Subject: Discrete Mathematics

Scientific Area:

Mathematics

80 Hours

Number of ECTS:

7,5 ECTS

Language:

Portuguese

Overall objectives:

1 - Develop modeling, abstraction, calculus and deduction capabilities.
2 - Introduction (or revision) of the basic elementary mathematics that is the basis of the computing foundations and of the analysis of the efficiency of algorithms.

Syllabus:

1 - Informal introduction to the logical connectives and quantifiers.
2 - Sets: power set, major operations on sets, unions and intersections of generalized sets; sets, "bags" ("multiset") and sequences (lists); Cartesian product of sets.
3 - Relations: n-relations and binary relations; equivalence relations and quotient set; order relations and related concepts, partially and totally ordered sets, well order and well-founded relations.
4 - Functions: (partial) functions and applications, composition of functions, operations and algebraic structures, families of elements of E indexed by I; applications Injective, surjective and bijective and some results.
5 - The problem of the cardinality of a set: equipotent sets, finite and infinite sets, countable and numerable sets; fundamental results and some useful criteria for demonstrating that a set is countable or not (illustration of the diagonal method).
6 - Structures (sets with structure ") and morphisms between structures: the essential idea; morphisms and isomorphisms between relational structures; morphisms and isomorphisms between algebraic structures.
7 - Inductively defined sets and proofs by induction (finite, structural and well-founded).
8 - Sums and series.
9 - Recurrence relations.
10 - Applications in the analysis of the efficiency of algorithms and key notations for describing the behavior (growth) of asymptotic functions.

Literature/Sources:

J. Carmo , 2005 , Noções Básicas para a Matemática do Discreto , Universidade da Madeira

Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
Two tests to solve individually.