Mathematics and Statistics
1st Cycle Studies
Mathematics, 9th year of schooling.
The classes are of theoretical and of theoretical-practical type. So they are of expository nature and include examples and exercises that lead the students to understanding and applying the material being taught. The classes are, as far as possible, dynamic, in the sense that the theoretical presentation are followed by resolution of exercises. Autonomous work is encouraged, purposing problems for reflection/resolution at home. Tutorial support will be available, including guidance to solve the proposed problems.
The main goal of the course is to introduce some fundamental concepts of mathematics useful for the development of a scientific basis of digital technology and design. Is intended that the student learns some of the skills necessary for the mathematical manipulation of geometry and the description of statistical data. It is important that the student interprets concepts from the geometrical point of view, more technical treatment of data is out of the range of the course. The course aims at developing the following skills: analysis and synthesis, organization and planning, oral and written communication, problem-solving skills. On the personal level it also allows to develop self-learning skills and independent thinking.
1. Introduction (the Pythagoras Theorem, the summation symbol, etc.). 2. Trigonometry. 2.1. Trigonometric functions. 2.2. Operations with trigonometric functions. 3. Introduction to the study of functions and curves, including parametrization. Introduction to continuity and derivatives. 4. Introduction to matrices. 4.1. Matrices. Definition and basic operations. 4.2. Special classes of matrices. 4.3 Determinants and inverse matrices. 5. Vectorial calculus and Transformation geometry 5.1. Vectors. Definition and basic operations. 5.2. Inner product and vectorial product of vectors 5.3. Lines and planes 5.4 Transformation Geometry 6. Descriptive Statistics 6.1. Introduction and summary of basic notions (sample, bar chart, histogram, measures of central tendency...) 6.2 . Measures of statistical dispersion 6.3 . Notions of probability and distribution, geometrical characterizations.
Paulo dos Santos Antunes
- Iniciação ao Estudo das Funções Reais de Variável Real, Luiz Sanchez (com a colaboração de Maria Luísa Mascarenhas),
Projecto REANIMAT (Faculdade de Ciências da Univ. Lisboa/Fundação Gulbenkian) http://www.ptmat.fc.ul.pt/~armac/Reanimat/materias10.htm
- Cálculo, 5ª ed., James Stewart, Pioneira Thomson Learning, 2006
- Introdução à Álgebra Linear e Geometria Analítica, A.P. Santana, J.F. Queiró, Gradiva, Lisboa, 2010
- Algebra and Trigonometry, Cynthia Young, 2nd edition, John Wiley & Sons, Inc, 2010
- Curso de Geometria, P. V. Araújo, Colecção Trajectos Ciência, Gradiva, 1998
- Isometrias, E. E. Lima, Isometrias, Colecção do Professor de Matemática, Sociedade Brasileira de Matemática, 1996
- Geometry, 2nd edition, S. Lang, G. Murrow, Springer-Verlag, New York, 1988
- Introduction to the Practice of Statistics, D. S. Moore, G. P. McCabe, W.H. Freeman and Company, 2003
- Manuais do Ensino Básico e do Ensino Secundário / Handbooks of High School