Invitation To Geometry

Author : Z. A. Melzak
Publisher : Courier Corporation
Page : 244 pages
File Size : 47,6 Mb
Release : 2014-01-15
Category : Mathematics
ISBN : 9780486789484

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Invitation to Geometry by Z. A. Melzak Pdf

Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. Only a slight acquaintance with mathematics beyond the high-school level is necessary, including some familiarity with calculus and linear algebra. This text's introductions to several branches of geometry feature topics and treatments based on memorability and relevance. The author emphasizes connections with calculus and simple mechanics, focusing on developing students' grasp of spatial relationships. Subjects include classical Euclidean material, polygonal and circle isoperimetry, conics and Pascal's theorem, geometrical optimization, geometry and trigonometry on a sphere, graphs, convexity, and elements of differential geometry of curves. Additional material may be conveniently introduced in several places, and each chapter concludes with exercises of varying degrees of difficulty.

Author : Karen E. Smith,Lauri Kahanpää,Pekka Kekäläinen,William Traves
Publisher : Springer Science & Business Media
Page : 173 pages
File Size : 43,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475744972

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An Invitation to Algebraic Geometry by Karen E. Smith,Lauri Kahanpää,Pekka Kekäläinen,William Traves Pdf

This is a description of the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.

Author : Masoud Khalkhali,Matilde Marcolli
Publisher : World Scientific
Page : 515 pages
File Size : 45,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812814333

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An Invitation to Noncommutative Geometry by Masoud Khalkhali,Matilde Marcolli Pdf

A walk in the noncommutative garden / A. Connes and M. Marcolli -- Renormalization of noncommutative quantum field theory / H. Grosse and R. Wulkenhaar -- Lectures on noncommutative geometry / M. Khalkhali -- Noncommutative bundles and instantons in Tehran / G. Landi and W. D. van Suijlekom -- Lecture notes on noncommutative algebraic geometry and noncommutative tori / S. Mahanta -- Lectures on derived and triangulated categories / B. Noohi -- Examples of noncommutative manifolds: complex tori and spherical manifolds / J. Plazas -- D-branes in noncommutative field theory / R. J. Szabo.

Author : Martin R. Bridson,Simon Salamon
Publisher : Unknown
Page : 352 pages
File Size : 54,9 Mb
Release : 2002
Category : Mathematics
ISBN : 0198507720

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Invitations to Geometry and Topology by Martin R. Bridson,Simon Salamon Pdf

This volume presents an array of topics that introduce the reader to key ideas in active areas in geometry and topology. The material is presented in a way that both graduate students and researchers should find accessible and enticing. The topics covered range from Morse theory and complex geometry theory to geometric group theory, and are accompanied by exercises that are designed to deepen the reader's understanding and to guide them in exciting directions for future investigation.

Author : Stephanie Alexander,Vitali Kapovitch,Anton Petrunin
Publisher : Springer
Page : 88 pages
File Size : 52,8 Mb
Release : 2019-05-08
Category : Mathematics
ISBN : 9783030053123

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An Invitation to Alexandrov Geometry by Stephanie Alexander,Vitali Kapovitch,Anton Petrunin Pdf

Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem and applies it to the billiards problems. The Hadamard–Cartan globalization theorem is explored and applied to construct exotic aspherical manifolds.

Author : Dino Lorenzini
Publisher : American Mathematical Society
Page : 397 pages
File Size : 48,7 Mb
Release : 2021-12-23
Category : Mathematics
ISBN : 9781470467258

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An Invitation to Arithmetic Geometry by Dino Lorenzini Pdf

Extremely carefully written, masterfully thought out, and skillfully arranged introduction … to the arithmetic of algebraic curves, on the one hand, and to the algebro-geometric aspects of number theory, on the other hand. … an excellent guide for beginners in arithmetic geometry, just as an interesting reference and methodical inspiration for teachers of the subject … a highly welcome addition to the existing literature. —Zentralblatt MATH The interaction between number theory and algebraic geometry has been especially fruitful. In this volume, the author gives a unified presentation of some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry, and for the first time in a book at this level, brings out the deep analogies between them. The geometric viewpoint is stressed throughout the book. Extensive examples are given to illustrate each new concept, and many interesting exercises are given at the end of each chapter. Most of the important results in the one-dimensional case are proved, including Bombieri's proof of the Riemann Hypothesis for curves over a finite field. While the book is not intended to be an introduction to schemes, the author indicates how many of the geometric notions introduced in the book relate to schemes, which will aid the reader who goes to the next level of this rich subject.

