Authors: Dr. J. Raji, Dr. M. Praveen Kumar, Dr. Deepasree S Kumar and Dr. H.S. Kavya

ISBN: 978-81-987720-9-1

DOI: https://doi.org/10.59646/dms/372

Date of Publication: May 21, 2025

About the Book:

“Discrete Mathematical Structures” is a comprehensive textbook designed to equip students with the foundational tools and advanced techniques necessary for understanding and applying discrete mathematics in the context of computer science, mathematics, and engineering. Spanning five richly detailed units, the book presents a structured and application-oriented approach to key topics such as logic, number theory, set theory, functions, relations, combinatorics, group theory, and recursion. Beginning with the Fundamentals of Logic, the book offers an accessible entry into logical reasoning, truth tables, rules of inference, and quantifiers — all essential for algorithm design and programming. The text then transitions into the Properties of the Integers, where learners explore mathematical induction, recursive definitions, counting principles, permutations, and combinations. This lays the groundwork for analyzing problems with mathematical rigor and precision. In Relations and Functions, the book delves into mappings, function types, relations, graphs, and orderings — core to understanding databases, state machines, and algorithm analysis. The subsequent unit on the Principle of Inclusion and Exclusion introduces sophisticated counting methods and recurrence relations, empowering students to tackle complex enumeration problems and discrete probability scenarios. The final unit, Introduction to Group Theory, introduces the abstract algebraic structures that underpin symmetry, cryptography, coding theory, and modular arithmetic. With focused discussions on subgroups, cyclic groups, permutations, cosets, and Lagrange’s Theorem, students gain both theoretical insight and practical analytical tools. Each topic is reinforced with real-world applications, illustrative examples, and clearly explained proofs. The book is especially suitable for undergraduate students of computer science, information technology, mathematics, and related disciplines, and it aligns well with curricula that emphasize computational thinking and problem-solving. Whether used for coursework, competitive exam preparation, or independent learning, “Discrete Mathematical Structures” serves as a reliable and engaging companion on the journey to mastering the discrete mathematical foundations essential for modern computing and beyond.