Cursos / 1º Ciclo / Faculty of Architecture and Arts :: Architecture ( Integrated Master)

MATEMÁTICA - 2021/2022

1º curricular year
Semestralidade: 1st semester
ECTS: 4

Teachers

Leading Teacher: Mestre Carlos Garcia
Assistant Professor: Arqtª Cristina Pereira

Class type and School hours

Teórico-prática : 4 Horas

Teaching Language

Portuguese

Main Aims/Objectives

This curricular unit aims to contribute to the basic training of the student, as a future architect, so that he can interpret the mathematical formulation of the various areas in which he has to intervene, as well as using mathematics as an aid to architectural design, allowing him to increase their critical capacity and obtain bases that will be useful, both from the point of view of the tool to be used, and of structuring material in the development of reasoning.

Specific Aims/Objectives

It is intended to contribute to the student´s ability to interpret the architectural object and to understand modern and contemporary architecture, helping him to think, communicate, reflect with logic, manage knowledge and emotions and develop critical skills.

Skills to be acquired

Obtain and deepen knowledge, by learning the minimum concepts necessary to understand structures and graphic elements, proportions, spatial design and interpretation, developing bases for architectural design.

Teaching Procedures

This curricular unit has a weekly schooling of four hours, with two hours of formal theoretical exposition, and the other two dedicated to solving exercises.

Programme

LINEAR ALGEBRA AND ANALYTIC GEOMETRY:
I. Concepts and generalities.
II. Matrices.
III. Square matrices.
IV. Transposed of a matrix.
V. Adding matrices and multiplying matrices by a scalar.
VI. Multiplication of two matrices.
VII. Equality of matrices.
VIII. Symmetric and anti-symmetric matrices (square matrices).
IX. Elementary matrix operations.
X. Matrix equivalence.
XI. Inversion of square matrices.
XII. Algebra of square matrices.
XIII. Proposed problems.
XIV. Determinants. Geometric method. Sarrus´ method. Properties of determinants. Calculation of the determinant of a matrix of any order. Algebraic complement. Laplace´s theorem.
XV. Systems of linear equations. Gauss-Jordan diagonalization method. Explicit method. Cramer´s method.
XVI. Characteristics of one matrix.

THEORY OF PROPORTION:
I. Theory of proportion in architecture.
II. Elementary properties of the proportion.
III. Commensurable proportions, rational or static.
IV. Immeasurable, irrational or dynamic proportions.
V. The gold number: the divine proportion.
VI. Measures and proportion.
VII. The Le Corbusier Modulor.

Evaluation Type

Students perform evolutionary work on the material taught in class. Continuous assessment includes attendance to classes, the performance of students in carrying out the proposed exercises, all complemented with two written tests, of theoretical / practical nature.

Teaching Resources

The theoretical introduction of the material is carried out with the visualization of elements that are available to students on the moodle platform. After the theoretical introduction, exercises related to the subject follow, with the statements of these same exercises also available to students on the moodle platform.

Sustainability Objectives

Keywords

Think;
Logic;
Matrix;
Proportion.

Main Bibliography

Complementary Bibliography