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Geometry of the Unit Sphere in Polynomial Spaces (SpringerBriefs in Mathematics)
by Jesús Ferrer Domingo García Manuel Maestre Gustavo A. Muñoz Daniel L. Rodríguez Juan B. SeoaneThis brief presents a global perspective on the geometry of spaces of polynomials. Its particular focus is on polynomial spaces of dimension 3, providing, in that case, a graphical representation of the unit ball. Also, the extreme points in the unit ball of several polynomial spaces are characterized. Finally, a number of applications to obtain sharp classical polynomial inequalities are presented.The study performed is the first ever complete account on the geometry of the unit ball of polynomial spaces. Nowadays there are hundreds of research papers on this topic and our work gathers the state of the art of the main and/or relevant results up to now. This book is intended for a broad audience, including undergraduate and graduate students, junior and senior researchers and it also serves as a source book for consultation. In addition to that, we made this work visually attractive by including in it over 50 original figures in order to help in the understanding of all the results and techniques included in the book.
Geometry (Ohio)
by Cindy J. Boyd Jerry Cummins Carol E. MalloyA 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)
by Ron Larson Laurie Boswell Timothy D. KanoldThis 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 Over Nonclosed Fields
by Fedor Bogomolov Brendan Hassett Yuri TschinkelBased on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and outlined applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higher-dimensional generalizations. One main recent insight the books covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail.
Geometry Student Text
by Steven P. Demme Miriam HomerGeometry Math U See Student Text. This three-holed binder copy is designed to encourage students to be confident problem solvers who understand and enjoy math. Students will learn their math facts, rules, and formulas, but most importantly, they will be able to apply this knowledge in everyday life.
Geometry Student Workbook
by Ags SecondaryGo beyond the basics of Geometry and investigate the world of planes and solids. Chapter openers and colorful photos invite exploration of geometric solids, triangles, the Pythagorean Theorem, quadratic equations, length, area, and volume. Throughout, Geometry presents short, lively lessons, and illustrated examples. Features include Estimation Activities, Algebra Review, and Geometry in Your Life. Calculator Practice exercises make use of the special features of graphing calculators. Best of all, your child will learn to apply geometry to situations in their own life.
Geometry Super Review (Super Reviews Study Guides)
by The Editors of REAGet all you need to know with Super Reviews! Each Super Review is packed with in-depth, student-friendly topic reviews that fully explain everything about the subject. The Geometry Super Review includes a review of the methods of proof, points, lines, planes, angles, triangles, quadrilaterals, geometric inequalities, and geometric proportions and similarity. Advanced topics include the study of circles, polygons, coordinate geometry, and solid geometry. Take the Super Review quizzes to see how much you've learned - and where you need more study. Makes an excellent study aid and textbook companion. Great for self-study! DETAILS - From cover to cover, each in-depth topic review is easy-to-follow and easy-to-grasp - perfect when preparing for homework, quizzes, and exams! - Review questions after each topic that highlight and reinforce key areas and concepts - Student-friendly language for easy reading and comprehension - Includes quizzes that test your understanding of the subject
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 Texas: Interactive Student Edition (Volume #2)
by Timothy D. Kanold Edward B. Burger Juli K. DixonVolume 2 of the first edition of this geometry textbook for students.
Geometry Through History: Euclidean, Hyperbolic, And Projective Geometries
by Meighan I. DillonPresented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises.For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the field.
Geometry to Go: A Mathematics Handbook
by Great Source Education GroupGeometry to Go is a reference book. The book covers logic and proof, basic elements of geometry, polygons, measurements, similarity, congruence, transformations, circles, solids, problem solving and non-Euclidean geometry. Also includes an almanac with math prefixes and suffixes, study tips, guidelines for using geometry software, a graphing calculator, test-taking strategies, and tables.
The Geometry Toolbox for Graphics and Modeling
by Gerald Farin Dianne HansfordThe Geometry Toolbox takes a novel and particularly visual approach to teaching the basic concepts of two- and three-dimensional geometry. It explains the geometry essential for today's computer modeling, computer graphics, and animation systems. While the basic theory is completely covered, the emphasis of the book is not on abstract proofs but rather on examples and algorithms. The Geometry Toolbox is the ideal text for professionals who want to get acquainted with the latest geometric tools. The chapters on basic curves and surfaces form an ideal stepping stone into the world of graphics and modeling. It is also a unique textbook for a modern introduction to linear algebra and matrix theory.
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, 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 Workbook For Dummies
by Mark RyanDon't be a square! Strengthen your geometrical skills Lots of students need extra practice to master geometry. Thankfully, there's Geometry Workbook For Dummies. Packed with hundreds of practice problems and easy-to-understand concept explanations, this book takes a hands-on approach to showing you the geometric ropes. Inside, you'll find a helpful review of basic terms and concepts, so you can hit the ground running when you get to the more advanced stuff. In classic Dummies style, this workbook offers easy ways to understand theorems, proofs, and other geometry fundamentals. Figure out congruent triangles, wrap your mind around angle-arc theorems, connect radii and chords, and get smart about all the core concepts of geometry. Work through hundreds of practice problems to solidify your geometry know-how Clear up any confusion with easy-to-understand explanations of all key concepts Get tips for avoiding common mistakes and improving your test scores For students or parents looking for a hands-on approach to learning geometry, this is the perfect Dummies guide. It's great resource all on its own, or pair it with Geometry For Dummies for even more effective book learning.
Geomorphic Risk Reduction Using Geospatial Methods and Tools (Disaster Risk Reduction)
by Raju Sarkar Sunil Saha Basanta Raj Adhikari Rajib ShawThis 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
Georgia Mathematics 1: Student Text
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
Georgia Middle School Mathematics Course 2
by Ron Larson Laurie Boswell Lee Stiff Timothy KanoldNIMAC-sourced textbook
Geospatial Algebraic Computations
by Joseph L. Awange Béla PalánczImproved geospatial instrumentation and technology such as in laser scanning has now resulted in millions of data being collected, e. g. , point clouds. It is in realization that such huge amount of data requires efficient and robust mathematical solutions that this third edition of the book extends the second edition by introducing three new chapters: Robust parameter estimation, Multiobjective optimization and Symbolic regression. Furthermore, the linear homotopy chapter is expanded to include nonlinear homotopy. These disciplines are discussed first in the theoretical part of the book before illustrating their geospatial applications in the applications chapters where numerous numerical examples are presented. The renewed electronic supplement contains these new theoretical and practical topics, with the corresponding Mathematica statements and functions supporting their computations introduced and applied. This third edition is renamed in light of these technological advancements.