1

2018-2019

01001121

Mathematics

Portuguese

Face-to-face

SEMESTRIAL

6.0

Compulsory

1st Cycle Studies

Good knowledge of High School Mathematics.

The discipline encompasses:

- expository classes, appealing to the participation of students;

- classes where the student is expected to present proofs of some theorems and to solve exercises proposed by the teacher.

Get the students familiar with:

- the processes of argumentation/deduction, proof and refutation in Mathematics;

- the arguments, reasoning over pictures, the architecture and writing of convincing arguments based on pictures;

- the visualization of problems and geometric objects; illustrations of the axiomatic viewpoint in plane geometry;

- the theorems and methods of geometry.

The main competencies to develop are: knowledge of mathematical results; generalization and abstraction; to formulate and solve problems; logic argumentation; conception or use of mathematical models to real situations; individual initiative; clear and rigorous written and oral expression; autonomous learning capabilities; imagination and creativity; critical sense; communication skills.

An axiomatic system for Geometry. Congruence and properties of triangles. Circumference properties. The axiom of parallels. Euclidian geometry. Similar triangles. Centers of a triangle. Determination of the measures of a triangle. Area. Isometries. Compass and ruler constructions. Hyperbolic geometry. Parallelism in the hyperbolic plane. Hyperbolic Pythagoras theorem. Area in hyperbolic plane.

António Manuel Freitas Gomes Cunha Salgueiro

Assessment

*Exam or Midterm exam: 100.0%*

A. Salgueiro, Geometria, Universidade de Coimbra, 2012

G. E. Martin, The foundation of Geometry and the Non-Euclidian Plane, UTM Springer Verlag, 1998

H. S. M. Coxeter, Introduction to Geometry, 2ª ed, John Wiley & Sons, 1989

P. Araújo, Curso de Geometria, Gradiva, 1998