ISLA IPGT 24103

Discrete Mathematics and Linear Algebra

• ApresentaçãoPresentation

  Discrete Mathematics and Linear Algebra provides knowledge in the area of Mathematical Analysis, which is an essential tool in solving various types of problems. Mathematics is a means of communication, a formal and precise language. It is one of the essential and necessary theoretical bases of all the great systems of interpretation of reality that guarantee social intervention with responsibility and give meaning to the human condition. Mathematical knowledge is part of the cultural heritage of humanity because it has its own characteristics and procedures that have also evolved in the context of other sciences.
• ProgramaProgramme

  Introduction to Mathematical Logic Designations and propositions Definition and properties of logical operations Boolean Algebra Introduction Definitions. Axioms. theorems Logical functions and truth tables Logic functions and their representation in a logic circuit Canonical form of a logic function Set Theory Notion of set Representation of a set Relationship of belonging and non-belonging finite and infinite sets Inclusion ratio Fundamental operations with sets Set properties Binary Relations Ordered pair Cartesian product Representation of binary relations Inverse relationship Binary relations in a set Equivalence and order relations Matrices and Determinants Matrix calculation Transpose of a matrix Gauss form Inverse matrix Calculation of 2nd and 3rd order determinants Sarrus and Laplace rule Graphs Directed and undirected graphs Representation by matrices Isomorphisms Connected graphs Trees
• ObjectivosObjectives

  This curricular unit intends to develop the capacity of abstract reasoning (logical-mathematical), necessary for the development of competences to equate problems in general contexts. Knowledge: Know the concepts of Discrete Mathematics as a tool for investigations and precise applications in Computing and Informatics. Know some of the main application areas of the MDAL. Know fundamental concepts and results of Linear Algebra, providing learning, algebraic manipulation capacity and abstraction, and mathematical reasoning. Skills: Be able to understand/construct mathematical arguments. Be able to relate concepts and model problems involving the acquired knowledge. Be able to apply the concepts in modeling and solving problems related to technology and computing. Skills: Use a critical spirit in the analysis of the obtained results. Use mathematical symbology and achieve greater accuracy
• BibliografiaBibliography

  Gomes, C. & Gomes, R (2022). Material de Apoio à Unidade Curricular de Matemática Discreta e Álgebra Algebra. ISLA-Instituto Politécnico de Gestão e Tecnologia. Wiitala, Stephen A.1987. Discrete Mathematics A Unified Approach. McGraw-Hill International Editions Ayres, F. & Mendelson, E. 2000. Cálculo. McGraw-Hill Schaums Easy Outlines. Sarrico, C. (1999). Análise Matemática-leituras e exercícios (3ª ed.). Lisboa: Editora Gradiva. Budnick, F. S. (1993). Applied Mathematics for Business, Economics, and the Social Sciences (4ª ed.). McGraw-Hill.
• MetodologiaMethodology

  Use of moodle where the student has access to digital sebentas that allows him to absorb the content through the virtual medium and when arriving at the classroom is already aware of the subject to be developed. The "inverted classroom" makes it possible to know the concepts before approaching them allowing to monetize the time of learning.   Use of applications (PhotoMath, Maple Calculator, Microsoft Math Solver ...) that, in real time, allow the student not only to acquire knowledge but also to support their study.   Use of the interactive whiteboard to make presentations more dynamic.   Use of platforms (such as Zoom) to allow students who cannot be in person not to miss the possibility of integrating the class.
• LínguaLanguage

  Português
• TipoType

  Semestral
• ECTS

  6
• NaturezaNature

  Mandatory
• EstágioInternship

  Não