Texts and Readings in Mathematics

Foundations of Data Science
Avrim Blum, John Hopcroft, Ravi Kannan
trim 78 coverThis book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counter-intuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. In addition, important structural and complexity measures, such as matrix norms and VC-dimension, are discussed. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.

This beautifully written text is a scholarly journey through the mathematical and algorithmic foundations of data science. Rigorous but accessible, and with many exercises, it will be a valuable resource for advanced undergraduate and graduate classes. Peter Bartlett, University of California, Berkeley.

A lucid account of mathematical ideas that underlie today's data analysis and machine learning methods. I learnt a lot from it, and I am sure it will become an invaluable reference for many students, researchers and faculty around the world. Sanjeev Arora, Princeton University, New Jersey.
Table of Contents
Texts and Readings in Mathematics 78
2020; 520 pp; Soft Cover, 9789386279804, Price: Rs. 820.00