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Geometry, Symmetries, and Classical Physics: A Mosaic
by Manousos MarkoutsakisThis book provides advanced undergraduate physics and mathematics students with an accessible yet detailed understanding of the fundamentals of differential geometry and symmetries in classical physics. Readers, working through the book, will obtain a thorough understanding of symmetry principles and their application in mechanics, field theory, and general relativity, and in addition acquire the necessary calculational skills to tackle more sophisticated questions in theoretical physics. Most of the topics covered in this book have previously only been scattered across many different sources of literature, therefore this is the first book to coherently present this treatment of topics in one comprehensive volume. Key features: Contains a modern, streamlined presentation of classical topics, which are normally taught separately Includes several advanced topics, such as the Belinfante energy-momentum tensor, the Weyl-Schouten theorem, the derivation of Noether currents for diffeomorphisms, and the definition of conserved integrals in general relativity Focuses on the clear presentation of the mathematical notions and calculational technique
Geometry, Topology and Operator Algebras: Global Analysis, Invariants and Their Significance in Theoretical Physics (Mathematical Physics Studies)
by Alexander Cardona Andrés F. Reyes LegaThis book offers a comprehensive exploration of contemporary intersections between geometry, topology, and theoretical physics, emphasizing their mathematical foundations and applications. Originating from lectures presented by experts during two summer schools held in Villa de Leyva, Colombia, the book reflects the synergy between global analysis, operator algebras, and their role in modern physics. The chapters present state-of-the-art developments on a wide range of topics: the geometry and topology of foliations, affine manifolds, C*-algebras, and the pseudo-differential calculus of boundary value problems. These are enriched by applications to the theory of topological quantum matter. The book is suitable for graduate students and researchers, offering detailed introductions to advanced topics such as the longitudinal index theorem for foliations, the geometry of the Poincaré half-space in a C*-algebra, and mathematical frameworks for topological matter. With a balance of foundational material and novel insights, it serves as both a learning resource and a reference for advanced studies at the intersection of mathematics and physics.
Geometry, Topology and Physics
by Mikio NakaharaDifferential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields.The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view.Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.
Geometry, Topology, and Dynamics in Negative Curvature
by C. S. Aravinda F. T. Farrell J. F. LafontThe ICM 2010 satellite conference 'Geometry, Topology and Dynamics in Negative Curvature' afforded an excellent opportunity to discuss various aspects of this fascinating interdisciplinary subject in which methods and techniques from geometry, topology, and dynamics often interact in novel and interesting ways. Containing ten survey articles written by some of the leading experts in the field, this proceedings volume provides an overview of important recent developments relating to negative curvature. Topics covered include homogeneous dynamics, harmonic manifolds, the Atiyah Conjecture, counting circles and arcs, and hyperbolic buildings. Each author pays particular attention to the expository aspects, making the book particularly useful for graduate students and mathematicians interested in transitioning from other areas via the common theme of negative curvature.
Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)
by Amber Kuang Allen Maeasy, medium, and hardFree one-year access to the online questions bankWith 1,001 Geometry Practice Problems For Dummies, you'll get the practice you need to master geometry and gain confidence in the classroom.
Geometry: A Common Core Curriculum
by Houghton Mifflin Harcourt Publishing Company StaffGeometry A Common Core Curriculum
Geometry: A Comprehensive Course
by Dan Pedoe"A lucid and masterly survey." — Mathematics GazetteProfessor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to help students enjoy geometry.Among the topics discussed: the use of vectors and their products in work on Desargues' and Pappus' theorem and the nine-point circle; circles and coaxal systems; the representation of circles by points in three dimensions; mappings of the Euclidean plane, similitudes, isometries, mappings of the inversive plane, and Moebius transformations; projective geometry of the plane, space, and n dimensions; the projective generation of conics and quadrics; Moebius tetrahedra; the tetrahedral complex; the twisted cubic curve; the cubic surface; oriented circles; and introduction to algebraic geometry.In addition, three appendices deal with Euclidean definitions, postulates, and propositions; the Grassmann-Pluecker coordinates of lines in S3, and the group of circular transformations. Among the outstanding features of this book are its many worked examples and over 500 exercises to test geometrical understanding.