Author : Karen Smith,Lauri Kahanpaa,Pekka Kekalainen
Publisher : Unknown
Page : 184 pages
File Size : 40,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1475744986

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An Invitation to Algebraic Geometry by Karen Smith,Lauri Kahanpaa,Pekka Kekalainen Pdf

Author : Frederick J. Almgren
Publisher : American Mathematical Soc.
Page : 96 pages
File Size : 41,9 Mb
Release : 1966
Category : Differential topology
ISBN : 9780821827475

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Plateau's Problem by Frederick J. Almgren Pdf

There have been many wonderful developments in the theory of minimal surfaces and geometric measure theory in the past 25 to 30 years. Many of the researchers who have produced these excellent results were inspired by this little book - or by Fred Almgren himself. The book is indeed a delightful invitation to the world of variational geometry. A central topic is Plateau's Problem, which is concerned with surfaces that model the behavior of soap films.When trying to resolve the problem, however, one soon finds that smooth surfaces are insufficient: Varifolds are needed. With varifolds, one can obtain geometrically meaningful solutions without having to know in advance all their possible singularities. This new tool makes possible much exciting new analysis and many new results. Plateau's problem and varifolds live in the world of geometric measure theory, where differential geometry and measure theory combine to solve problems which have variational aspects. The author's hope in writing this book was to encourage young mathematicians to study this fascinating subject further. Judging from the success of his students, it achieves this exceedingly well.

Author : Mateusz Michałek,Bernd Sturmfels
Publisher : American Mathematical Society
Page : 226 pages
File Size : 53,7 Mb
Release : 2021-03-05
Category : Mathematics
ISBN : 9781470453671

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Invitation to Nonlinear Algebra by Mateusz Michałek,Bernd Sturmfels Pdf

Nonlinear algebra provides modern mathematical tools to address challenges arising in the sciences and engineering. It is useful everywhere, where polynomials appear: in particular, data and computational sciences, statistics, physics, optimization. The book offers an invitation to this broad and fast-developing area. It is not an extensive encyclopedia of known results, but rather a first introduction to the subject, allowing the reader to enter into more advanced topics. It was designed as the next step after linear algebra and well before abstract algebraic geometry. The book presents both classical topics—like the Nullstellensatz and primary decomposition—and more modern ones—like tropical geometry and semidefinite programming. The focus lies on interactions and applications. Each of the thirteen chapters introduces fundamental concepts. The book may be used for a one-semester course, and the over 200 exercises will help the readers to deepen their understanding of the subject.

Author : Jorge Vitório Pereira,Luc Pirio
Publisher : Springer
Page : 213 pages
File Size : 53,6 Mb
Release : 2015-02-23
Category : Mathematics
ISBN : 9783319145624

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An Invitation to Web Geometry by Jorge Vitório Pereira,Luc Pirio Pdf

This book takes an in-depth look at abelian relations of codimension one webs in the complex analytic setting. In its classical form, web geometry consists in the study of webs up to local diffeomorphisms. A significant part of the theory revolves around the concept of abelian relation, a particular kind of functional relation among the first integrals of the foliations of a web. Two main focuses of the book include how many abelian relations can a web carry and which webs are carrying the maximal possible number of abelian relations. The book offers complete proofs of both Chern’s bound and Trépreau’s algebraization theorem, including all the necessary prerequisites that go beyond elementary complex analysis or basic algebraic geometry. Most of the examples known up to date of non-algebraizable planar webs of maximal rank are discussed in detail. A historical account of the algebraization problem for maximal rank webs of codimension one is also presented.

