This chapter introduces the reader to the big picture of what analytics science is. What is analytics science? What types does it have, and what is its scope? How can analytics science be used to improve various tasks that society needs to carry out? Is analytics science all about using data? Or can it work without data? What is the role of data versus models? How can one develop and rely on a model to answer essential questions when the model can be wrong due to its assumptions? What is ambiguity in analytics science? Is that different from risk? And how do analytics scientists address ambiguity? What is the role of simulation in analytics science? These are some of the questions that the chapter addresses. Finally, the chapter discusses the notion of "centaurs" and how a successful use of analytics science often requires combining human intuition with the power of strong analytical models.

A panoramic view of the digital era and how AI affects today's teaching, introducing the opportunities and simultaneous challenges that technology brings.

The fifth chapter explores the application of spectral graph theory to network data analysis. The chapter begins with an introduction to fundamental graph theory concepts, including undirected and directed graphs, graph connectivity, and matrix representations such as the adjacency and Laplacian matrices. It then discusses the variational characterization of eigenvalues and their significance in understanding the structure of graphs. The chapter highlights the spectral properties of the Laplacian matrix, particularly its role in graph connectivity and partitioning. Key applications, such as spectral clustering for community detection and the analysis of random graph models like Erdős–Rényi random graphs and stochastic blockmodels, are presented. The chapter concludes with a detailed exploration of graph partitioning algorithms and their practical implementations using Python.

The fourth chapter introduces the singular value decomposition (SVD), a fundamental matrix factorization with broad applications in data science. The chapter begins by reviewing key linear algebra concepts, including matrix rank and the spectral theorem. It then explores the problem of finding the best low-dimensional approximating subspace to a set of data points, leading to the formal definition of the SVD. The power iteration method is presented as an efficient way to compute the top singular vectors and values. The chapter then demonstrates the application of SVD to principal components analysis (PCA), a dimensionality reduction technique that identifies the directions of maximum variance in data. Further applications of the SVD are discussed, including low-rank matrix approximations and ridge regression, a regularization technique for handling multicollinearity in linear systems.

An introduction to AI, including an overview of essential technologies such as machine learning and deep learning, and a discussion on generative AI and its potential limitations. The chapter includes an exploration of AI's history, including its relationship to cybernetics, its role as a codebreaker, periods of optimism and “AI winters,” and today's global development with generative AI. Chapter 1 also include an analysis of AI's role in the international and national context, focusing on potential conflicts of goals and threats that can arise from technology.

This chapter presents mathematical programming as the science of one-shot decisions. It clarifies important ways analytics scientists implement problem solving by benefiting from tools and ideas in mathematical programming both in scenarios where the world behaves linearly and where it does not. It also introduces integer programming and inverse optimization, showcasing how the main ideas and insights obtained from mathematical programming have been applied to various impactful problems ranging from designing effective diets to allowing the military to improve the efficiency of its operations to make bike sharing systems more accessible.

The chapter highlights the importance of AI literacy. Opportunities and challenges that AI creates in the educational context, such as strategies for technology use, and what AI tools like ChatGPT can enable and hinder in the learning process.