Geometry

Author : Shun-ichi Amari
Publisher : Springer
Page : 378 pages
File Size : 52,8 Mb
Release : 2016-02-02
Category : Mathematics
ISBN : 9784431559788

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Information Geometry and Its Applications by Shun-ichi Amari Pdf

This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.

Author : Harold Abelson,Andrea Disessa
Publisher : MIT Press
Page : 502 pages
File Size : 49,9 Mb
Release : 1986-07-09
Category : Computers
ISBN : 0262510375

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Turtle Geometry by Harold Abelson,Andrea Disessa Pdf

Turtle Geometry presents an innovative program of mathematical discovery that demonstrates how the effective use of personal computers can profoundly change the nature of a student's contact with mathematics. Using this book and a few simple computer programs, students can explore the properties of space by following an imaginary turtle across the screen. The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates.

Author : D. A. Brannan
Publisher : Unknown
Page : 0 pages
File Size : 50,8 Mb
Release : 2012
Category : Geometry
ISBN : OCLC:988141769

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Geometry by D. A. Brannan Pdf

Author : Stephen Skinner
Publisher : Sterling Publishing Company, Inc.
Page : 164 pages
File Size : 47,5 Mb
Release : 2009
Category : Mathematics
ISBN : 1402765827

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Sacred Geometry by Stephen Skinner Pdf

A fascinating and inspirational look at the vital link between the hidden geometrical order of the universe, geometry in nature, and the geometry of the man-made world. The Da Vinci Code has awakened the public to the powerful and very ancient idea that religious truths and mathematical principles are intimately intertwined. Sacred Geometry offers an accessible way of understanding how that connection is revealed in nature and the arts. Over the centuries, temple builders have relied on magic numbers to shape sacred spaces, astronomers have used geometry to calculate holy seasons, and philosophers have observed the harmony of the universe in the numerical properties of music. By showing how the discoveries of mathematics are manifested over and over again in biology and physics, and how they have inspired the greatest works of art, this illuminating study reveals the universal principles that link us to the infinite.

Author : Andreĭ Petrovich Kiselev
Publisher : Unknown
Page : 192 pages
File Size : 53,7 Mb
Release : 2008
Category : Geometry
ISBN : UCSD:31822037285152

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Kiselev's Geometry by Andreĭ Petrovich Kiselev Pdf

This volume completes the English adaptation of a classical Russian textbook in elementary Euclidean geometry. The 1st volume subtitled "Book I. Planimetry" was published in 2006 (ISBN 0977985202). This 2nd volume (Book II. Stereometry) covers solid geometry, and contains a chapter on vectors, foundations, and introduction in non-Euclidean geometry added by the translator. The book intended for high-school and college students, and their teachers. Includes 317 exercises, index, and bibliography.

Author : Dan Pedoe
Publisher : Courier Corporation
Page : 466 pages
File Size : 44,5 Mb
Release : 2013-04-02
Category : Mathematics
ISBN : 9780486131733

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Geometry: A Comprehensive Course by Dan Pedoe Pdf

Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.

Author : Melvin Hausner
Publisher : Courier Dover Publications
Page : 417 pages
File Size : 50,5 Mb
Release : 2018-10-17
Category : Mathematics
ISBN : 9780486835396

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A Vector Space Approach to Geometry by Melvin Hausner Pdf

A fascinating exploration of the correlation between geometry and linear algebra, this text portrays the former as a subject better understood by the use and development of the latter rather than as an independent field. The treatment offers elementary explanations of the role of geometry in other branches of math and science — including physics, analysis, and group theory — as well as its value in understanding probability, determinant theory, and function spaces. Outstanding features of this volume include discussions of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. Students and other mathematically inclined readers will find that this inquiry into the interplay between geometry and other areas offers an enriched appreciation of both subjects.

Author : Richard Rusczyk
Publisher : Aops Incorporated
Page : 557 pages
File Size : 45,6 Mb
Release : 2007-07-01
Category : Juvenile Nonfiction
ISBN : 1934124087

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Introduction to Geometry by Richard Rusczyk Pdf

Author : Daniel Huybrechts
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 47,6 Mb
Release : 2005
Category : Computers
ISBN : 3540212906

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Complex Geometry by Daniel Huybrechts Pdf

Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

Author : Daniel Hug,Wolfgang Weil
Publisher : Springer Nature
Page : 287 pages
File Size : 43,6 Mb
Release : 2020-08-27
Category : Mathematics
ISBN : 9783030501808

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Lectures on Convex Geometry by Daniel Hug,Wolfgang Weil Pdf

This book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn–Minkowski theory, with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including the isoperimetric inequality. Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations. Finally, an introduction to integral-geometric formulas in Euclidean space is provided. The numerous exercises and the supplementary material at the end of each section form an essential part of the book. Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry. Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.

Author : David Hilbert
Publisher : Read Books Ltd
Page : 98 pages
File Size : 52,5 Mb
Release : 2014-07-07
Category : Mathematics
ISBN : 9781473395947

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The Foundations of Geometry by David Hilbert Pdf

This early work by David Hilbert was originally published in the early 20th century and we are now republishing it with a brand new introductory biography. David Hilbert was born on the 23rd January 1862, in a Province of Prussia. Hilbert is recognised as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.

Author : David Acheson
Publisher : Oxford University Press
Page : 240 pages
File Size : 43,8 Mb
Release : 2020-10-22
Category : Mathematics
ISBN : 9780192585370

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The Wonder Book of Geometry by David Acheson Pdf

How can we be sure that Pythagoras's theorem is really true? Why is the 'angle in a semicircle' always 90 degrees? And how can tangents help determine the speed of a bullet? David Acheson takes the reader on a highly illustrated tour through the history of geometry, from ancient Greece to the present day. He emphasizes throughout elegant deduction and practical applications, and argues that geometry can offer the quickest route to the whole spirit of mathematics at its best. Along the way, we encounter the quirky and the unexpected, meet the great personalities involved, and uncover some of the loveliest surprises in mathematics.

Author : Bruce E. Meserve
Publisher : Courier Corporation
Page : 336 pages
File Size : 42,8 Mb
Release : 2014-12-08
Category : Mathematics
ISBN : 9780486152264

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Fundamental Concepts of Geometry by Bruce E. Meserve Pdf

Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.

Author : Mark de Berg,Marc van Krefeld,Mark Overmars,Otfried Cheong
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 40,7 Mb
Release : 2013-04-17
Category : Computers
ISBN : 9783662042458

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Computational Geometry by Mark de Berg,Marc van Krefeld,Mark Overmars,Otfried Cheong Pdf

This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.

Author : M. N. Aref,William Wernick
Publisher : Courier Corporation
Page : 274 pages
File Size : 45,6 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9780486477206

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Problems and Solutions in Euclidean Geometry by M. N. Aref,William Wernick Pdf

Based on classical principles, this book is intended for a second course in Euclidean geometry and can be used as a refresher. Each chapter covers a different aspect of Euclidean geometry, lists relevant theorems and corollaries, and states and proves many propositions. Includes more than 200 problems, hints, and solutions. 1968 edition.