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Author : Joyce Markovics
Publisher : Carson-Dellosa Publishing
Page : 24 pages
File Size : 50,5 Mb
Release : 2019-03-27
Category : Juvenile Nonfiction
ISBN : 9781731619921
Teaches Young Students About Basic Concepts Of Geometry, Such As Angles And Planes.
Author : Workman Publishing,Christy Needham
Publisher : Workman Publishing Company
Page : 624 pages
File Size : 52,8 Mb
Release : 2020-09-29
Category : Juvenile Nonfiction
ISBN : 9781523512027
The Big Fat Notebooks go to high school! A lively, fully illustrated guide to acing high school geometry, with clear notes on the big ideas, helpful tips for memorizing processes and remembering definitions, and lively doodles that make math easier to understand (and fun to study).
Author : Jordan Ellenberg
Publisher : Penguin
Page : 481 pages
File Size : 41,5 Mb
Release : 2021-05-25
Category : Mathematics
ISBN : 9781984879066
An instant New York Times Bestseller! “Unreasonably entertaining . . . reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning.” —The New York Times From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry. For real. If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry"comes from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.
Author : Shoo Rayner
Publisher : Unknown
Page : 54 pages
File Size : 50,5 Mb
Release : 2017-11-02
Category : Juvenile Nonfiction
ISBN : 1908944366
Geometry is brought to life as Euclid explains principles of Geometry to his friends. With jokes and lots of illustrations, discover the beauty of geometry and, before you know it, you too will soon be a friend of Euclid! Shoo Rayner adds humour and simplicity to a tricky subject. A perfect introduction.
Author : Shun-ichi Amari
Publisher : Springer
Page : 378 pages
File Size : 42,6 Mb
Release : 2016-02-02
Category : Mathematics
ISBN : 9784431559788
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 : Nihat Ay,Jürgen Jost,Hông Vân Lê,Lorenz Schwachhöfer
Publisher : Springer
Page : 407 pages
File Size : 42,6 Mb
Release : 2017-08-25
Category : Mathematics
ISBN : 9783319564784
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, information theory, or the foundations of statistics, to statisticians as well as to scientists interested in the mathematical foundations of complex systems.
Author : Robert Bix
Publisher : Elsevier
Page : 549 pages
File Size : 45,8 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9781483296463
This volume presents an accessible, self-contained survey of topics in Euclidean and non-Euclidean geometry. It includes plentiful illustrations and exercises in support of the thoroughly worked-out proofs. The author's emphasis on the connections between Euclidean and non-Euclidean geometry unifies the range of topics covered. The text opens with a brief review of elementary geometry before proceeding to advanced material. Topics covered include advanced Euclidean and non-Euclidean geometry, division ratios and triangles, transformation geometry, projective geometry, conic sections, and hyperbolic and absolute geometry. Topics in Geometry includes over 800 illustrations and extensive exercises of varying difficulty.
Author : M.K. Murray
Publisher : Routledge
Page : 164 pages
File Size : 47,6 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351455114
Several years ago our statistical friends and relations introduced us to the work of Amari and Barndorff-Nielsen on applications of differential geometry to statistics. This book has arisen because we believe that there is a deep relationship between statistics and differential geometry and moreoever that this relationship uses parts of differential geometry, particularly its 'higher-order' aspects not readily accessible to a statistical audience from the existing literature. It is, in part, a long reply to the frequent requests we have had for references on differential geometry! While we have not gone beyond the path-breaking work of Amari and Barndorff- Nielsen in the realm of applications, our book gives some new explanations of their ideas from a first principles point of view as far as geometry is concerned. In particular it seeks to explain why geometry should enter into parametric statistics, and how the theory of asymptotic expansions involves a form of higher-order differential geometry. The first chapter of the book explores exponential families as flat geometries. Indeed the whole notion of using log-likelihoods amounts to exploiting a particular form of flat space known as an affine geometry, in which straight lines and planes make sense, but lengths and angles are absent. We use these geometric ideas to introduce the notion of the second fundamental form of a family whose vanishing characterises precisely the exponential families.
Author : Shun-ichi Amari,Hiroshi Nagaoka
Publisher : American Mathematical Soc.
Page : 220 pages
File Size : 47,7 Mb
Release : 2000
Category : Computers
ISBN : 0821843028
Information geometry provides the mathematical sciences with a fresh framework of analysis. This book presents a comprehensive introduction to the mathematical foundation of information geometry. It provides an overview of many areas of applications, such as statistics, linear systems, information theory, quantum mechanics, and convex analysis.
Author : Britannica Educational Publishing
Publisher : Britannica Educational Publishing
Page : 316 pages
File Size : 49,6 Mb
Release : 2010-04-01
Category : Juvenile Nonfiction
ISBN : 9781615302178
More than a study of shapes and angles, geometry reflects an amalgamation of discoveries over time. This book not only provides readers with a comprehensive understanding of geometric shapes, axioms, and formulas, it presents the fields brilliant mindsfrom Euclid to Wendelin Werner and many in betweenwhose works reflect a progression of mathematical thought throughout the centuries and have helped produce the various branches of geometry as they are known today. Detailed diagrams illustrate various concepts and help make geometry accessible to all.
Author : Anonim
Publisher : Remedia Publications
Page : 28 pages
File Size : 52,9 Mb
Release : 2006
Category : Mathematics
ISBN : 1596398558
Author : Bruce E. Meserve
Publisher : Courier Corporation
Page : 336 pages
File Size : 51,5 Mb
Release : 2014-12-08
Category : Mathematics
ISBN : 9780486152264
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 : Andreĭ Petrovich Kiselev
Publisher : Unknown
Page : 192 pages
File Size : 49,8 Mb
Release : 2008
Category : Geometry
ISBN : UCSD:31822037285152
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 : Frank Nielsen
Publisher : Springer Nature
Page : 274 pages
File Size : 42,5 Mb
Release : 2021-03-14
Category : Science
ISBN : 9783030654597
This book focuses on information-geometric manifolds of structured data and models and related applied mathematics. It features new and fruitful interactions between several branches of science: Advanced Signal/Image/Video Processing, Complex Data Modeling and Analysis, Statistics on Manifolds, Topology/Machine/Deep Learning and Artificial Intelligence. The selection of applications makes the book a substantial information source, not only for academic scientist but it is also highly relevant for industry. The book project was initiated following discussions at the international conference GSI’2019 – Geometric Science of Information that was held at ENAC, Toulouse (France).
Author : Geert Verdoolaege
Publisher : MDPI
Page : 355 pages
File Size : 40,9 Mb
Release : 2019-04-04
Category : Juvenile Nonfiction
ISBN : 9783038976325
This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience.