Application of Discrete Mathematics for Programming Discrete Mathematics Calculations

Abstract

In the discrete mathematics courses, topics, such as the calculation of the element in any position of a sequence of numbers generated by some recurrence relation, calculation of multiplicative inverses in algebraic ring structures modulo a number n, obtaining the complete list of combinations without repetition, for which you can take advantage of the computing power of computers and perform such calculations using computer programs in some programming language. The implementations of these calculations can be carried out in many ways and therefore their algorithmic performance can be very varied. In this chapter, I propose to illustrate by means of some Matlab programs, how the use of results of the same discrete mathematics allows to improve the algorithmic performance of said computer programs. Another topic addressed in regular discrete mathematics courses where calculations arise that could become very expensive both in time and in occupied space, if the calculations are implemented directly from the definitions is modular arithmetic. Such calculations can be carried out much more efficiently by making use of results from discrete mathematics and number theory. The application of these ideas will be developed in the following sections of this chapter.