This book builds a single, coherent pathway from linear algebra to probability and statistical learning―the twin pillars behind modern Data Science, AI, and ML. With equal emphasis on geometry (matrices, spectra, projections) and uncertainty (randomness, estimation, generalization), it equips readers to derive algorithms from first principles and implement them robustly at scale. Throughout, geometric pictures (projections, angles, spectra) and probabilistic arguments (risk, concentration, generalization) are developed side-by-side. Each concept is motivated by a real ML use case―denoising with PCA, ill-conditioning in regression, choosing regularization via validation curves, or accelerating large least-squares with sketching.
Dr. Pradeep Singh is serving as an Assistant Professor (Grade--I) at the Indian Institute of Information Technology Surat, where he also serves as Associate Dean (R&D). He is faculty in the Department of Mathematics and Computational Sciences, and joint faculty in the Department of Computer Science & Engineering. His research spans Geometric Deep Learning, Neuro-symbolic AI, and Dynamical Systems. His research has appeared in premier venues, including IEEE Transactions; Knowledge-Based Systems; Neurocomputing; Chaos, Solitons & Fractals; and ECAI, contributing to the wider dialogue in AI and dynamical-systems research. He has authored multiple books: the Springer monographs Deep Learning Through the Prism of Tensors and The Geometry of Intelligence: Foundations of Transformer Networks, and the McGraw-Hill text Machine Learning and Artificial Intelligence. He earned his Ph.D. (2022) and Master’s degree from IIT Delhi, specializing in Symbolic Systems, and a Bachelor’s degree in Data Science from IIT Madras. Dr Singh secured All-India Rank 1 in GATE 2020, JAM 2015, and CSIR-NET 2019. He has also received highly competitive awards, including the National Board for Higher Mathematics (NBHM) Master’s, Doctoral, and Post-Doctoral Fellowships awarded by the Department of Atomic Energy, India. In 2019, he was one of only two researchers nationwide to receive the Dr Shyama Prasad Mukherjee (SPM) Fellowship in Mathematics from CSIR, India. He is also a recipient of the prestigious Human Frontier Science Program Postdoctoral Fellowship, an international fellowship supporting frontier cross-disciplinary 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.
