Matemática I

NA

In this UC the following teaching methodologies are used:

1) Verbal Methodologies (say), making use of pedagogical resources: Exposition, Explanation, Dialogue and Interrogation;

2) Intuitive Methodologies (show), making use of pedagogical resources: Demonstration, Audiovisual and Written Texts.

This UC aims to allow the student to master the principles, techniques and methodologies associated with discrete structure problems.

It is intended to provide the student with bases to be able to:

-recognize mathematical structures in discrete systems;

-manipulate discrete structures through specific techniques for each type of structure;

– prove properties of discrete structures

-Use discrete mathematics as a problem solving language;

-develop abstract reasoning, from a logical and mathematical point of view.

set theory

Sets: definition and representations

Subsets

Operations on sets: reunion, intersection and difference

Cardinality

Partitions and Power of Sets

math induction

Cartesian product of sets

Relationships: definitions, representations and properties

Functions: definition, injectivity, superjectivity and inversion

Logic and propositional calculus

Elementary Logic Propositions and Operations

real tables

Tautologies and counts

Equivalence. Algebra of propositions. Modus ponens and syllogisms

Combinatorial Analysis and Probabilities

Introduction

Fundamentals of counting

Permutations and Combinations

Inclusion/Exclusion Principle

combinatorial calculus

Paschal’s Triangle

 Introduction to Graph Theory

Introduction

Basic definitions

Incidence and degree

isomorphisms

Subgraphs

Tour, Route and Path

Connected Graph and Bipartite Graph

Digraphs: isomorphism and connectedness

Representation of graphs by matrices

trees

• - Individual Written Exams and Individual Works - 100.0%

• - Exam - 100.0%

NAO