Author : Dino Lorenzini
Publisher : American Mathematical Soc.
Page : 418 pages
File Size : 43,9 Mb
Release : 1996-02-22
Category : Arithmetical algebraic geometry
ISBN : 9780821802670

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An Invitation to Arithmetic Geometry by Dino Lorenzini Pdf

Extremely carefully written, masterfully thought out, and skillfully arranged introduction ... to the arithmetic of algebraic curves, on the one hand, and to the algebro-geometric aspects of number theory, on the other hand. ... an excellent guide for beginners in arithmetic geometry, just as an interesting reference and methodical inspiration for teachers of the subject ... a highly welcome addition to the existing literature. --Zentralblatt MATH The interaction between number theory and algebraic geometry has been especially fruitful. In this volume, the author gives a unified presentation of some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry, and for the first time in a book at this level, brings out the deep analogies between them. The geometric viewpoint is stressed throughout the book. Extensive examples are given to illustrate each new concept, and many interesting exercises are given at the end of each chapter. Most of the important results in the one-dimensional case are proved, including Bombieri's proof of the Riemann Hypothesis for curves over a finite field. While the book is not intended to be an introduction to schemes, the author indicates how many of the geometric notions introduced in the book relate to schemes, which will aid the reader who goes to the next level of this rich subject.

Author : Yi Ma,Stefano Soatto,Jana Kosecká,S. Shankar Sastry
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 42,5 Mb
Release : 2012-11-06
Category : Computers
ISBN : 9780387217796

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An Invitation to 3-D Vision by Yi Ma,Stefano Soatto,Jana Kosecká,S. Shankar Sastry Pdf

This book introduces the geometry of 3-D vision, that is, the reconstruction of 3-D models of objects from a collection of 2-D images. It details the classic theory of two view geometry and shows that a more proper tool for studying the geometry of multiple views is the so-called rank consideration of the multiple view matrix. It also develops practical reconstruction algorithms and discusses possible extensions of the theory.

Author : Michael P. Hitchman
Publisher : Jones & Bartlett Learning
Page : 255 pages
File Size : 49,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9780763754570

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Geometry with an Introduction to Cosmic Topology by Michael P. Hitchman Pdf

The content of Geometry with an Introduction to Cosmic Topology is motivated by questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have and edge? Is it infinitely big? Dr. Hitchman aims to clarify this fascinating area of mathematics. This non-Euclidean geometry text is organized intothree natural parts. Chapter 1 provides an overview including a brief history of Geometry, Surfaces, and reasons to study Non-Euclidean Geometry. Chapters 2-7 contain the core mathematical content of the text, following the ErlangenProgram, which develops geometry in terms of a space and a group of transformations on that space. Finally chapters 1 and 8 introduce (chapter 1) and explore (chapter 8) the topic of cosmic topology through the geometry learned in the preceding chapters.

Author : Maurice Fréchet,Ky Fan
Publisher : Courier Corporation
Page : 148 pages
File Size : 50,8 Mb
Release : 2012-08-13
Category : Mathematics
ISBN : 9780486147888

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Invitation to Combinatorial Topology by Maurice Fréchet,Ky Fan Pdf

An elementary text that can be understood by anyone with a background in high school geometry, Invitation to Combinatorial Topology offers a stimulating initiation to important topological ideas. This translation from the original French does full justice to the text's coherent presentation as well as to its rich historical content. Subjects include the problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, and topological polygons. Considerations of the topological classification of closed surfaces cover elementary operations, use of normal forms of polyhedra, reduction to normal form, and application to the geometric theory of functions. 1967 edition. 108 figures. Bibliography. Index.

Author : Victor M. Panaretos,Yoav Zemel
Publisher : Springer Nature
Page : 157 pages
File Size : 50,6 Mb
Release : 2020-03-10
Category : Mathematics
ISBN : 9783030384388

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An Invitation to Statistics in Wasserstein Space by Victor M. Panaretos,Yoav Zemel Pdf

This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph.