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ISLA Santarém 1

Mathematics I

Business Processes and Operations Management
  • ApresentaçãoPresentation
    The course of Mathematics I is a fundamental component of several undergraduate courses, particularly in the areas of Science, Technology, Economics, Management and Engineering, such as the Bachelor's Degree in Business Process and Operations Management. Its main objective is to provide students with a solid foundation in essential concepts of linear algebra, mathematical logic, set theory, binary relations and graphs, preparing them for more advanced subjects. The course presents theoretical and practical tools that are indispensable for modeling and solving problems in different areas of knowledge. Students are expected to develop structured logical-mathematical reasoning, which will allow them to interpret, formulate and solve problems, creating a knowledge base that can be applied in subsequent subjects. The course encourages students' critical and analytical thinking with practical applications in order to contribute positively to their academic and professional future.
  • ProgramaProgramme
    1. Elements of linear algebra 1.1 Notion of vector and operations between vectors 1.2 Matrices and operations with and on matrices 1.3 Determinants 1.4 Brief reference to vector spaces 1.5 Linear combination, dependence and linear independence of vectors 2. Introduction to elements of logic mathematical 2.1 Terms and propositions 2.2 Expressions with meaning 2.3 Logical operations 3. Elements of set theory 3.1 Generalities 3.2 Operations with sets 3.3 Power set 4. Binary relations 4.1 Overview of binary relations 4.2 Operations with binary relations 4.3 Properties of binary relations 4.4 Equivalence relations 5. Graphs and applications 5.1 Graphs and simple graphs 5.2 Isomorphic graphs 5.3 Euler Paths 5.4 Oriented graphs
  • ObjectivosObjectives
    The objectives of the curricular unit are: O1. Develop students' reasoning skills; O2. Develop skills related to linear algebra; O3. Introduce set theory; O4. Present the basic principles of logic, logical operations and their properties; O5. Present the principles of binary relations; O6. Provide students with knowledge related to graph theory. At the end of the curricular unit students should be able to: C1. Master the techniques associated with matrix calculus; C2. Master the basic principles of logic, logical operations and their properties; C3. Understand the fundamental concepts of graph theory and its applications.
  • BibliografiaBibliography
    Cabral, I., Perdigão, C., Saiago, C. (2021). Álgebra Linear: Teoria, Exercícios Resolvidos e Exercícios Propostos com Soluções. 6.ª Edição, Escolar Editora. Cardoso, D. M., Szyma¿ski, J. e Rostami, J. (2009). Matemática Discreta. Escolar Editora. Ferreira, M., Amaral, I., (2020). Álgebra Linear: Matrizes e Determinantes. Vol. 1, 8.ª Edição, Edições Sílabo. Howard, A., Rorres, C. (2012). Álgebra Linear com Aplicações. 10.ª Edição, Bookman. Lipschutz, S. & Lipson, M. (2013) Matemática Discreta. Bookman. Rosen, K. (2018). Discrete Mathematics and Its Applications. 8th Edition, McGraw Hill.  
  • MetodologiaMethodology
    The classes will address the concepts of the different themes and, later, show their practical application, with a series of exercises inside and outside the classroom, inducing the active and autonomous participation of students.   For this purpose, the use of the expository method is foreseen to introduce the concepts and structure the reasoning and the interrogative method for the learning evaluation, in the theoretical aspect of each chapter. With regard to the practical aspect, the use of the demonstrative method is foreseen for the practical illustration of the contents, as well as active, participatory and autonomous methods to make the connection with the experience of each one.   In summary: (1) Expository and Interrogative Methodology - participatory teaching, resorting whenever necessary to Motivation strategies and to (2) Active Pedagogical Methodologies such as Flipped Classroom, Gamification and Problem/Project Based Learning.
  • LínguaLanguage
    Português
  • TipoType
    Semestral
  • ECTS
    6
  • NaturezaNature
    Mandatory
  • EstágioInternship
    Não
  • AvaliaçãoEvaluation

    Época Normal - Avaliação curricular (contínua) (*): O estudante constrói um portfólio com base nas atividades de avaliação ativa desenvolvidas ao longo do semestre e realiza dois testes de avaliação individual. O estudante aprova se a classificação final for superior ou igual a 9.5 valores em 20 valores. A classificação final é calculada pela fórmula Classificação Final = 0.3*P+0.35*T1+0.35*T2, onde P, T1 e T2 denotam, respetivamente, as notas no portfólio e nos testes de avaliação individual.

    (*) A realizar no decorrer do semestre.

    Época Normal - Avaliação final: O estudante realiza o exame completo e aprova se obtiver classificação superior ou igual a 9.5 valores em 20 valores.

    Épocas de Recurso e Especial: O estudante realiza o exame completo e aprova se obtiver classificação superior ou igual a 9.5 valores em 20 valores.

     

    Descrição

    Data 

    Ponderação

    Portfólio

    Consultar Moodle, consoante a turma.

    30%

    Teste 1

    Consultar Moodle, consoante a turma.

    35%

    Teste 2

    		 Consultar Moodle, consoante a turma. 35%

    Exames

    		 A agendar pelos serviços. 100%