ISLA Santarém 2091

Linear Algebra

• ApresentaçãoPresentation

  Fornecer as ferramentas matemáticas essenciais para compreender e desenvolver algoritmos utilizados em várias áreas da informática.
• ProgramaProgramme

  1 Elements of Set Theory 1.1 Relation of belonging. Equality of sets. Empty set. Inclusion relation. Set of parts. Difference of sets. Complementary sets. Union and intersection. 1.2 Cartesian product. Relations. Operations with relations. 1.3 Whole numbers. Divisibility. Prime numbers. Division algorithm. Congruence. 1.4 Functions. Injective, surjective and bijective functions. Inverse functions. Permutations. 2. Algebraic structures 2.1 Semigroups and Groups. Commutative groups. Notion of isomorphism. Subgroups. Finite groups. 2.2 Lagrange's theorem. Rings and bodies. Finite bodies. 3. Elements of Linear Algebra 3.1 Systems of linear equations. Gauss elimination. 3.2 Matrices. Operations with matrices. Inverse matrix. 3.3 Determinants. Properties of determinants. Applications of determinants. 3.4 Linear spaces. Subspaces. Bases and dimension of a linear space.
• ObjectivosObjectives

  O1. To provide students with knowledge of set theory. O2. To introduce the concepts of algebraic structures. O3. Introduce the fundamentals of linear algebra. Competences: C1. Solve problems using equations and functions. C2. Use matrix theory to study and solve systems of linear equations. C3. Calculate determinants, eigenvalues and eigenvectors. C4. Apply linear algebra techniques to analytic geometry. C5. Interpret and apply the concepts associated with vector spaces and eigenvalues and eigenvectors. C6. Present problem-solving clearly and concisely.
• BibliografiaBibliography

  Ferreira, M. A & Amaral, I. (2020). Álgebra Linear Vol.1 e 2. Edições Sílabo. Gonçalves, R. (2022). Álgebra Linear, Teoria e Prática. Edições Sílabo. Johnston, N. (2021). Introduction to Linear and Matrix Algebra. Springer. Lay, D. C., Lay, S. R., & McDonald, J. J. (2021). Linear Algebra and its applications 6th edition. Pearson. Poole, D. (2016). Álgebra linear: uma introdução moderna. 2a Edição. Cengage Learning, São Paulo (Brasil).
• MetodologiaMethodology

  Synchronize remotely: 1. Expository methodology: address the concepts of different themes, following the demonstrative method in practical exemplification of the content. In person: 2. Practical application: carrying out a series of exercises inside and outside the classroom, inducing active and autonomous participation from students. 3. Active methods, using Motivation strategies and Active Pedagogical Methodologies such as Flipped Classrooms and Gamification. Autonomous: 4. Consolidation of the content taught in class through research for additional information on the different topics covered and development of additional work proposed by the teacher through the Moodle platform. The teacher provides feedback (Tutorial Guidance – OT) on the results obtained by the student in solving the proposed problems, in person in a classroom context or remotely in asynchronous mode via the Moodle platform
• LínguaLanguage

  Português
• TipoType

  Semestral
• ECTS

  6
• NaturezaNature

  Mandatory
• EstágioInternship

  Não
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  Descrição	Data limite	Ponderação
  Teste de avaliação	17-11-2025	50%
  Teste de avaliação	12-01-2026	50%
  (...)

   

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