Geometry: Applying, Reasoning, Measuring (Mcdougal Littell High School Math Ser.)
by Ron Larson Laurie BoswellGeometry, like much of mathematics and science, developed when people began recognizing and describing patterns. In this course, you will study many amazing patterns that were discovered by people throughout history and all around the world. You will also learn to recognize and describe patterns of your own. Sometimes, patterns allow you to make accurate predictions.
Geometry: Concepts and Applications
by Mcgraw-Hill StaffAn ideal program for struggling students Geometry: Concepts and Applications covers all geometry concepts using an informal approach.
Geometry: Euclid And Beyond (Undergraduate Texts In Mathematics)
by Robin HartshorneIn recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And in the last chapter we provide what is missing from Euclid's treatment of the five Platonic solids in Book XIII of the Elements. For a one-semester course such as I teach, Chapters 1 and 2 form the core material, which takes six to eight weeks.
Geometry: Explorations and Applications
by Miriam A. Leiva Stuart J. Murphy Douglas B. Aichele Patrick W Hopfensperger Marguerite M. Mason Vicki J. Schell Matthias C. VheruThis book will help you use mathematics in your daily life and prepare you for success in future courses and careers.
Geometry: Explorations and Applications, Practice Workbook
by Mcdougal LittellThis book contains a good collection of math exercises and examples.
Geometry: GRE Math Strategy Guide 2nd Edition
by The Editors ar the Manhattan GREThis volume guides students through the intricacies of shapes, planes, lines, angles, and objects, illustrating every geometric principle, formula, and problem type tested on the GRE.
Geometry: Homework Practice Workbook
by Glencoe Mcgraw-HillThe Homework Practice Workbook contains two worksheets for every lesson in the Student Edition. This workbook helps students: Practice the skills of the lesson, Use their skills to solve word problems.
Geometry: Integration - Applications - Connections
by Timothy D. Kanold Carol Malloy Robert Cummings Allan BereleThis textbook talks about real-world uses of geometry
Geometry: Integration, Applications, Connections
by Glencoe Mcgraw-HillGeometry is designed to answer questions such as why mathematics is important through integration, applications, and connections.
Geometry: Mathematics in Context (2nd edition)
by Cord CommunicationsPoints, lines, and planes are the basic figures of geometry. In algebra, you used ordered pairs of numbers to locate points on a coordinate plane. You also used tables of ordered pairs and linear equations to locate and draw straight lines on a coordinate plane. Geometry on the coordinate plane is called coordinate geometry.
Geometry: Our Cultural Heritage
by Audun HolmeThis book contains selected topics from the history of geometry, with "modern" proofs of some of the results, as well as a fully modern treatment of selected basic issues in geometry. It is geared towards the needs of future mathematics teachers. All too often the geometry which goes into the syllabus for these students presents the material in a pedantic and formalistic style, suppressing its dynamic character and its role as part of the foundation of our common cultural heritage. As such, one of my goals is to open up these aspects of the field; another is to extend an invitation to mathematics in general. It is an unfortunate fact that today, at a time when mathematics and knowledge of mathematics are more important than ever, phrases like math avoidance and math anxiety are very much in the public vocabulary. Making a serious effort to heal these ills is an essential task. Thus the book also aims at an informed public, interested in making a new beginning in math. <p><p> For the 2nd edition, some of the historical material giving historical context has been expanded and numerous illustrations have been added. The main difference is however the inclusion of a large number of exercises with some suggestions for solutions.
