Fundamental approach to discrete mathematics

Salient Features Mathematical logic, fundamental concepts, proofs and mathematical induction (Chapter 1) Set theory, fundamental concepts, theorems, proofs, Venn diagrams, product of sets, application of set theory and fundamental products (Chapter 2) An introduction to binary relations and concepts, graphs, arrow diagrams, relation matrix, composition of relations, types of relation, partial order relations, total order relation, closure of relations, poset, equivalence classes and partitions. (Chapter 3) An introduction to functions and basic concepts, graphs, composition of functions, floor and ceiling function, characteristic function, remainder function, signum function and introduction to hash function. (Chapter 4) The algebraic structure includes group theory and ring theory. Group theory includes group, subgroups, cyclic group, cosets, homomorphism, introduction to codes and group codes and error correction for block code. The ring theory includes general definition, fundamental concepts, integral domain, division ring, subring, homomorphism, an isomorphism and pigeonhole principle (chapters 5, 6 and 7

Fundamental approach to discrete mathematics

About the Book: The book `Fundamental Approach to Discrete Mathematics` is a required part of pursuing a computer science degree at most universities. It provides in-depth knowledge to the subject for beginners and stimulates further interest in the topic. The salient features of this book include: Strong coverage of key topics involving recurrence relation, combinatorics, Boolean algebra, graph theory and fuzzy set theory. Algorithms and examples integrated throughout the book to bring clarity to the fundamental concepts. Each concept and definition is followed by thoughtful examples

Computational intelligence for big data analysis: frontier advances and applications

The work presented in this book is a combination of theoretical advancements of big data analysis, cloud computing, and their potential applications in scientific computing. The theoretical advancements are supported with illustrative examples and its applications in handling real life problems. The applications are mostly undertaken from real life situations. The book discusses major issues pertaining to big data analysis using computational intelligence techniques and some issues of cloud computing. An elaborate bibliography is provided at the end of each chapter. The material in this book includes concepts, figures, graphs, and tables to guide researchers in the area of big data analysis and cloud computing

Classifying Big Data Analytic Approaches: A Generic Architecture

The explosion of the huge amount of generated data to be analyzed by several applications, imposes the trend of the moment, the Big Data boom, which in turn causes the existence of a vast landscape of architectural solutions. Non expert users who have to decide which analytical solutions are the most appropriates for their particular constraints and specific requirements in a Big Data context, are today lost, faced with a panoply of disparate and diverse solutions. To support users in this hard selection task, in a previous work, we proposed a generic architecture to classify Big Data Analytical Approaches and a set of criteria of comparison/evaluation. In this paper, we extend our classification architecture to consider more types of Big Data analytic tools and approaches and improve the list of criteria to evaluate them. We classify different existing Big Data analytics solutions according to our proposed generic architecture and qualitatively evaluate them in terms of the criteria of comparison. Additionally, we propose a preliminary design of a decision support system, intended to generate suggestions to users based on such classification and on a qualitative evaluation in terms of previous users experiences, users requirements, nature of the analysis they need, and the set of evaluation criteria