In the rapidly evolving field of artificial intelligence, this book serves as a crucial resource for understanding the mathematical foundations of AI. It explores the intricate world of tensors, the fundamental elements powering today's advanced deep learning models. Combining theoretical depth with practical insights, the text navigates the complex landscape of tensor calculus, guiding readers to master the principles and applications of tensors in AI. From the basics of tensor algebra and geometry to the sophisticated architectures of neural networks, including multi-layer perceptrons, convolutional, recurrent, and transformer models, this book provides a comprehensive examination of the mechanisms driving modern AI innovations. It delves into the specifics of autoencoders, generative models, and geometric interpretations, offering a fresh perspective on the complex, high-dimensional spaces traversed by deep learning technologies. Concluding with a forward-looking view, the book addresses the latest advancements and speculates on the future directions of AI research, preparing readers to contribute to or navigate the next wave of innovations in the field. Designed for academics, researchers, and industry professionals, it serves as both an essential textbook for graduate and postgraduate students and a valuable reference for experts in the field. With its rigorous approach to the mathematical frameworks of AI and a strong focus on practical applications, this book bridges the gap between theoretical research and real-world implementation, making it an indispensable guide in the realm of artificial intelligence.

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Dr. Pradeep Singh earned his Ph.D. and Master's degrees from the Indian Institute of Technology (IIT) Delhi, specializing in Dynamical Systems, and an undergraduate degree in Data Science from IIT Madras. Currently, he is a Post-Doctoral Researcher and Principal Investigator at the Machine Intelligence Lab within the Department of Computer Science and Engineering at IIT Roorkee, where he is actively engaged in research at the intersection of Geometric Deep Learning, Neuro-symbolic AI, and Dynamical Systems. His research is supported by the National Post Doctoral Fellowship (N-PDF) from the Science and Engineering Research Board (SERB), Department of Science and Technology. Dr. Singh has earned multiple accolades, including All India Rank 1 in IIT GATE 2020, IIT JAM 2015, and CSIR NET 2019, along with prestigious fellowships such as the National Board for Higher Mathematics (NBHM) Masters, Doctoral, and Post Doctoral Fellowships from the Department of Atomic Energy, and the SPM Doctoral Fellowship from the Council of Scientific and Industrial Research. Dr. Balasubramanian Raman received his Ph.D. from IIT Madras and his B.Sc. and M.Sc. in Mathematics from the University of Madras. He is a Professor and the Head of the Department of Computer Science and Engineering at IIT Roorkee, as well as the iHUB Divyasampark Chair Professor. He is also a Joint Faculty member in the Mehta Family School of Data Science and Artificial Intelligence at IIT Roorkee. With over 200 research papers published in reputed journals and conferences, his research interests span Machine Learning, Image and Video Processing, Computer Vision, and Pattern Recognition. Dr. Raman has served as a Guest Professor and Visiting Researcher at prestigious institutions such as Osaka Metropolitan University, Curtin University, the University of Cyberjaya, and the University of Windsor. He has held postdoctoral positions at Rutgers University and the University of Missouri-Columbia. Under his coaching, teams have achieved notable rankings in the ACM International Collegiate Programming Contest (ICPC) World Finals. He has been recognized with several awards, including the BOYSCAST Fellowship and the Ramkumar Prize for Outstanding Teaching and Research.