ISLA Santarém 1

Mathematics I

• ApresentaçãoPresentation

  The course introduces essential concepts of algebra, logic, sets, relations, and graphs, developing structured mathematical reasoning and the ability to model and solve problems, preparing students for advanced courses and academic and professional challenges.  
• 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. 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

  Avaliação Curricular: O estudante realiza 2 fichas de exercícios em grupo e dois testes individuais. O estudante aprova se a classificação final for superior ou igual a 9.5 valores. A classificação final é calculada pela fórmula Classificação Final = 0.2*F1+0.3*T1+0.2*F2+0.3*T2, onde F1, F2, T1 e T2 denotam, respetivamente, as notas nas fichas de exercícios e nos testes individuais. 

  Avaliação Final: O estudante realiza o exame completo e aprova se obtiver classificação superior ou igual a 9.5 valores.

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