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Author: Сергей Петрович Новиков
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 658
ISBN-13: 0821839292
DOWNLOAD EBOOK →Presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the important structures on them. This book shows that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications.
Author: Walter A. Poor
Publisher: Courier Corporation
Published: 2015-04-27
Total Pages: 352
ISBN-13: 0486151913
DOWNLOAD EBOOK →This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Author: Douglas B. Aichele
Publisher: Prentice Hall
Published: 2007-04
Total Pages: 0
ISBN-13: 9780131483927
DOWNLOAD EBOOK →For prospective elementary and middle school teachers. This text provides a creative, inquiry-based experience with geometry that is appropriate for prospective elementary and middle school teachers. The coherent series of text activities supports each student's growth toward being a confident, independent learner empowered with the help of peers to make sense of the geometric world. This curriculum is explicitly developed to provide future elementary and middle school teachers with experience recalling and appropriately using standard geometry ideas, experience learning and making sense of new geometry, experience discussing geometry with peers, experience asking questions about geometry, experience listening and understanding as others talk about geometry, experience gaining meaning from reading geometry, experience expressing geometry ideas through writing, experience thinking about geometry, and experience doing geometry. These activities constitute an "inquiry based" curriculum. In this style of learning and teaching, whole class discussions and group work replace listening to lectures as the dominant class activity.
Author: Frédéric Barbaresco
Publisher: Springer Nature
Published: 2021-06-27
Total Pages: 466
ISBN-13: 3030779572
DOWNLOAD EBOOK →Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract representation spaces. This volume collects selected contributions on the interplay of statistical physics and artificial intelligence. The aim is to provide a constructive dialogue around a common foundation to allow the establishment of new principles and laws governing these two disciplines in a unified manner. The contributions were presented at the workshop on the Joint Structures and Common Foundation of Statistical Physics, Information Geometry and Inference for Learning which was held in Les Houches in July 2020. The various theoretical approaches are discussed in the context of potential applications in cognitive systems, machine learning, signal processing.
Author: Aurel Bejancu
Publisher: Springer Science & Business Media
Published: 2006-01-17
Total Pages: 309
ISBN-13: 1402037201
DOWNLOAD EBOOK →Offers basic material on distributions and foliations. This book introduces and builds the tools needed for studying the geometry of foliated manifolds. Its main theme is to investigate the interrelations between foliations of a manifold on the one hand, and the many geometric structures that the manifold may admit on the other hand.
Author: Jianzhong Wang
Publisher: Springer Science & Business Media
Published: 2012-04-28
Total Pages: 363
ISBN-13: 3642274978
DOWNLOAD EBOOK →"Geometric Structure of High-Dimensional Data and Dimensionality Reduction" adopts data geometry as a framework to address various methods of dimensionality reduction. In addition to the introduction to well-known linear methods, the book moreover stresses the recently developed nonlinear methods and introduces the applications of dimensionality reduction in many areas, such as face recognition, image segmentation, data classification, data visualization, and hyperspectral imagery data analysis. Numerous tables and graphs are included to illustrate the ideas, effects, and shortcomings of the methods. MATLAB code of all dimensionality reduction algorithms is provided to aid the readers with the implementations on computers. The book will be useful for mathematicians, statisticians, computer scientists, and data analysts. It is also a valuable handbook for other practitioners who have a basic background in mathematics, statistics and/or computer algorithms, like internet search engine designers, physicists, geologists, electronic engineers, and economists. Jianzhong Wang is a Professor of Mathematics at Sam Houston State University, U.S.A.
Author: Edmond Saliklis
Publisher: Springer
Published: 2018-11-07
Total Pages: 332
ISBN-13: 3319987461
DOWNLOAD EBOOK →Graphic methods for structural design essentially translate problems of algebra into geometric representations, allowing solutions to be reached using geometric construction (ie: drawing pictures) instead of tedious and error-prone arithmetic. This was the common method before the invention of calculators and computers, but had been largely abandoned in the last half century in favor of numerical techniques. However, in recent years the convenience and ease of graphic statics has made a comeback in architecture and engineering. Several professors have begun using graphic statics in the classroom.and.studio environment. But until now, there had been no guidebook that rapidly brings students up to speed on the fundamentals of how to create graphical solutions to statics problems.Graphic Statics introduces all of the traditional graphic statics techniques in a parametric drawing format, using the free program GeoGebra. Then, advanced topics such as indeterminate beams and three dimensional curved surfaces are be covered. Along the way, links to wider design ideas are introduced in a succinct summary of the steps needed to create elegant solutions to many staticequilibrium problems.Meant for students in civil and architectural engineering, architecture,and construction, this practical introduction will also be useful to professionals looking to add the power of graphic statics to their work.
Author: Frank Nielsen
Publisher: Springer
Published: 2018-11-19
Total Pages: 392
ISBN-13: 3030025209
DOWNLOAD EBOOK →This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing. The book collects the most important contributions to the conference GSI’2017 – Geometric Science of Information.
Author: Tiansi Dong
Publisher: Springer Nature
Published: 2020-08-24
Total Pages: 155
ISBN-13: 3030562751
DOWNLOAD EBOOK →The unification of symbolist and connectionist models is a major trend in AI. The key is to keep the symbolic semantics unchanged. Unfortunately, present embedding approaches cannot. The approach in this book makes the unification possible. It is indeed a new and promising approach in AI. -Bo Zhang, Director of AI Institute, Tsinghua It is indeed wonderful to see the reviving of the important theme Nural Symbolic Model. Given the popularity and prevalence of deep learning, symbolic processing is often neglected or downplayed. This book confronts this old issue head on, with a historical look, incorporating recent advances and new perspectives, thus leading to promising new methods and approaches. -Ron Sun (RPI), on Governing Board of Cognitive Science Society Both for language and humor, approaches like those described in this book are the way to snickerdoodle wombats. -Christian F. Hempelmann (Texas A&M-Commerce) on Executive Board of International Society for Humor Studies
Author: Vladimir Rovenski
Publisher: Springer Nature
Published:
Total Pages: 323
ISBN-13: 3031505867
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