This book presents a philosophical approach to probability and probabilistic thinking, considering the underpinnings of probabilistic reasoning and modeling, which effectively underlie everything in data science. The ultimate goal is to call into question many standard tenets and lay the philosophical and probabilistic groundwork and infrastructure for statistical modeling. It is the first book…
This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equat…
Providing a self-contained resource for upper undergraduate courses in combinatorics, this text emphasizes computation, problem solving, and proof technique. In particular, the book places special emphasis the Principle of Inclusion and Exclusion and the Multiplication Principle. To this end, exercise sets are included at the end of every section, ranging from simple computations (evaluate a fo…
This publication showcases the work of UK mathematicians and statisticians by describing industrial problems that have been successfully solved, together with a summary of the financial and/or societal impact that arose from the work. The articles are grouped by sector, and include contributions to climate modelling, engineering and health. The articles are based on Impact Case Studies that wer…
This book explores some of the major turning points in the history of mathematics, ranging from ancient Greece to the present, demonstrating the drama that has often been a part of its evolution. Studying these breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, can help illuminate the importance of the history of mathematics for its teaching, learning, and …
Normal 0 false false false EN-US X-NONE X-NONE This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Conference on Trusted Systems, INTRUST 2014, held in Beijing, China, in December 2014. The conference brings together academic and industrial researchers, designers, and implementers with end-users of trusted systems, in order to foster the exchan…
This work examines the main directions of research conducted on the history of mathematics education. It devotes substantial attention to research methodologies and the connections between this field and other scholarly fields. The results of a survey about academic literature on this subject are accompanied by a discussion of what has yet to be done and problems that remain unsolved. The m…
Annotation This survey of the state of the art on research in early algebra traces the evolution of a relatively new field of research and teaching practice. With its focus on the younger student, aged from about 6 years up to 12 years, this volume reveals the nature of the research that has been carried out in early algebra and how it has shaped the growth of the field. The survey, in presenti…
This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra. The emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is…
This book focuses on the discrete Fourier transform (DFT), discrete convolution, and, particularly, the fast algorithms to calculate them. These topics have been at the center of digital signal processing since its beginning, and new results in hardware, theory and applications continue to keep them important and exciting.