em verde e 0,3% às soluções químicas. Da potência térmica de saída, 65,2% correspondem aos gases de combustão e exaustão, 3,1% à tela impregnada e 31,7% às perdas térmicas. Foram sugeridas como medidas de optimização a redução dos caudais de exaustão das estufas e o aumento de temperatura do ar fresco. O aumento da temperatura do ar fresco da máquina de impregnar Single End para 50 ºC, usando ar quente dos torcedores, leva a uma poupança de 0,22 €/h, com um período de retorno do investimento de 13 anos e 4 meses enquanto o aumento para 120 ºC, usando o calor dos gases de combustão e exaustão, reduz os custos em 0,88 €/h, sendo o período de retorno para esse investimento de 2 anos e 6 meses. Na máquina de impregnar Zell, uma redução de 15% no caudal de exaustão numa das estufas leva a ganhos de 3,43 €/h. O aumento de temperatura do ar fresco para 45 ºC, usando o calor de gases de combustão e exaustão, leva a uma poupança de 9,93 €/h sendo o período de retorno para cada uma das duas sugestões de investimento de 5 meses e 9 meses.

LSP communication in a digital age: the outcomes of teaching and learning in tertiary education

This paper discusses the changes brought by the communication revolution in teaching and learning in the scope of LSP. Its aim is to provide an insight on how teaching which was bi-dimensional, turned into a multidimensional system, gathering other complementary resources that have transformed, in a incredibly short time, the ways we receive share and store information, for instance as professionals, and keep in touch with our peers. The increasing rise of electronic publications, the incredible boom of social and professional networks, search engines, blogs, list servs, forums, e-mail blasts, Facebook pages, YouTube contents, Tweets and Apps, have twisted the way information is conveyed. Classes ceased to be predictable and have been empowered by digital platforms, innumerous and different data repositories (TILDE, IATE, LINGUEE, and so many other terminological data banks) that have definitely transformed the academic world in general and tertiary education in particular. There is a bulk of information to be digested by students, who are no longer passive but instead responsible and active for their academic outcomes. The question is whether they possess the tools to select only what is accurate and important for a certain subject or assignment, due to that overflow? Due to the reduction of the number of course years in most degrees, after the implementation of Bologna and the shrinking of the curricula contents, have students the possibility of developing critical thinking? Both teaching and learning rely on digital resources to improve the speed of the spreading of knowledge. But have those changes been effective to promote really communication? Furthermore, with the increasing Apps that have already been developed and will continue to appear for learning foreign languages, for translation among others, will the students feel the need of learning them once they have those Apps. These are some the questions we would like to discuss in our paper.

The impact of an online mathematics education project (MATACTIVA) on higher education students

The Online Mathematics Education Project (MatActiva) is an exciting new initiative which aims to support and enhance mathematics education. The project is led by the Institute of Accounting and Administration of Porto (ISCAP), part of the Polytechnic Institute of Porto (IPP). It provides innovative resources and carefully constructed materials around themes such as Elementary Mathematics, Calculus, Algebra, Statistics and Financial Mathematics to help support and inspire students and teachers of mathematics. The goal is to increase mathematical understanding, confidence and enjoyment, enrich the mathematical experience of each person, and promote creative and imaginative approaches to mathematics. Furthermore the project can be used to deliver engaging and effective mathematics instruction through the flipped classroom model. This paper also presents the findings of a large survey, whose propose was to study the student’s reaction to the project.