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Geometrodynamics of Gauge Fields: On the Geometry of Yang-Mills and Gravitational Gauge Theories (Mathematical Physics Studies)

This monograph aims to provide a unified, geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included. By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed. Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de Sitter type gauge theory in the spirit of Yang-Mills, some new progress in its topological form is presented. After symmetry breaking, Einstein’s standard general relativity with cosmological constant emerges as a classical background. The geometrical structure of BRST quantization with non-propagating topological ghosts is developed in some detail.

Geometry

THE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT! "Glencoe Geometry" is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scores on today's high-stakes assessments.

Geometry

A flexible program with the solid content students need Glencoe Geometry is the leading geometry program on the market. Algebra and applications are embedded throughout the program and an introduction to geometry proofs begins in Chapter 2.

Geometry

Geometry is a full-year course, written to help students understand and explore the concepts of geometry as well as prepare them for the new end-of-course assessments. All instruction, model problems, and practice items were developed to support the latest college and career readiness standards, as well as core standards. Each chapter opens with lesson-by-lesson alignment with the standards. The eight Mathematical Practice Standards are embedded throughout in selected Model Problems, extensive practice problem sets, and the comprehensive Chapter and Cumulative Reviews.

Geometry

Louisiana Geometry End of Course Test Preparation

Geometry

This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. In each case they carefully explain the key results and discuss the relationships between the geometries. New features in this second edition include concise end-of-chapter summaries to aid student revision, a list of further reading and a list of special symbols. The authors have also revised many of the end-of-chapter exercises to make them more challenging and to include some interesting new results. Full solutions to the 200 problems are included in the text, while complete solutions to all of the end-of-chapter exercises are available in a new Instructors' Manual, which can be downloaded from www. cambridge. org/9781107647831.

Geometry

NIMAC-sourced textbook

Geometry

NIMAC-sourced textbook

Geometry

NIMAC-sourced textbook

Geometry

This book provides exploratory exercises that lead students to discover geometric properties and develop geometric intuition.

Geometry

In this textbook, every chapter contains biblically based material, providing a scriptural foundation. Questions about the Bible text help you grasp what is important to the chapter. The Bible as truth makes what you learn personal and practical. The Bible as the basis for geometry sheds light on the purpose of the subject. The theme verse helps you to link the temporary with the eternal in your studies. Many examples help you do the homework. Two-column proofs help you develop your reasoning skills. Exercises with different levels of difficulty help guide your progress. Dominion Thru Math helps you apply technology to problem solving. Level C exercises challenge your thinking skills. Cumulative Reviews help you stay on top of the subject. Geometry Around Us reveals some of geometry’s secret hideouts. Analytic Geometry helps you make the algebra- geometry connection. Geometry Through History brings the subject to life. The Mind over Math brain teasers exercise your gray matter. Chapter openers are your ticket to new achievements.

Geometry

NIMAC-sourced textbook

Geometry

Advanced Placement Calculus is aligned with the NCTM Standards and the latest AP guidelines and retains the solid, carefully motivated mathematics that characterize previous editions. The Seventh Edition embraces the best aspects of reform by integrating the latest technological tools and by emphasizing real-life data, practical applications, and mathematical models.

Geometry

The book covers basics of geometry in detail with very useful student help sections like Application of Mathematics in real life,Skill Review,Quizzes,Test Preparation techniques etc.

Geometry

In addition to its geometry content, this book includes numerous examples and exercises involving algebra, data analysis, and probability. It also helps students to prepare for standardized tests.

Geometry (2018 Edition): Student Edition

Geometry (Big Ideas Math)

Geometry (Fourth Edition)

The BJU Press Geometry curriculum covers the fundamental key concepts of geometry, including reasoning, proof, parallel and perpendicular lines, triangles, quadrilaterals, area, circles, similarity, an introduction to trigonometry, and more. Fun features are included throughout; "Geometry in history" historical-fiction narratives highlight key mathematical contributions, "Technology Corner" notes use dynamic geometry software to visualize and discover geometric concepts, while "Geometry Around Us" features show how geometry is used in careers and daily life. Chapters introduce the concept and are followed by multiple step-by-step examples. Expanded exercise sets reinforce new concepts and connect skills to previously learned concepts. A cumulative review helps keeps concepts fresh throughout the year.

Geometry (Life of Fred)

This is not a traditional math book. This is a child-directed course. The student reads the adventure story, does the math problems that occur as a natural part of the story, and checks their answers (the solutions are right there for the looking.) And learns to love math in the process! (Compare to Saxon at $50-70) Contents: Points and Lines, Angles, Triangles, Parallel Lines, Perpendicular Lines, Quadrilaterals, Area, Geometry Theories, Similar Triangles, Symbolic Logic, Right Triangles, Circles, Constructions, Non-Euclidean Geometry, Solid Geometry, Geometry in 4D, Coordinate Geometry, and Modern Geometry.

Geometry (Maryland)

This traditional text offers a balanced approach that combines the theoretical instruction of calculus with the best aspects of reform, including creative teaching and learning techniques such as the integration of technology, the use of real data, real-life applications, and mathematical models. The Calculus with Analytic Geometry Alternate, 6/e, offers a late approach to trigonometry for those instructors who wish to introduce it later in their courses.

Geometry (Michigan)

Math textbook for high school

Geometry (Navigating Through Geometry)

Geometry (Ohio)

A flexible program with the solid content students need Glencoe Geometry is the leading geometry program on the market. Algebra and applications are embedded throughout the program and an introduction to geometry proofs begins in Chapter 2.

Geometry (Ohio)

This traditional text offers a balanced approach that combines the theoretical instruction of calculus with the best aspects of reform, including creative teaching and learning techniques such as the integration of technology, the use of real data, real-life applications, and mathematical models. The Calculus with Analytic Geometry Alternate, 6/e, offers a late approach to trigonometry for those instructors who wish to introduce it later in their courses.

Geometry - Intuition and Concepts: Imagining, understanding, thinking beyond. An introduction for students

This book deals with the geometry of visual space in all its aspects. As in any branch of mathematics, the aim is to trace the hidden to the obvious; the peculiarity of geometry is that the obvious is sometimes literally before one's eyes.Starting from intuition, spatial concepts are embedded in the pre-existing mathematical framework of linear algebra and calculus. The path from visualization to mathematically exact language is itself the learning content of this book. This is intended to close an often lamented gap in understanding between descriptive preschool and school geometry and the abstract concepts of linear algebra and calculus. At the same time, descriptive geometric modes of argumentation are justified because their embedding in the strict mathematical language has been clarified.The concepts of geometry are of a very different nature; they denote, so to speak, different layers of geometric thinking: some arguments use only concepts such as point, straight line, and incidence, others require angles and distances, still others symmetry considerations. Each of these conceptual fields determines a separate subfield of geometry and a separate chapter of this book, with the exception of the last-mentioned conceptual field "symmetry", which runs through all the others: - Incidence: Projective geometry - Parallelism: Affine geometry - Angle: Conformal Geometry - Distance: Metric Geometry - Curvature: Differential Geometry - Angle as distance measure: Spherical and Hyperbolic Geometry - Symmetry: Mapping Geometry.The mathematical experience acquired in the visual space can be easily transferred to much more abstract situations with the help of the vector space notion. The generalizations beyond the visual dimension point in two directions: Extension of the number concept and transcending the three illustrative dimensions.This book is a translation of the original German 1st edition Geometrie – Anschauung und Begriffe by Jost-Hinrich Eschenburg, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.