In this chapter, we describe the main goal of the book, its organization, course outline, and suggestions for instructions and self-study. The textbook material is aimed for a one-semester undergraduate/graduate course for mathematics and computer science students. The course might also be recommended for students of physics, interested in networks and the evolution of large systems, as well as engineering students, specializing in telecommunication. Our textbook aims to give a gentle introduction to the mathematical foundations of random graphs and to build a platform to understand the nature of real-life networks. The text is divided into three parts and presents the basic elements of the theory of random graphs and networks. To help the reader navigate through the text, we have decided to start with describing in the preliminary part (Part I) the main technical tools used throughout the text. Part II of the text is devoted to the classic Erdős–Rényi–Gilbert uniform and binomial random graphs. Part III concentrates on generalizations of the Erdős–Rényi–Gilbert models of random graphs whose features better reflect some characteristic properties of real-world networks.

Bayesian optimization is a methodology for optimizing expensive objective functions that has proven success in the sciences, engineering, and beyond. This timely text provides a self-contained and comprehensive introduction to the subject, starting from scratch and carefully developing all the key ideas along the way. This bottom-up approach illuminates unifying themes in the design of Bayesian optimization algorithms and builds a solid theoretical foundation for approaching novel situations.

The core of the book is divided into three main parts, covering theoretical and practical aspects of Gaussian process modeling, the Bayesian approach to sequential decision making, and the realization and computation of practical and effective optimization policies.

Following this foundational material, the book provides an overview of theoretical convergence results, a survey of notable extensions, a comprehensive history of Bayesian optimization, and an extensive annotated bibliography of applications.

We describe the new field of the mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding generalization power of overparametrized neural networks, the role of depth in deep architectures, the apparent absence of the curse of dimensionality, the surprisingly successful optimization performance despite the non-convexity of the problem, understanding what features are learned, why deep architectures perform exceptionally well in physical problems, and which fine aspects of an architecture affect the behavior of a learning task in which way. We present an overview of modern approaches that yield partial answers to these questions. For selected approaches, we describe the main ideas in more detail.

This chapter first defines data science, its primary objectives, and several related terms. It continues by describing the evolution of data science from the fields of statistics, operations research, and computing. The chapter concludes with historical notes on the emergence of data science and related topics.

This chapter discusses the fundamentally different mental images of large-dimensional machine learning (versus its small-dimensional counterpart), through the examples of sample covariance matrices and kernel matrices, on both synthetic and real data. Random matrix theory is presented as a flexible and powerful tool to assess, understand, and improve classical machine learning methods in this modern large-dimensional setting.

This chapter introduces the basic concepts of cybersecurity and the data analytics perspective to cybersecurity. It lays out the areas of study and how data analytics should be a key part of the spectrum of cybersecurity solutions.