Download or read book Geometry and analysis of projective spaces written by Charles E. Springer and published by . This book was released on 1986 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry and Analysis of Projective Spaces written by Charles Eugene Springer and published by . This book was released on 1964 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry and Analysis of Projective Spaces written by Donald G. Cooney and published by . This book was released on 1964 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Projective Geometry written by C. R. Wylie and published by Courier Corporation. This book was released on 2011-09-12 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include worked-through examples, introductions and summaries for each topic, and numerous theorems, proofs, and exercises that reinforce each chapter's precepts. Two helpful indexes conclude the text, along with answers to all odd-numbered exercises. In addition to its value to undergraduate students of mathematics, computer science, and secondary mathematics education, this volume provides an excellent reference for computer science professionals.
Download or read book Topics in the Geometry of Projective Space written by R. Lazarsfeld and published by Birkhäuser. This book was released on 2012-12-06 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topics discussed at the D. M. V. Seminar were the connectedness theorems of Fulton and Hansen, linear normality and subvarieties of small codimension in projective spaces. They are closely related; thus the connectedness theorem can be used to prove the inequality-part of Hartshorne's conjecture on linear normality, whereas Deligne's generalisation of the connectedness theorem leads to a refinement of Barth's results on the topology of varieties with small codimension in a projective space. The material concerning the connectedness theorem itself (including the highly surprising application to tamely ramified coverings of the projective plane) can be found in the paper by Fulton and the first author: W. Fulton, R. Lazarsfeld, Connectivity and its applications in algebraic geometry, Lecture Notes in Math. 862, p. 26-92 (Springer 1981). It was never intended to be written out in these notes. As to linear normality, the situation is different. The main point was an exposition of Zak's work, for most of which there is no reference but his letters. Thus it is appropriate to take an extended version of the content of the lectures as the central part of these notes.
Download or read book Perspectives on Projective Geometry written by Jürgen Richter-Gebert and published by Springer Science & Business Media. This book was released on 2011-02-04 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.
Download or read book Projective Geometry written by Albrecht Beutelspacher and published by Cambridge University Press. This book was released on 1998-01-29 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Projective geometry is not only a jewel of mathematics, but has also many applications in modern information and communication science. This book presents the foundations of classical projective and affine geometry as well as its important applications in coding theory and cryptography. It also could serve as a first acquaintance with diagram geometry. Written in clear and contemporary language with an entertaining style and around 200 exercises, examples and hints, this book is ideally suited to be used as a textbook for study in the classroom or on its own.
Download or read book Projective Duality and Homogeneous Spaces written by Evgueni A. Tevelev and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Projective duality is a very classical notion naturally arising in various areas of mathematics, such as algebraic and differential geometry, combinatorics, topology, analytical mechanics, and invariant theory, and the results in this field were until now scattered across the literature. Thus the appearance of a book specifically devoted to projective duality is a long-awaited and welcome event. Projective Duality and Homogeneous Spaces covers a vast and diverse range of topics in the field of dual varieties, ranging from differential geometry to Mori theory and from topology to the theory of algebras. It gives a very readable and thorough account and the presentation of the material is clear and convincing. For the most part of the book the only prerequisites are basic algebra and algebraic geometry. This book will be of great interest to graduate and postgraduate students as well as professional mathematicians working in algebra, geometry and analysis.
Download or read book Projective Geometry written by Elisabetta Fortuna and published by Springer. This book was released on 2016-12-17 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book starts with a concise but rigorous overview of the basic notions of projective geometry, using straightforward and modern language. The goal is not only to establish the notation and terminology used, but also to offer the reader a quick survey of the subject matter. In the second part, the book presents more than 200 solved problems, for many of which several alternative solutions are provided. The level of difficulty of the exercises varies considerably: they range from computations to harder problems of a more theoretical nature, up to some actual complements of the theory. The structure of the text allows the reader to use the solutions of the exercises both to master the basic notions and techniques and to further their knowledge of the subject, thus learning some classical results not covered in the first part of the book. The book addresses the needs of undergraduate and graduate students in the theoretical and applied sciences, and will especially benefit those readers with a solid grasp of elementary Linear Algebra.
Download or read book On the Geometry of Some Special Projective Varieties written by Francesco Russo and published by Springer. This book was released on 2016-01-25 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an introduction to both classical and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varieties embedded in projective spaces, their secant and tangent lines, the behavior of tangent linear spaces, the algebro-geometric and topological obstructions to their embedding into smaller projective spaces, and the classification of extremal cases. It also provides a solution of Hartshorne’s Conjecture on Complete Intersections for the class of quadratic manifolds and new short proofs of previously known results, using the modern tools of Mori Theory and of rationally connected manifolds. The new approach to some of the problems considered can be resumed in the principle that, instead of studying a special embedded manifold uniruled by lines, one passes to analyze the original geometrical property on the manifold of lines passing through a general point and contained in the manifold. Once this embedded manifold, usually of lower codimension, is classified, one tries to reconstruct the original manifold, following a principle appearing also in other areas of geometry such as projective differential geometry or complex geometry.
