This book is a comprehensive, unifying introduction to the field of mathematical analysis and the mathematics of computing. It develops the relevant theory at a modern level and it directly relates modern mathematical ideas to their diverse applications. The authors develop the whole theory. Starting with a simple axiom system for the real numbers, they then lay the foundations, developing the theory, exemplifying where it's applicable, in turn motivating further development of the theory. They progress from sets, structures, and numbers to metric spaces, continuous functions in metric spaces, linear normed spaces and linear mappings; and then differential calculus and its applications, the integral calculus, the gamma function, and linear integral operators. They then present important aspects of approximation theory, including numerical integration. The remaining parts of the book are devoted to ordinary differential equations, the discretization of operator equations, and numerical solutions of ordinary differential equations. This textbook contains many exercises of varying degrees of difficulty, suitable for self-study, and at the end of each chapter the authors present more advanced problems that shed light on interesting features, suitable for classroom seminars or study groups. It will be valuable for undergraduate and graduate students in mathematics, computer science, and related fields such as engineering. This is a rich field that has experienced enormous development in recent decades, and the book will also act as a reference for graduate students and practitioners who require a deeper understanding of the methodologies, techniques, and foundations.
This book provides a unique treatment of an important area of machine learning and answers the question of how kernel methods can be applied to structured data. Kernel methods are a class of state-of-the-art learning algorithms that exhibit excellent learning results in several application domains. Originally, kernel methods were developed with data in mind that can easily be embedded in a Euclidean vector space. Much real-world data does not have this property but is inherently structured. An example of such data, often consulted in the book, is the (2D) graph structure of molecules formed by their atoms and bonds. The book guides the reader from the basics of kernel methods to advanced algorithms and kernel design for structured data. It is thus useful for readers who seek an entry point into the field as well as experienced researchers.
All of us have learned a lot during this exercise, and the enormous success of the first edition of this book shows the great international interest for the topic and the results. A French edition appeared last year and met with equal interest. Springer-Verlag has therefore decided to publish a second edition of this book, which is not just a reprint but brings the literature and results to the newest state. This is a rare occurrence in the history of the LNCS series. We congratulate Thomas Schael on this success, and we are sure that reader- scientists and practitioners - will likewise profit from it. Aachen and Milan Giorgio De Michelis, Klaus Henning, Matthias Jarke August 1998 Preface to the Second Edition This book is a bit of a mixture of scientific and management literature. It is based on my research activities in the CSCW community, and also reflects the last ten years of my professional experience in consulting. I have had the opportunity to live in different cultural settings, to work in many companies, and to meet people all over the world, which has helped me to reflect on what I was doing and to focus on the content of this book. This second edition reflects the fast moving field of Computer Supported Cooperative Work (CSCW) and the discussion on Business Process Re-engineering (BPR). It contains the latest developments in the scientific and managerial discussion of the issues developed in the first edition.
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