Fundamentals of Mathematics

Scholar Year: 2018/2019 - 1S

Courses

Head Teacher Responsability Sandra Cristina Dias Nunes Head

Weekly workload Hours/week T TP P PL L TC E OT OT/PL TPL O S Type of classes 4 Lectures Type Teacher Classes Hours Theoretical-practical Totals 2 8,00 Sandra Nunes   4,00 Sandra Monteiro   4,00

Teaching language

Portuguese

Intended learning outcomes (Knowledges, skills and competencies to be developed by the students)

Management Students need several important mathematical tools; such as logic and set theory, calculus and linear algebra, both present in economic theory and econometrics, which are key disciplines in this area. Mastering the basics of these areas is essential to the pursuit of studies in the field of business administration. Besides the knowledge of mathematical concepts is also an aim of this curricular unit to encourage and develop the ability to acquire and transmit certainty concerning the validity of certain statements from the recognition of the validity of simpler ones. Thus the course of Mathematics aims to enable students in acquiring basic mathematical skills necessary for the development of logical reasoning, articulate and apply the various concepts to solve problems, develop reasoning analysis, scientific thinking and critical attitude. The student should be able to apply information, to develop creative solutions and to solve complex problems.

Syllabus

1. LOGIC AND SET THEORY
1.1 Designations and mathematical statements
1.2 Propositional calculus
1.3 Designatorial and propositional expressions
1.4 Quantifiers
1.5 Set theory
2. VECTORS AND MATRICES
2.1 Definition of vector
2.2 Operations with vectors
2.3 Inner product and vector norm
2.4 Definition of matrix
2.5 Operations with matrices
2.6 Determinant of a matrix
2.7 Matrix inverse
2.8 Solving systems of linear equations in a matrix form
3. REAL FUNCTIONS OF REAL VARIABLES
3.1 Definition of function
3.2 Real Function of a real variable
3.3 Graphic representation and properties
3.4 Elementary functions
3.5 Operations with functions
3.6 Limits and continuity
4. DIFFERENTIAL AND INTEGRAL CALCULUS
4.1 Definition and geometrical interpretation of a function derivative
4.2 Rules of derivation
4.3 Derivative applications
4.4 The Riemann integral: definition and geometrical interpretation
4.5 Definition of primitive
4.6 Primitivation rules

Demonstration of the syllabus coherence with the UC intended learning outcomes

Foundations of Mathematics is a course of basic sciences essential to the development of reasoning. The contents are built to allow the acquisition of theoretical background needed in several areas of business and management for the consequent practical application of them. The program begins with mathematical logic and set theory arming students with mathematical language which is essential to understand the following contents. Then are introduced the most important concepts in the field of calculus and linear algebra, fulfilling one of the main goals of this course. In parallel the students are encouraged to solve practical exercises, real cases and problems that arise in a number of more specific courses fulfilling another objective of the course.

Teaching methodologies

The teaching methods applied are defined according to the type of classes and also on the type of objective. The classes are classified as theoretical –practical:
Theoretical part - Methodology Expository / Interrogative, by making use of participatory methodology; Practical part - Participatory Methodology through exercises and practical cases;
Continuous Evaluation: comprises two individual minitests and a final test.

Final Grade=20%xfirst minitest+20%xsecond minitest+60%xfinal test.

The two minitests has no minimum score; the final test has a minimum score of 7,0 and if this value is not reached, or if the final score is less than 10, there is no approval. Final evaluation - first season consists of a final exam, if the grade is less than 10, there is no approval. Second season. The evaluation system is the same of the Regular Season. Special season: the evaluation system is the same of the Final Season.

Demonstration of the teaching methodologies coherence with the curricular unit's intended learning outcomes

The selection of methods to be used is based on defined objectives.
In the curricular unit of Foundations of Mathematics the lectures theoretical part aims to develop predominantly a cognitive knowledge.
This theoretical part are mainly based on expository methods but also supported by pratical examples and, whenever possible, encouraging students participation. The student participation helps to clarify concepts, helps to reflect on the contents and help students in structuring, discrimination and integration of cognitive elements, developing the critical thinking and the mathematical reasoning.
The practical parts of classes are focused on the idea of “know-how”. These classes are supported on practical activities of solving exercises and problems through the application of concepts provided before, in the theoretical part. These activities should be performed mainly by the students; the teacher should only facilitate.
The theoretical part is followed by sequential practical exercises in order to apply all the knowledge learned in previous theoretical classes. These sequential exercises help and reinforce the knowledge and to understand that the theoretical knowledge is essential to a good practical application of it.

Assement and Attendance registers

Bibliography

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AZENHA, A., e JERÓNIMO, M. A. (2000). Elementos de Cálculo Diferencial e Integral em IR e IRn, McGraw-Hill, Lisboa.
Bandeira, L., Coelho, F. e Franco, N. (2016). Introdução à Matemática – Álgebra, Análise e Otimização. LIDEL-Edições Técnicas, Lda.
FERREIRA, J. C. (2001). Elementos de Lógica Matemática e Teoria de Conjuntos, Dep. Matemática do IST.
FERREIRA, M. A. (2004). Matemática - Exercícios de Álgebra Linear - Vol.1: Matrizes e Determinantes (4ª edição). Edições Sílabo, Lisboa.
FERREIRA, M. A. e AMARAL, I. (2008). Matemática - Álgebra Linear - Vol. 1: Matrizes e Determinantes (7ª edição). Edições Sílabo, Lisboa.
FERREIRA, M. A. e AMARAL, I. (2006). Matemática – Primitivas e Integrais (6ª edição). Edições Sílabo, Lisboa.
LARSON, R., HOSTETLER R. P. e EDWARDS, B. H. (2006). Cálculo – Volume I (8ª edição), MacGraw-Hill.
LUZ, C., MATOS, A. e NUNES, S. (2002). Álgebra Linear, vol I, Escola Superior de Tecnologia de Setúbal.
SARRICO, C. (2002). Análise Matemática – Leitura e Exercícios (8ª edição). Edições Gradiva.
SYDSAETER, K., e HAMMOND, P. J. (1995). Mathematics for Economic Analysis, Prentice- Hall International, Inc.