Download or read book Symmetry and Pattern in Projective Geometry written by Eric Lord and published by Springer Science & Business Media. This book was released on 2012-12-14 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry and Pattern in Projective Geometry is a self-contained study of projective geometry which compares and contrasts the analytic and axiomatic methods. The analytic approach is based on homogeneous coordinates, and brief introductions to Plücker coordinates and Grassmann coordinates are presented. This book looks carefully at linear, quadratic, cubic and quartic figures in two, three and higher dimensions. It deals at length with the extensions and consequences of basic theorems such as those of Pappus and Desargues. The emphasis throughout is on special configurations that have particularly interesting symmetry properties. The intricate and novel ideas of ‘Donald’ Coxeter, who is considered one of the great geometers of the twentieth century, are also discussed throughout the text. The book concludes with a useful analysis of finite geometries and a description of some of the remarkable configurations discovered by Coxeter. This book will be appreciated by mathematics students and those wishing to learn more about the subject of geometry. It makes accessible subjects and theorems which are often considered quite complicated and presents them in an easy-to-read and enjoyable manner.
Download or read book Oriented Projective Geometry written by Jorge Stolfi and published by Academic Press. This book was released on 2014-05-10 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Oriented Projective Geometry: A Framework for Geometric Computations proposes that oriented projective geometry is a better framework for geometric computations than classical projective geometry. The aim of the book is to stress the value of oriented projective geometry for practical computing and develop it as a rich, consistent, and effective tool for computer programmers. The monograph is comprised of 20 chapters. Chapter 1 gives a quick overview of classical and oriented projective geometry on the plane, and discusses their advantages and disadvantages as computational models. Chapters 2 through 7 define the canonical oriented projective spaces of arbitrary dimension, the operations of join and meet, and the concept of relative orientation. Chapter 8 defines projective maps, the space transformations that preserve incidence and orientation; these maps are used in chapter 9 to define abstract oriented projective spaces. Chapter 10 introduces the notion of projective duality. Chapters 11, 12, and 13 deal with projective functions, projective frames, relative coordinates, and cross-ratio. Chapter 14 tells about convexity in oriented projective spaces. Chapters 15, 16, and 17 show how the affine, Euclidean, and linear vector spaces can be emulated with the oriented projective space. Finally, chapters 18 through 20 discuss the computer representation and manipulation of lines, planes, and other subspaces. Computer scientists and programmers will find this text invaluable.
Download or read book Projective Geometry written by Pierre Samuel and published by Springer. This book was released on 1988-09-26 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to revive some of the beautiful results obtained by various geometers of the 19th century, and to give its readers a taste of concrete algebraic geometry. A good deal of space is devoted to cross-ratios, conics, quadrics, and various interesting curves and surfaces. The fundamentals of projective geometry are efficiently dealt with by using a modest amount of linear algebra. An axiomatic characterization of projective planes is also given. While the topology of projective spaces over real and complex fields is described, and while the geometry of the complex projective libe is applied to the study of circles and Möbius transformations, the book is not restricted to these fields. Interesting properties of projective spaces, conics, and quadrics over finite fields are also given. This book is the first volume in the Readings in Mathematics sub-series of the UTM. From the reviews: "...The book of P. Samuel thus fills a gap in the literature. It is a little jewel. Starting from a minimal background in algebra, he succeeds in 160 pages in giving a coherent exposition of all of projective geometry. ... one reads this book like a novel. " D.Lazard in Gazette des Mathématiciens#1
Download or read book Projective Geometry and Algebraic Structures written by R. J. Mihalek and published by Academic Press. This book was released on 2014-05-10 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Projective Geometry and Algebraic Structures focuses on the relationship of geometry and algebra, including affine and projective planes, isomorphism, and system of real numbers. The book first elaborates on euclidean, projective, and affine planes, including axioms for a projective plane, algebraic incidence bases, and self-dual axioms. The text then ponders on affine and projective planes, theorems of Desargues and Pappus, and coordination. Topics include algebraic systems and incidence bases, coordinatization theorem, finite projective planes, coordinates, deletion subgeometries, imbedding theorem, and isomorphism. The publication examines projectivities, harmonic quadruples, real projective plane, and projective spaces. Discussions focus on subspaces and dimension, intervals and complements, dual spaces, axioms for a projective space, ordered fields, completeness and the real numbers, real projective plane, and harmonic quadruples. The manuscript is a dependable reference for students and researchers interested in projective planes, system of real numbers, isomorphism, and subspaces and dimensions.
Download or read book Algebraic Curves and Riemann Surfaces written by Rick Miranda and published by American Mathematical Soc.. This book was released on 1995 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking centre stage. But the main examples come fromprojective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Dualtiy Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves andcohomology are introduced as a unifying device in the later chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one term of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-term course in complex variables or a year-long course in algebraic geometry.
Download or read book The Four Pillars of Geometry written by John Stillwell and published by Springer Science & Business Media. This book was released on 2005-08-09 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic Abundantly supplemented with figures and exercises
Download or read book A Vector Space Approach to Geometry written by Melvin Hausner and published by Courier Dover Publications. This book was released on 2018-10-17 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fascinating exploration of the correlation between geometry and linear algebra, this text also offers elementary explanations of the role of geometry in other branches of math and science. 1965 edition.
