This accessible and self-contained guide provides a comprehensive introduction to the popular programming language Python, with a focus on applications in chemistry and chemical physics. Ideally suited to students and researchers of chemistry learning to employ Python for problem-solving in their research, this fast-paced primer first builds a solid foundation in the programming language before progressing to advanced concepts and applications in chemistry. The required syntax and data structures are established, and then applied to solve problems computationally. Popular numerical packages are described in detail, including NumPy, SciPy, Matplotlib, SymPy, and pandas. End of chapter problems are included throughout, with worked solutions available within the book. Additional resources, datasets, and Jupyter Notebooks are provided on a companion website, allowing readers to reinforce their understanding and gain confidence applying their knowledge through a hands-on approach.

The first chapter describes the main structure of the book, but also reveals an algorithm that the book is built on. The ultimate goal is the creation of a strategy that can be used for modelling fluid flows laden with particles. Therefore, this chapter depicts the main steps: first, modelling the flow with a single particle, then introducing two particles that may interact, and finally, modelling of the whole set of particles. The details are provided in the subsequent chapters.

A quick introduction to the standard model of particle physics is given. The general concepts of elementary particles, interactions and fields are outlined. The experimental side of particle physics is also briefly discussed: how elementary particles are produced with accelerators or from cosmic rays and how to observe them with detectors via the interactions of particles with matter. The various detector technologies leading to particle identification are briefly presented. The way in which the data collected by the sensors is analysed is also presented: the most frequent probability density functions encountered in particle physics are outlined. How measurements can be used to estimate a quantity from some data and the question of the best estimate of that quantity and its uncertainty are explained. As measurements can also be used to test a hypothesis based on a particular model, the hypothesis testing procedure is explained.

In this chapter we provide an overview of data modeling and describe the formulation of probabilistic models. We introduce random variables, their probability distributions, associated probability densities, examples of common densities, and the fundamental theorem of simulation to draw samples from discrete or continuous probability distributions. We then present the mathematical machinery required in describing and handling probabilistic models, including models with complex variable dependencies. In doing so, we introduce the concepts of joint, conditional, and marginal probability distributions, marginalization, and ancestral sampling.

This chapter starts with an introductory survey on the physical background and historical events that lead to the emergence of the density matrix renormalization group (DMRG) and its tensor network generalization. We then briefly overview the major progress on the renormalization group methods of tensor networks and their applications in the past three decades. The tensor network renormalization was initially developed to solve quantum many-body problems, but its application field has grown constantly. It has now become an irreplaceable tool for investigating strongly correlated problems, statistical physics, quantum information, quantum chemistry, and artificial intelligence.

The central message of the introduction is one must understand science if one wants to do science well. This requires a holistic educational approach, one that not only teaches the whats and hows of science, but most critically, it's whys. Why is the sky blue? Why do normal cells turn into cancer cells? Why do we use the scientific method and from where did it come? Why would one want to be a scientist in the first place? Why is science done in the way it is, that is, what is the gestalt of science? The whats and whys of science are practical in nature. The whys, in contrast, encompass theoretical, philosophical, historical, and social underpinnings of science. The whys are particularly important now when the probity and veracity of science are being attacked, and people seek to replace actual facts with "alternative facts" (falsehoods) for political, religious, or economic purposes or out of plain ignorance.

An overview of what the point of category theory is, without formality, and an overview of the contents of the book. We will present category theory as “the mathematics of mathematics”, so first we explain what aspects of mathematics we are focusing on. We present mathematics as starting from abstraction, as a way of elucidating analogies between situations, finding connections between them, and unifying them. Category theory is then a rigorous framework for making analogies and finding connections between different parts of mathematics. It focuses on relationships between things, rather than on intrinsic characteristics, and uses those relationships to put objects in context rather than treat them in isolation. Once the framework has been set up, we have, among other things, a way to express more nuanced notions of “sameness”, and a way to characterize things by the role they play in that context. Category theory also works at many different levels, so we can zoom in and out and study details close up, or broad contexts with more of an overview.