Learning any area of mathematics requires a comprehension of the concepts occurring in the area (each of which requires a clear definition) and a knowledge of certain valid statements, each of which is either an axiom (whose truth is accepted without proof) or a theorem (whose truth can be established with the aid of concepts and other statements). This is best accomplished if we can understand proofs of theorems and are able to write some proofs of our own. In course discrete mathematocs will be introduced to several methods of proof that can be used to establish the truth of theorems as well as ways to show that statements are false. These methods are based on logic, which allow us to use reasoning to show that a given statement is true or false. Although it is not our intention to go into any of this in great depth, it is our goal to present enough details and examples so that a sound introduction to proofs can be obtained. Developing a good understanding of proofs requires a great deal of practice and experience and comprehending how others prove theorems. The main areas of study are logic and proofs, predicates and Quantifiers theory, set theory, number theory, relations and functions, sequences, numerical series and induction

The objective of the Discrete Mathematics course is to provide students broad and accessible guide to the fundamentals of discrete mathematics and to show how it may be applied to various areas, especially computer science and information technology. Through this course it is intended to learn students schemes and algorithms of mathematical logic in order to have them as effective tools for solving various problem situations. To achieve this goal, in the teaching materials of the discrete mathematics course, concepts related to mathematical logic, predicates and quantifier, mathematical theory of sets, mathematical reasoning, number theory, relations, functions, recurrences, algorithms, sequence, numerical series and mathematical induction.