This chapter discusses the broader role and impact of analytics science in improving various aspects of society. It introduces what the book is about, and what the reader should expect to learn from reading this book. It also discusses the analytics revolution in the private and public sector, and introduces a key element of the book — insight-driven problem solving — by highlighting its vital role in addressing various societal problems.

In this chapter, the reader learns about the main ideas developed by analytics scientists in problem solving that requires decision-making over time. The reader realizes that various decision-making problems, including those made in everyday life such as which parking spot to take or which job offer to accept, can be addressed using these main ideas. The chapter also illustrates how the same ideas have been used to improve the world around us by citing various examples, including assisting policymakers to gain insights into the impact of different social mobility policies or to find better lockdown policies during a pandemic such as COVID-19.

This chapter explores the behavior of random walks on graphs, framed within the broader context of Markov chains. It introduces finite-state Markov chains, explaining key concepts such as transition matrices, the Markov property, and the computation of stationary distributions. The chapter then discusses the long-term behavior of Markov chains, including the convergence to equilibrium under conditions of irreducibility and aperiodicity. The chapter delves into the application of random walks on graphs, particularly in the context of PageRank, a method for identifying central nodes in a network. It also discusses Markov chain Monte Carlo (MCMC) methods, specifically the Metropolis–Hastings algorithm and Gibbs sampling, which are used to generate samples from complex probability distributions. The chapter concludes by illustrating the application of Gibbs sampling to generate images of handwritten digits using a restricted Boltzmann machine.

Chapter 2 explores the fundamental concept of least squares, covering its geometric, algebraic, and numerical aspects. The chapter begins with a review of vector spaces and matrix inverses, then introduces the geometry of least squares through orthogonal projections. It presents the QR decomposition and Householder transformations as efficient methods for solving least-squares problems. The chapter concludes with an application to regression analysis, demonstrating how to fit linear and polynomial models to data. Key topics include the normal equations, orthogonal decomposition, and the Gram–Schmidt algorithm. The chapter also addresses the issue of overfitting in polynomial regression, highlighting the importance of model selection in data analysis. The chapter includes practical Python implementations and numerical examples to reinforce the theoretical concepts.

A detailed analysis of how AI can be used in the classroom, including methods for measuring knowledge and abilities, student-adapted teaching with AI, general principles for technology use, and considerations of reading, writing, digital distractions, effective methods, and desirable difficulties. Research from the global north is included in the chapter.

This chapter introduces the foundational mathematical concepts behind neural networks, backpropagation, and stochastic gradient descent (SGD). It begins by generalizing the Chain Rule and providing a brief overview of automatic differentiation, which is essential for efficiently computing derivatives in machine learning models. The chapter then explains backpropagation within the context of multilayer neural networks, specifically focusing on multilayer perceptrons (MLPs). It covers the implementation of SGD, highlighting its advantages in optimizing large datasets. Practical examples using the PyTorch library are provided, including the classification of images from the Fashion-MNIST dataset. The chapter provides a solid foundation in the mathematical tools and techniques that underpin modern AI.

A comprehensive chapter exploring AI's role in education, with insights into democratic, ethical, and social reflections, different views on technology in schools, and an analysis model for AI as a resource in school, including ethical reflections and management. The chapter gives room especially for global educational guidelines and presents guidelines and standards for how AI should be implemented and used responsibly in educational environments.

This chapter focuses on the core concepts of optimization theory and its application in data science and AI. It begins with a review of differentiable functions of several variables, including the gradient and Hessian matrices, and key results like the Chain Rule and the Mean Value Theorem. The chapter then introduces optimality conditions for unconstrained optimization, explaining first-order and second-order conditions, and the role of convexity in ensuring global optimality. A detailed discussion of the gradient descent algorithm is provided, including its convergence analysis under different assumptions. The chapter concludes with an application to logistic regression, demonstrating how gradient descent is used to optimize the cross-entropy loss function in a supervised learning context. Practical Python examples are integrated throughout to illustrate the theoretical concepts.

This chapter is focused on game theory and mechanism design, presenting them as an important branch of analytics science that has impacted our world. Like all other chapters, it starts by presenting the big picture ideas, and showcasing various real-world examples in which those ideas have been impactful. It educates the reader though various familiar examples such as the simple decisions involved in cutting a cake and more critical decision-making scenarios such as what happened during the Battle of the Bismarck Sea or finding ways to reduce racial segregation in the society, and from policies that revolutionized life-saving ideas for those who are in dire need of transplantation to governments’ complex efforts in improving voting mechanisms. The chapter provides engaging stories showcasing how the main ideas in game theory and mechanism design have been impactful in a myriad of ways.

The concluding chapter, with a humanistic perspective on learning and technology, emphasizes the unique human aspects that AI cannot replicate, such as factuality, creativity, and humanity.

This chapter is devoted to understanding how the main ideas in graph theory and combinatorics optimization can assist insight-driven problem solving, and thereby, create public impact. The reader sees how such ideas have laid the foundation for apps such as Google Maps and how they are being used to improve our understanding of social networks, design transportation networks, create efficiency schedules for sports events, enhance cryptosystems, and improve the efficiency of supply chains. The reader also learns how analytics scientists have been able to learn from the amazing ability of nature in problem solving (swarm intelligence) and use this to develop effective insight-driven problem solving approaches that can yield powerful insights in addressing complex societal problems.

This chapter starts by communicating how various aspects of our lives involve interacting with queues. It then provides a brief history of the main inception of queueing theory and its main governing princples, and discusses how it has impacted various aspects of our lives. It educates the reader about the main ideas and principles in queueing theory and also elaborates on the psychological aspects of waiting in queues. Showcasing various examples of how the main ideas in queueing theory have enabled important improvements, ranging from what happened during Queen Elizabeth II’s memorial, to the creation of the internet and modern telephones, to our experiences in airports or on roads, the chapter presents queueing theory as a potent branch of analytics science that has enabled scholars to make the world a better place. The chapter also discusses the vital interplays between queueing theory, public policy, and technology.

This chapter is devoted to data analysis and its critical role in analytics science. The reader is introduced to the science of inference from observations and experiments and learns about the main ideas in data analysis that have been influential in addressing societal problems. Real-world examples are used throughout to convey the main ideas and illustrate why data analyses performed without sufficient care can yield wrong insights. Successful examples of insight-driven problem solving approaches in data analysis are contrasted with those that can yield wrong insights, and the reader is taken on an engaging yet educational journey that depicts how and why successful insight-driven problem solving approaches using data can have significant public impact.