The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergradua…
This professional treatise on engineering graphics emphasizes engineering geometry as the theoretical foundation for communication of design ideas with real world structures and products. It considers each theoretical notion of engineering geometry as a complex solution of direct- and inverse-problems of descriptive geometry and each solution of basic engineering problems presented is accompani…
The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book “5000 Jahre Geometrie,” in which geometry is presented as a chain of developments in cultural history and their interaction with arch…
This volume is an attempt to provide a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, with special emphasis placed on fundamental classes of models and algorithms as well as on their applications. This book has a strong focus on simulations and includes extensive code in Matlab and R, which are widely used in the mathematical comm…
This modern translation of Sophus Lie's and Friedrich Engel's “Theorie der Transformationsgruppen I” will allow readers to discover the striking conceptual clarity and remarkably systematic organizational thought of the original German text. Volume I presents a comprehensive introduction to the theory and is mainly directed towards the generalization of ideas drawn from the study of example…
This book provides a brief introduction to the theory of finite dimensional differential inclusions, and deals in depth with control of three kinds of differential inclusion systems. The authors introduce the algebraic decomposition of convex processes, the stabilization of polytopic systems, and observations of Luré systems. They also introduce the elemental theory of finite dimensional diffe…
This book focuses on theoretical aspects of the affine projection algorithm (APA) for adaptive filtering. The APA is a natural generalization of the classical, normalized least-mean-squares (NLMS) algorithm. The book first explains how the APA evolved from the NLMS algorithm, where an affine projection view is emphasized. By looking at those adaptation algorithms from such a geometrical point o…
The book is inspired by the third seminar in a cycle connected to the celebrations of the 150th anniversary of the Politecnico di Milano (July 2013). "Educating by Image. Teaching Styles vs Learning Styles" was the motto of this meeting. The contributions (coming from lectures, the poster session, interviews and round table) aim to propose an updated look at visual education, highlighting how d…
This 4-th edition of the leading reference volume on distance metrics is characterized by updated and rewritten sections on some items suggested by experts and readers, as well a general streamlining of content and the addition of essential new topics. Though the structure remains unchanged, the new edition also explores recent advances in the use of distances and metrics for e.g. generalized d…
This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22–26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non…