Class Discrete Mathematics

Discrete Mathematics is an area of mathematics of growing interest to computer sciences, life sciences, telecommunications, electronics, processor industry, integrated circuit design, cryptography and security in communications transmission, automobile traffic systems. The reciprocal influence of discrete mathematics with other areas of mathematics is increasingly visible, as in the case of operational research, algebra, number theory, geometry and topology. 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, recursivity and graph theory.  

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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. RECURSIVITY   4. 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.

Conducting a group test utilizing gamification techniques fosters increased student motivation for more active participation and also facilitates the development of teamwork skills.

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.