Geometry: Seeing, Doing, Understanding
by Harold JacobsJacob's Geometry textbook has guided nearly one million students through the process of developing not just knowledge about Geometry, but a lasting understanding of Geometry concepts, principles, and application. Considered by many to be the authoritative Geometry text, Jacobs' math has solidified its reputation of preparing students for academic & career success and is a highly respected standard for teaching high school Geometry. Harold Jacobs' clear, engaging, conversational approach guides students through practical, real-world Geometry, allowing them to develop a true understanding of deductive reasoning, lines & angles, congruence, inequalities, quadrilaterals, area, triangles, circles, theorems, polygons, geometric solids, and more! <P><P><i>Advisory: Bookshare has learned that this book offers only partial accessibility. We have kept it in the collection because it is useful for some of our members. Benetech is actively working on projects to improve accessibility issues such as these.</i>
Geometry: Tutorial and Practical Problems (Idiot's Guides)
by Rebecca Dayton Sonal BhattCovering everything a student would encounter in a high school or college course, Idiot's Guides: Geometry explains concepts in the easiest possible manner. Content includes everything from the basics of geometry; reasoning and proof; triangles; quadrilaterals; area and volume; similarity, perpendicular and parallel lines; and much more. This all-new book integrates a practice problems section to reinforce lessons. In addition, a glossary of geometry terms, postulates, and theorems provides a quick reference to need-to-know information.
Geometry: from Isometries to Special Relativity (Undergraduate Texts in Mathematics)
by Nam-Hoon LeeThis textbook offers a geometric perspective on special relativity, bridging Euclidean space, hyperbolic space, and Einstein’s spacetime in one accessible, self-contained volume. Using tools tailored to undergraduates, the author explores Euclidean and non-Euclidean geometries, gradually building from intuitive to abstract spaces. By the end, readers will have encountered a range of topics, from isometries to the Lorentz–Minkowski plane, building an understanding of how geometry can be used to model special relativity. Beginning with intuitive spaces, such as the Euclidean plane and the sphere, a structure theorem for isometries is introduced that serves as a foundation for increasingly sophisticated topics, such as the hyperbolic plane and the Lorentz–Minkowski plane. By gradually introducing tools throughout, the author offers readers an accessible pathway to visualizing increasingly abstract geometric concepts. Numerous exercises are also included with selected solutions provided. Geometry: from Isometries to Special Relativity offers a unique approach to non-Euclidean geometries, culminating in a mathematical model for special relativity. The focus on isometries offers undergraduates an accessible progression from the intuitive to abstract; instructors will appreciate the complete instructor solutions manual available online. A background in elementary calculus is assumed.
Geomorphic Risk Reduction Using Geospatial Methods and Tools (Disaster Risk Reduction)
by Rajib Shaw Basanta Raj Adhikari Raju Sarkar Sunil SahaThis book explores the use of advanced geospatial techniques in geomorphic hazards modelling and risk reduction. It also compares the accuracy of traditional statistical methods and advanced machine learning methods and addresses the different ways to reduce the impact of geomorphic hazards.In recent years with the development of human infrastructures, geomorphic hazards are gradually increasing, which include landslides, flood and soil erosion, among others. They cause huge loss of human property and lives. Especially in mountainous, coastal, arid and semi-arid regions, these natural hazards are the main barriers for economic development. Furthermore, human pressure and specific human actions such as deforestation, inappropriate land use and farming have increased the danger of natural disasters and degraded the natural environment, making it more difficult for environmental planners and policymakers to develop appropriate long-term sustainability plans. The most challenging task is to develop a sophisticated approach for continuous inspection and resolution of environmental problems for researchers and scientists. However, in the past several decades, geospatial technology has undergone dramatic advances, opening up new opportunities for handling environmental challenges in a more comprehensive manner.With the help of geographic information system (GIS) tools, high and moderate resolution remote sensing information, such as visible imaging, synthetic aperture radar, global navigation satellite systems, light detection and ranging, Quickbird, Worldview 3, LiDAR, SPOT 5, Google Earth Engine and others deliver state-of-the-art investigations in the identification of multiple natural hazards. For a thorough examination, advanced computer approaches focusing on cutting-edge data processing, machine learning and deep learning may be employed. To detect and manage various geomorphic hazards and their impact, several models with a specific emphasis on natural resources and the environment may be created.
Georgia High School Mathematics 2
by William S. HadleyGeorgia Mathematics, a cognitive approach to learning math covers relations and functions, algebraic functions, logic, quadrilaterals, functions, and geometry. By Carnegie Learning