Geometry with an Introduction to Cosmic Topology
Geometry with an Introduction to Cosmic Topology

Author: Michael P. Hitchman

Publisher: Jones & Bartlett Learning

Published: 2009

Total Pages: 255

ISBN-13: 0763754579

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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.

The Wraparound Universe
The Wraparound Universe

Author: Jean-Pierre Luminet

Publisher: CRC Press

Published: 2008-03-21

Total Pages: 334

ISBN-13: 1439864969

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What shape is the universe? Is it curved and closed in on itself? Is it expanding? Where is it headed? Could space be wrapped around itself, such that it produces ghost images of faraway galaxies? Such are the questions posed by Jean-Pierre Luminet in The Wraparound Universe, which he then addresses in clear and accessible language. An expert in bl

Noncommutative Geometry and Particle Physics
Noncommutative Geometry and Particle Physics

Author: Walter D. van Suijlekom

Publisher: Springer

Published: 2014-07-21

Total Pages: 246

ISBN-13: 9401791627

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This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. It is intended for graduate students in mathematics/theoretical physics who are new to the field of noncommutative geometry, as well as for researchers in mathematics/theoretical physics with an interest in the physical applications of noncommutative geometry. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we show how noncommutative spin manifolds naturally give rise to gauge theories, applying this principle to specific examples. We subsequently geometrically derive abelian and non-abelian Yang-Mills gauge theories, and eventually the full Standard Model of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model.

An Introduction to Riemannian Geometry
An Introduction to Riemannian Geometry

Author: Leonor Godinho

Publisher: Springer

Published: 2014-07-26

Total Pages: 476

ISBN-13: 3319086669

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Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.

The Shape of Space
The Shape of Space

Author: Jeffrey R. Weeks

Publisher: CRC Press

Published: 2001-12-12

Total Pages: 248

ISBN-13: 1135542651

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Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.

An Introduction to Modern Cosmology
An Introduction to Modern Cosmology

Author: Andrew Liddle

Publisher: John Wiley & Sons

Published: 2015-03-09

Total Pages: 200

ISBN-13: 1118690273

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An Introduction to Modern Cosmology Third Edition is an accessible account of modern cosmological ideas. The Big Bang Cosmology is explored, looking at its observational successes in explaining the expansion of the Universe, the existence and properties of the cosmic microwave background, and the origin of light elements in the universe. Properties of the very early Universe are also covered, including the motivation for a rapid period of expansion known as cosmological inflation. The third edition brings this established undergraduate textbook up-to-date with the rapidly evolving observational situation. This fully revised edition of a bestseller takes an approach which is grounded in physics with a logical flow of chapters leading the reader from basic ideas of the expansion described by the Friedman equations to some of the more advanced ideas about the early universe. It also incorporates up-to-date results from the Planck mission, which imaged the anisotropies of the Cosmic Microwave Background radiation over the whole sky. The Advanced Topic sections present subjects with more detailed mathematical approaches to give greater depth to discussions. Student problems with hints for solving them and numerical answers are embedded in the chapters to facilitate the reader’s understanding and learning. Cosmology is now part of the core in many degree programs. This current, clear and concise introductory text is relevant to a wide range of astronomy programs worldwide and is essential reading for undergraduates and Masters students, as well as anyone starting research in cosmology. The accompanying website for this text, http://booksupport.wiley.com, provides additional material designed to enhance your learning, as well as errata within the text.

The Shape of Inner Space
The Shape of Inner Space

Author: Shing-Tung Yau

Publisher: Il Saggiatore

Published: 2010-09-07

Total Pages: 398

ISBN-13: 0465020232

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The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.

Introductory Business Statistics 2e
Introductory Business Statistics 2e

Author: Alexander Holmes

Publisher:

Published: 2023-12-13

Total Pages: 1801

ISBN-13:

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Introductory Business Statistics 2e aligns with the topics and objectives of the typical one-semester statistics course for business, economics, and related majors. The text provides detailed and supportive explanations and extensive step-by-step walkthroughs. The author places a significant emphasis on the development and practical application of formulas so that students have a deeper understanding of their interpretation and application of data. Problems and exercises are largely centered on business topics, though other applications are provided in order to increase relevance and showcase the critical role of statistics in a number of fields and real-world contexts. The second edition retains the organization of the original text. Based on extensive feedback from adopters and students, the revision focused on improving currency and relevance, particularly in examples and problems. This is an adaptation of Introductory Business Statistics 2e by OpenStax. You can access the textbook as pdf for free at openstax.org. Minor editorial changes were made to ensure a better ebook reading experience. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License.

Introduction to General Relativity, Black Holes, and Cosmology
Introduction to General Relativity, Black Holes, and Cosmology

Author: Yvonne Choquet-Bruhat

Publisher: Oxford University Press, USA

Published: 2015

Total Pages: 301

ISBN-13: 0199666466

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A precise yet simple introduction to the foundations and main consequences of General Relativity. The first five chapters from Choquet-Bruhat's General Relativity and the Einstein Equations (2008) have been updated with new sections and chapters on black holes, gravitational waves, singularities and more to form this textbook.