Matrices and Calculus with Discrete Mathematics is a comprehensive textbook designed to develop a strong mathematical foundation among undergraduate students in engineering, computer science, information technology, and related disciplines. The book presents essential mathematical concepts in a systematic and accessible manner, combining theoretical explanations with definitions, properties, theorems, derivations, and step-by-step solved examples.
The book covers a wide range of topics, including vectors, eigenvalues and eigenvectors, properties of eigenvalues, the Cayley–Hamilton theorem, similarity and orthogonal transformations, quadratic forms, calculus, propositional logic, predicates and quantifiers, logical equivalences, mathematical proofs, partial ordering, partially ordered sets (posets), lattices, and Boolean algebra. Each topic is organized to help readers progress from fundamental principles to more advanced concepts while strengthening their analytical and logical reasoning abilities.
With its structured presentation and illustrative examples, this book supports conceptual understanding, mathematical problem-solving, and examination preparation. It also highlights the importance of mathematical methods in engineering applications, computational techniques, digital systems, and computer science. The book serves as a useful academic resource for students and educators seeking to understand mathematical principles and apply them effectively.
Whether used for classroom learning, independent study, or revision, Matrices and Calculus with Discrete Mathematics aims to make mathematical learning clear, practical, and meaningful while providing a solid foundation for advanced studies and professional development.
About the Authors’
Dr. Archana Shukla, is presently working as Head, Department of Mathematics, Nehru Gram Bharati University, Prayagraj. She received Ph.D degree in the field of Fluid Mechanics. She has 8 years teaching experience as well as administrative experience as a proctorial board. She has presented and published a number of research papers in reputed Journals and one patent. Two students awarded Ph.D degree under her supervision and now six is going on. She was honoured by the Silver Jubilee award from IAPS and recently, She has been honoured by the best teacher award from Nehru Gram Bharati University in 2022, Prayagraj, Uttar Pradesh.
Dr. A.P.Pushpalatha received her Master’s degree in Mathematics in 1995 and her Ph.D. degree in 2011 from Madurai Kamaraj University, Madurai, India. She is currently a Professor and Head of the Mathematics Department at Velammal College of Engineering and Technology, Madurai, India. With 29 years of teaching experience and 20 years of research experience, Dr. Pushpalatha is renowned for being an excellent teacher and academician. She has published nearly 35 research articles and received the IJRULA Best Researcher award in 2018. Additionally, she serves as a reviewer for journals such as Advances and Applications in Mathematical Sciences and Discrete Mathematics, Algorithms, and Applications. Her research interests include graph theory, networking, discrete mathematics, and fuzzy graphs.
Dr. Rahul Singh is an Assistant Professor in the Department of Mathematics, School of Basic and Applied Sciences, at IILM University. His academic interests include applied mathematics and interdisciplinary research. He is committed to advancing mathematical education through research, teaching, and student engagement.
Dr. S. Suneetha is an Associate Professor in the Department of Applied Mathematics at Yogi Vemana University. She has made valuable contributions to mathematics education and research, with a strong focus on analytical methods, applied mathematics, and academic development.
Mr. A. Durai Ganesh is an Assistant Professor in the Department of Mathematics at PET Engineering College, Tamil Nadu. He is committed to excellence in mathematics education, inspiring students through innovative teaching, analytical thinking, and problem-solving approaches while actively contributing to academic development and scholarly pursuits in the field of mathematics.
