The Power and Art of Approximation (volume 2): A Data Science and Engineering Handbook

Enthused by the promising future of self-learning machines and the continuous advancement of technology, we write this book to cover a compendium of analytical and numerical techniques conflated into a common idea around the power and art of approximation. In this book, we review numerous approximation methods that can bring insight into some fundamental precursory requirements of Data Science and Machine Learning (ML) Engineering. This book avoids being specific to a target audience, whether one is an engineer or a researcher within a particular domain or, for that matter, an undergraduate student just trying to get into this field. Instead, the premise is that Data Science can be for everybody, especially those new to Data Science who are just beginning to develop an inclination toward this field and most likely need an introductory oversight. While we note that our common theme across the book is intuition, contemplating more on basic operations than mathematical rigor, it is essential to revive our understanding of mathematical concepts first. We base this on the view that most of what we do in Data Science is expressed in the language of mathematics - more numerically inclined, in fact, than analytical - meaning that we live to decide based on close approximation in many situations. Therefore, it is essential to have some introductory perspective of the mathematical foundations in which Machine Learning algorithms may have come about - if not at least what they depend upon fundamentally. Thus, we cover a list of mathematical concepts that are undoubtedly valuable to get us to Machine Learning concepts eventually. However, only a particular elementary and introductory portion of each field of mathematics is covered as we emphasize only relevant and essential areas. That said, this book comes in three volumes. Volumes I and II of this book briefly cover common topics in Linear Algebra, Numerical Analysis, Statistical Analysis, and Bayesian Analysis. The third part (or volume III) of this book covers Machine Learning and Deep Learning in detail.