A Comparative Review of Core Models and Techniques in Discrete Mathematics

Abstract

The investigation of only finite and countable structures becomes the foundation for many applications, which serve as a base for various computations and analysis in discrete mathematics. The comparative study on four fundamental areas of discrete mathematics – Graph Theory, Combinatorics, Mathematical Logic and Discrete Probability is presented in this paper. It will help to analyze their characteristics, computational and practical aspects of application in the different domains like computer science, artificial intelligence, networking and optimization. All four techniques were considered by providing an overview of the technique and describing the advantages and disadvantages of the approach. Such techniques like Graph Theory were praised for their capability to represent relationships and networks. Also, the exactness of Combinatorics for counting and ordering was mentioned while criticizing their inefficiency because of exponential growth. The possibility of using mathematical logic for reasoning and decision-making systems is discussed. Finally, the capabilities of Discrete Probability to manage uncertainties and perform predictive modeling in data driven systems were analyzed. Comparative Assessment will be developed to consider four techniques by a few selected criteria, such as Computational Complexity and Scalability. Results indicate that there is no ideal approach; all approaches are suitable depending on certain types of problems. Furthermore, the paper identifies contemporary trends in the area, among them being the application of these approaches to problems such as those solved by machine learning models using graphs and probabilistic logic. The current review will contribute towards improving knowledge on discrete mathematics approaches as well as generate ideas regarding which approach to apply for computing challenges.