Subject: Mathematics I

Scientific Area:

Mathematics

63 Hours

Number of ECTS:

6 ECTS

Language:

Portuguese

# Overall objectives:

1 - The main aim of the course is to equip all students with the same level of mathematical knowledge. Note that many of the students attended only the discipline of mathematics until the 9th grade, so it is necessary to provide the fundamental concepts missing, so that everyone has the opportunity to learn the new concepts. Thus, it is necessary to review several subjects of secondary school. It is intended that students acquire the basic concepts of mathematics by providing a maturation of the subjects studied. It is also expected their cognitive development. It is expected that students acquire fundamental concepts of sets, to manipulate the natural numbers, integers and real numbers. It is also expected the acquisition of the contents of binary operations and order relations. Finally, it is intended to promote discussion and solving problems.

# Syllabus:

1 - Resolução de Problemas.
2 - Maps.
3 - Cardinal of a set.
4 - Equipotent sets.
5 - Natural Numbers, Integers, Rational number, Real numbers.
6 - Binary Operations.
7 - Sum and product of natural numbers, integers, rational numbers, real numbers.
8 - Binary relations.
9 - Order relations.
10 - Partially Ordered Sets.
11 - Totally Ordered Sets.
12 - Well-ordered sets.
13 - Congruence relations.
14 - Solving and Discussing problems.

# Literature/Sources:

Costa, Liliana , s. d. , Matemática 11º ano , s. ed
J. Campos Ferreira , 2001 , Elementos de Lógica Matemática e Teoria dos Conjuntos , Instituto Superior Técnico
J. Carmo, P. Gouveia, F. M. Dionísio , 2013 , Elementos de Matemática Discreta , Milton Keynes: College Publications
J. S. Pinto , 1999 , Tópicos de Matemática Discreta , Universidade de Aveiro
Lopes, Ana Vieira. , 1993 , Matemática 10 , Ed. Contraponto
Neves, Conceição , 1991 , Descobrir os números: Matemática , Porto Editora
Richard W. , 2008 , Pre-Algebra Concepts , Fisher
Williams , Elizabeth , 1994 , Primary Mathematics Today: Towards the 21st Century , Ed. Longman
Zegarelli,Mark , 2009 , Matemática Básica & Pré-Algebra para Leigos , Alta Books

# Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
In some classes the teacher exposes the contents and then proposes to the students the resolution of exercises. In others it proposes the resolution and discussion of problems as a starting point for the 'discovery' of mathematical contents. The evaluation is continuous and the participation in classes is weighted at 10%. The other 90% are evaluated in two tests with each of them being 45% percent.