| Code |
16776
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| Year |
1
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| Semester |
S1
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| ECTS Credits |
6
|
| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
N/A (We assume that knowledge in Mathematics has been acquired by the 9th year of schooling.)
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Learning outcomes |
The general objectives of this course unit (CU) are:
1) Provide students with basic concepts of Linear Algebra, Geometry and Statistics;
2) Provide students with the necessary mathematical tools for applications in other areas;
3) Help students to develop logical reasoning and critical thinking, learning basic methods of preparing proofs;
4) Provide students with basic skills in programming some mathematical topics on computer.
5) Develop in students the ability to carry out basic studies involving language, procedures and statistical measures.
With regard to the specific objectives of this course unit, after the learning process, students should be able at least to:
1) Define and graphically represent elementary functions;
2) Visualize and understand properties of geometric figures;
3) Recognize and apply geometric transformations;
4) Deepen the exploration, analysis, understanding, interpretation and production of statistical information.
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Syllabus |
1) Introduction: Pythagoras and Thales theorem, geometric figures.
2) Basic Matrix Calculus: matrices and operations, determinants and their applications.
3) Vectors and Geometry: vector definition and operations, geometry and measure, plane and space.
4) Functions and Models: Elementary functions, trigonometry, continuity and derivatives.
5) Parametric Equations: definition of curves and Bézier curves.
6) Descriptive Statistics: organization and treatment of data, notion of probability and distribution.
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Main Bibliography |
1) Nathaniel Johnston. Introduction to Linear and Matrix Algebra, Springer, ISBN: 978-3-030-52811-9, 2021.
2) Craig Finch. Sage Beginner's Guide (CoCalc.com), ISBN-13: 978-1849514460, 2011.
3) Isabel Cabral, C. Perdigão, C. Saiago: Álgebra Linear: Teoria, Exercícios Resolvidos e Exercícios Propostos com Soluções, Escolar Editora, Lisboa, 6ª edição, 2021. In Portuguese).
4) Peter Selinger. Matrix Theory and Linear Algebra, an open text, 1st Edition, 2018.
5) David C. Lay. Linear Algebra and Its Applications, 4th Edition
6) Luís T. Magalhães. Álgebra Linear como Introdução a Matemática Aplicada, Texto Editora, 1989.
7) James Stewart, Cálculo, Vol. 1 e 2, Translation to Portuguese from the 7th edition.
8) Manuals, from various publishers for Primary and Secondary Education.
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Teaching Methodologies and Assessment Criteria |
Teaching methodologies:
- Theoretical-Practical classes;
- Self-learning;
- Tutoring to clarify doubts and monitor the student in the in teaching-learning.
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Language |
Portuguese. Tutorial support is available in English.
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