Mathematical foundations of big data analytics is a very welcome and timely addition to the growing area of big data analytics. The authors develop--and strictly follow in each of the nine chapters--a template consisting of motivation, theory, case study, and exercises. In each chapter, a new application is used to illustrate the theory and algorithms developed in that unit.

The PageRank algorithm, which has become a prototypical example of the big data problem, is developed in the opening chapter 1. The importance of an online learning algorithm and the role of recommender systems are covered in chapters 2 and 3. The classic problem of classification and clustering are covered in chapters 4 and 5. An interesting account of the linear least squares, along with its applications to asset pricing in economics, is given in chapter 6. Two classes of popular algorithms for variable selection--Lasso regression and iterative shrinkage-thresholding algorithms--along with their application to the important problem of compressed sensing are covered in chapter 7. Chapters 8 and 9 contain a succinct discussion of neural networks and decision trees and their applications. The closing chapter 10 contains complete solutions to the problems listed in the previous nine chapters’ exercise sections and is a unique feature of this book.

Mathematical foundations are very carefully covered in each chapter, which justifies the title. There is a good listing of references for further study, as well as an index for easy reference. This book could be the basis for a one-semester graduate-level course with an emphasis on mathematical foundations, supplemented by good programming projects.