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Presentation
Presentation
In this course the student is faced with problem solving. For this, it is intended to promote logical reasoning and critical thinking, acquiring knowledge in the areas of propositional logic, sets and graph theory.
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Class from course
Class from course
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Degree | Semesters | ECTS
Degree | Semesters | ECTS
Bachelor | Semestral | 6
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Year | Nature | Language
Year | Nature | Language
1 | Mandatory | Português
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Code
Code
ULP452-1656
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Prerequisites and corequisites
Prerequisites and corequisites
Not applicable
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Professional Internship
Professional Internship
Não
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Syllabus
Syllabus
1. ELEMENTS OF MATHEMATICAL LOGIC.
Principle of non-contradiction and principle of excluded third party.
Propositional calculus: propositions and logical connectives.
Well-formulated formulas and semantics.
Correct arguments and normal forms.Natural deduction.
Logical equivalence. De Morgan formulas. Real tables.
Tautology, contradiction and contingency. De Morgan formulas.Logic of statement. Predicate Logic
2. ELEMENTS OF SET THEORY
Sets and set operations. Relationship algebra.
Cardinal of a finite set. Partition of a set.
Inclusion and exclusion principle.
3. GRAPH THEORY
Definition and Terminology of Graphs.
Cycles, paths and connectivity.
Matrix representation.
Graph of Euler and Hamilton.
Problem representation through graphs.
Problems in networks: Maximum flow and minimum path networks. Minimum cost spanning trees.
Graph Coloring.
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Objectives
Objectives
One of the main objectives of this course is to learn new tools and techniques of in order to facilitate the resolution of problems in several areas. Students must be able to analyze problems using mathematical methodologies in the area of ¿¿propositional logic, relations between sets and in the graphical (and schematic) representation of problems using graphs. It is intended that students acquire basic skills that allow them to advance in more advanced content in other curricular units of the course.
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Teaching methodologies and assessment
Teaching methodologies and assessment
Application of software tools to support and enhance the teaching-learning process.
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References
References
- Sridharan, S., & Balakrishnan, R. (2018). Foundations of Discrete Mathematics with Algorithms and Programming. Chapman and Hall/CRC.
- Balakrishnan, R., & Sridharan, S. (2019). Discrete Mathematics: Graph Algorithms, Algebraic Structures, Coding Theory, and Cryptography.
- Epp, S. S. (2018). Discrete mathematics with applications. Cengage Learning. Chapman and Hall/CRC.
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Office Hours
Office Hours
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Mobility
Mobility
No
