Discrete Mathematics and Graph Theory

This textbook can serve as a comprehensive manual of discrete mathematics and graph theory for non-Computer Science majors; as a reference and study aid for professionals and researchers who have not taken any discrete math course before. It can also be used as a reference book for a course on Discrete Mathematics in Computer Science or Mathematics curricula.

The study of discrete mathematics is one of the first courses on curricula in various disciplines such as Computer Science, Mathematics and Engineering education practices.

Graphs are key data structures used to represent networks, chemical structures, games etc. and are increasingly used more in various applications such as bioinformatics and the Internet. Graph theory has gone through an unprecedented growth in the last few decades both in terms of theory and implementations; hence it deserves a thorough treatment which is not adequately found in any other contemporary books on discrete mathematics, whereas about 40% of this textbook is devoted to graph theory.

The text follows an algorithmic approach for discrete mathematics and graph problems where applicable, to reinforce learning and to show how to implement the concepts in real-world applications.

Provides a detailed, thorough, and comprehensive review of concepts in discrete mathematics and graph theory Includes an introductory chapter on algorithms, and presents numerous concepts using algorithmic notation, where applicable Accessible enough to serve as a quick reference even for undergraduate students of disciplines other than computer science

Auteur

Dr. Kayhan Erciyes is a full Professor in the Department of Computer Engineering at Üsküdar University, Istanbul, Turkey. His other publications include the Springer titles Distributed Real-Time Systems, Guide to Graph Algorithms, Distributed and Sequential Algorithms for Bioinformatics, and Distributed Graph Algorithms for Computer Networks.

Résumé
"This accessible reference book should be well received by undergraduate-level CS, engineering, and mathematics students." (Soubhik Chakraborty, Computing Reviews, July 12, 2022)
"The book under review is an elementary introduction to mathematical logic, set theory, discrete mathematics, number theory, probability theory and graph theory. Its undoubted advantage is its good algorithmic support. ... I would recommend this book to students studying computer science at the bachelor's level." (I. M. Erusalimskiy, zbMATH 1477.68004, 2022)

Contenu
Preface .- Part I: Fundamentals of Discrete Mathematics .- Logic.- Proofs.- Algorithms.- Set Theory.- Relations and Functions.- Sequences, Induction and Recursion.- Introduction to Number Theory.- Counting and Probability.- Boolean Algebra and Combinational Circuits.- Introduction to the Theory of Computation.- Part II: Graph Theory .- Introduction to Graphs.- Trees and Traversals.- Subgraphs.- Connectivity, Network Flows and Shortest Paths.- Graph Applications.- A: .- Pseudocode Conventions.- Index .