Authors: Kavita Umesh Chavan, Priyanka B. Bhelonde, Dr. Dattatraya Pandurang Rane and Dr. Jyothi Pawar

Editor: Dr. Dilip Aher

ISBN: 978-81-987720-2-2

DOI: https://doi.org/10.59646/lab/368

Date of Publication: May 30, 2025

About the Book:

In the digital age, where algorithms shape the world and data drives decisions, a solid grounding in discrete mathematics has become more essential than ever. This textbook, “Discrete Mathematical Structures”, has been crafted to serve as a foundational yet comprehensive resource for undergraduate students in computer science, information technology, mathematics, and allied disciplines.

The goal of this book is to bridge the gap between theoretical principles and practical applications. Discrete mathematics provides the language and tools necessary for studying structures that are inherently discrete rather than continuous. Whether it’s understanding the logic behind programming constructs, analyzing data structures, designing networks, or exploring the theory behind cryptographic algorithms, discrete mathematical structures form the core of these explorations.

This book is organized into five logically structured units:

• Unit 1: Fundamentals of Logic introduces the essentials of propositional logic, logical connectives, rules of inference, and quantifiers—forming the basis for algorithmic thinking and automated reasoning.

• Unit 2: Properties of the Integers delves into mathematical induction, recursive definitions, and counting principles, equipping students to solve problems involving structure, enumeration, and algorithmic formulation.

• Unit 3: Relations and Functions explores mappings, injective and surjective functions, equivalence relations, and graphs—essential for understanding databases, programming, and systems modeling.

• Unit 4: The Principle of Inclusion and Exclusion addresses advanced counting techniques, derangements, rook polynomials, and recurrence relations, sharpening students’ combinatorial skills and problem-solving abilities.

• Unit 5: Introduction to Group Theory introduces abstract algebraic structures like groups, subgroups, cosets, and homomorphisms—key concepts for modern computing applications including cryptography and automata theory.

The content is structured to progress from elementary to advanced topics with a clear emphasis on clarity, rigor, and practical relevance. Each chapter includes definitions, theorems, illustrative examples, and exercises that reinforce understanding and encourage deeper engagement with the material. We have also included a variety of real-life scenarios and computer science applications to demonstrate the practical utility of discrete mathematics. The book aims not just to teach students how to compute, but to help them think critically, reason logically, and apply their knowledge in diverse computational contexts. We hope that this book serves as a valuable tool for students, educators, and self-learners alike. It is our sincere belief that a strong grasp of discrete mathematical structures will empower learners to succeed in both academic and professional endeavors in the digital world.

References

1. Cheeseman, H. R. (2018). Business law: Legal environment, online commerce, business ethics, and international issues (10th ed.). Pearson.
2. Beatty, J. F., Samuelson, S. S., & Abril, P. S. (2021). Business law and the regulation of business (13th ed.). Cengage Learning.
3. Clarkson, K. W., Miller, R. L., Cross, F. B., & Clarkson, B. (2021). Business law: Text and cases (15th ed.). Cengage Learning.
4. Mallor, J. P., Barnes, A. J., Bowers, T., & Langvardt, A. W. (2022). Business law: The ethical, global, and e-commerce environment (18th ed.). McGraw-Hill Education.
5. Kubasek, N. K., Brennan, B. A., & Browne, M. N. (2020). The legal environment of business: A critical thinking approach (9th ed.). Pearson.
6. Singh, A. (2019). Business law. Eastern Book Company.
7. Kapoor, N. D. (2020). Elements of mercantile law. Sultan Chand & Sons.
8. Tulsian, P. C. (2022). Business law. McGraw-Hill Education India.
9. Pinto, D., & Evans, D. (2018). Corporate law (2nd ed.). Oxford University Press.
10. Sharma, R. (2021). Legal aspects of business. Himalaya Publishing House.
11. Miller, R. L., & Jentz, G. A. (2020). Foundations of business law and the legal environment. Cengage Learning.
12. Pathak, A. (2022). Legal aspects of business. McGraw-Hill Education India.
13. Bainbridge, S. M. (2019). Corporate law (3rd ed.). Foundation Press.
14. Singh, H. (2023). Legal environment and business law. Vikas Publishing House.
15. Goldsby, M., & Knapp, C. L. (2021). Problems in contract law: Cases and materials (9th ed.). Aspen Publishers.