| Code |
16214
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| Year |
1
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
Knowledge covered up to 3rd Cycle Basic Education.
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Mode of delivery |
Face-to-face instruction.
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Work placements |
Not applicable.
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Learning outcomes |
This curricular unit's main objective is to study basic concepts in the following fundamental areas of Mathematics: Mathematical Analysis, Linear Algebra, Geometry, Logic and Graph Theory. They constitute an essential tool in the scientific area of ??IT and essential in the student's curricular path.
At the end of the curricular unit, the student must be able to:
- Identify a function, graphical representation;
- Calculate derivatives, primitives and integrals using basic and essential functions;
- Identify special matrices, operate with matrices, determine the characteristics of a matrix;
- Classify and solve systems of linear equations;
- Calculate determinants, identify their properties, application of determinants;
- Know the rules and methods of propositional calculus, prove elementary results with sets;
- Identify graphs and some definitions, adjacency matrix and incidence matrix of a graph.
- Identify Euler and Hamilton graphs.
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Syllabus |
Module 1 – Basic Education Reviews: Equations and Inequalities, 1st and 2nd grade; Range(s) of real numbers; Definition and Basic Concepts of functions.
Module 2 – Real functions of real variables: Basic functions and essential functions; Graphical representation of functions; Derivatives of functions by derivation rules; Basic primitives and integral calculus.
Module 3 – Introduction to Linear Algebra: Matrix definition and Matrix operations; Characteristic of a matrix; Resolution and Classification of systems of linear equations; Determinant of a square matrix; Properties; Laplace's theorem; Application of determinants to the existence of the Inverse of a square matrix and its calculation; Application of determinants to the resolution of SPD systems.
Module 4 – Vectors: Approach to Geometry in the Plane; Introduction to Geometry in Space.
Module 5 – Brief notions of Logic and Set Theory
Module 6 – Introduction to Graph Theory
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Main Bibliography |
Main Support for the discipline:
Notes (“files”) provided by the Teacher on the Moodle platform.
Supporting books:
- Calculation
James Stewart
Translation of the 7th North American edition, vol.1 and 2 (CENGAGE Learning)
- Linear Algebra with Applications
Howard Anton, Chris Rorres
10th edition By João P. (Bookman, 2012)
- Discrete Mathematics
D. Cardoso, J. Szymanski, M. Rostami
(School Editora, 2009)
- Sage Beginners’s Guide
Craig Finch
(Packt Publishing – open source)
- Logic and Sets
Francisco G. Muniz Cunha
(Open University of Brazil, Degree in Mathematics)
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Teaching Methodologies and Assessment Criteria |
Attendance is one of the parameters of the evaluation criteria. The UC requires first-time students to have an attendance of 85% (i.e., 21 classes out of the 24 classes in the semester) and requires students with more than one enrollment to attend 11 classes, except in the case of students in special regimes. . Continuous assessment (CA) consists of independent work on an online platform, mini-tests and in-person tests.
The granting of ATTENDANCE depends on the attendance regime previously established and on obtaining, in the AC tests, a minimum classification of 6 values ??(AC rounded to the nearest integer). Continuous assessment: final classification equal to or greater than 9.5 then the student will be exempt from the exam; final classification higher than 17, then the student can take a supplementary written test to obtain a final classification higher than 17. Only students granted ATTENDANCE can appear for the exam.
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Language |
Portuguese. Tutorial support is available in English.
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