Mathematics

Code	14100
Year	2
Semester	S2
ECTS Credits	5
Workload	TP(60H)
Scientific area	Ciências Exatas
Entry requirements	-
Learning outcomes	It is intended that students acquire mathematical knowledge related to art and gain a favorable attitude toward mathematics through understanding of its beauty and usefulness. It is intended that students: 1. See the aesthetic component of mathematics; 2. Look beyond the mathematics calculation, identifying meanings in it and its problematic nature; 3. See mathematics as a tool to understand the complexity of the world; 4. Look at math as an additional source of resources for job creation and development; and 5. Use ICT, particularly graphing calculators, interpreting and criticizing the results they provide in accordance with mathematical theories.
Syllabus	1. THE AESTHETIC COMPONENT OF MATHEMATICS 2. PRELIMINARIES 2.1. Brief notions of logic and set theory 2.2. The set of real numbers 2.2.1. Real numbers, inequalities and absolute value. Topological concepts. 2.2.2. Equations and inequalities 2.3. Trigonometry 3. NUMBERS AND GEOMETRY 3.1. Proportions 3.1.1. Gold number 3.1.2. The Modulor (Le Corbusier) 3.1.3. Thales Theorem 3.2 Geometric constructions 4. THE SPACE R^n 4.1. Generalization of topological concepts to R^n 4.2. Sets in R^2 4.2.1. Geometric representation 4.2. Conics 4.3. Sets in R^3 4.3.1. Cylinders and quadratic surfaces 4.4. Areas and volumes. The Cavalieri principle. 5. REAL VARIABLE FUNCTIONS 5.1. Sequences. 5.2 Real variable functions 5.3 Limits and continuity 5.4. Rate of change and tangent line. 5.6 Derivative function. Differentiation rules. 5.7. Linearization and differentials 6. PARAMETRIZED CURVES
Main Bibliography	Burry, J. & Burry, M. (2010). The new mathematics of architecture. Thames & Hudson. Davis, P. & Hersh, R. (1995). A experiência matemática. Lisboa: Gradiva. Ghyka, M. (1983). Estética de las proporciones en la naturaleza y en las artes. Barcelona: Poseidon. Ghyka, M. (2014). The geometry of art and life. New York: Dover Publications. Le Corbusier & Sequeira, M. (2010). Modulor. Lisboa: Orfeu Negro. %Ver também:\\ Lima, Elon Lages, Curso de Análise, Volume I, 11.a edição, Projecto Euclides, IMPA, 2004. Stewart, J. (2014). Cálculo - Volume I, 7a edição. Cengage Learning. Stewart, J. (2014). Cálculo - Volume II, 7a edição. Cengage Learning. Veloso, E. (2012). Simetria e transformações geométricas. Lisboa: Associação de Professores de Matemática
Language	Portuguese. Tutorial support is available in English.