Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re-evaluations of Gentzen’s original consistency proofs to the most recent developments in p…
This book presents an account of selected topics from key mathematical works of medieval Islam, based on the Arabic texts themselves. Many of these works had a great influence on mathematics in Western Europe. Topics covered in the first edition include arithmetic, algebra, geometry, trigonometry, and numerical approximation; this second edition adds number theory and combinatorics. Additionall…
Presenting a comprehensive resource for the mastery of network analysis in R, the goal of Network Analysis with R is to introduce modern network analysis techniques in R to social, physical, and health scientists. The mathematical foundations of network analysis are emphasized in an accessible way and readers are guided through the basic steps of network studies: network conceptualization, data…
This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise. Wit…
This book introduces readers to theories that play a crucial role in modern mathematics, such as integration and functional analysis, employing a unifying approach that views these two subjects as being deeply intertwined. This feature is particularly evident in the broad range of problems examined, the solutions of which are often supported by generous hints. If the material is split into two …
This brief goes back to basics and describes the Quantitative structure-activity/property relationships (QSARs/QSPRs) that represent predictive models derived from the application of statistical tools correlating biological activity (including therapeutic and toxic) and properties of chemicals (drugs/toxicants/environmental pollutants) with descriptors representative of molecular structure and/…
This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathem…
This book is a concise introduction to electromagnetics and electromagnetic fields that covers the aspects of most significance for engineering applications by means of a rigorous, analytical treatment. After an introduction to equations and basic theorems, topics of fundamental theoretical and applicative importance, including plane waves, transmission lines, waveguides and Green's functions, …
This book presents the fundamentals of concurrency theory with clarity and rigor. The authors start with the semantic structure, namely labelled transition systems, which provides us with the means and the tools to express processes, to compose them, and to prove properties they enjoy. The rest of the book relies on Milner's Calculus of Communicating Systems, tailored versions of which are used…
This book considers specific inferential issues arising from the analysis of dynamic shapes with the attempt to solve the problems at hand using probability models and nonparametric tests. The models are simple to understand and interpret and provide a useful tool to describe the global dynamics of the landmark configurations. However, because of the non-Euclidean nature of shape spaces, distri…