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.

A hybrid recommendation approach for a tourism system

Many current e-commerce systems provide personalization when their content is shown to users. In this sense, recommender systems make personalized suggestions and provide information of items available in the system. Nowadays, there is a vast amount of methods, including data mining techniques that can be employed for personalization in recommender systems. However, these methods are still quite vulnerable to some limitations and shortcomings related to recommender environment. In order to deal with some of them, in this work we implement a recommendation methodology in a recommender system for tourism, where classification based on association is applied. Classification based on association methods, also named associative classification methods, consist of an alternative data mining technique, which combines concepts from classification and association in order to allow association rules to be employed in a prediction context. The proposed methodology was evaluated in some case studies, where we could verify that it is able to shorten limitations presented in recommender systems and to enhance recommendation quality.