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Author : Robert A. Rosenbaum
Publisher :
ISBN 13 :
Total Pages : 360 pages
Book Rating : 4.F/5 ( download)
Download or read book Introduction to Projective Geometry and Modern Algebra written by Robert A. Rosenbaum and published by . This book was released on 1963 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lars Kadison
Publisher : Birkhäuser Boston
ISBN 13 : 0817639004
Total Pages : 228 pages
Book Rating : 4.8/5 (176 download)
Download or read book Projective Geometry and Modern Algebra written by Lars Kadison and published by Birkhäuser Boston. This book was released on 1996-01-26 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The techniques and concepts of modern algebra are introduced for their natural role in the study of projectile geometry; groups appear as automorphism groups of configurations, division rings appear in the study of Desargues' theorem and the study of the independence of the seven axioms given for projectile geometry.
Author : Lars Kadison
Publisher : Springer Science & Business Media
ISBN 13 :
Total Pages : 236 pages
Book Rating : 4.:/5 (318 download)
Download or read book Projective Geometry and Modern Algebra written by Lars Kadison and published by Springer Science & Business Media. This book was released on 1996-01-26 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook for a one-semester undergraduate course introducing modern algebra in the framework of geometric applications; also suitable for self-study by readers a background in linear algebra and the calculus of several variables. Assumes to knowledge of abstract algebra. Annotation copyright by Book News, Inc., Portland, OR
Author : Rey Casse
Publisher : OUP Oxford
ISBN 13 : 0191538361
Total Pages : 212 pages
Book Rating : 4.1/5 (915 download)
Download or read book Projective Geometry written by Rey Casse and published by OUP Oxford. This book was released on 2006-08-03 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lucid and accessible text provides an introductory guide to projective geometry, an area of mathematics concerned with the properties and invariants of geometric figures under projection. Including numerous worked examples and exercises throughout, the book covers axiomatic geometry, field planes and PG(r, F), coordinatising a projective plane, non-Desarguesian planes, conics and quadrics in PG(3, F). Assuming familiarity with linear algebra, elementary group theory, partial differentiation and finite fields, as well as some elementary coordinate geometry, this text is ideal for 3rd and 4th year mathematics undergraduates.
Author : John Stillwell
Publisher : Springer Science & Business Media
ISBN 13 : 0387255303
Total Pages : 240 pages
Book Rating : 4.3/5 (872 download)
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
Author : Erik V. Bohn
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (959 download)
Download or read book Introduction to Projective Geometry and Modern Algebra written by Erik V. Bohn and published by . This book was released on 1963 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jürgen Richter-Gebert
Publisher : Springer Science & Business Media
ISBN 13 : 3642172865
Total Pages : 573 pages
Book Rating : 4.6/5 (421 download)
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.
Author : Steven Dale Cutkosky
Publisher : American Mathematical Soc.
ISBN 13 : 1470435187
Total Pages : 498 pages
Book Rating : 4.4/5 (74 download)
Download or read book Introduction to Algebraic Geometry written by Steven Dale Cutkosky and published by American Mathematical Soc.. This book was released on 2018-06-01 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters. With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.
Author : R. J. Mihalek
Publisher : Academic Press
ISBN 13 : 148326520X
Total Pages : 233 pages
Book Rating : 4.4/5 (832 download)
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.
Author : Abraham Adrian Albert
Publisher : Courier Corporation
ISBN 13 : 0486789942
Total Pages : 116 pages
Book Rating : 4.4/5 (867 download)
Download or read book An Introduction to Finite Projective Planes written by Abraham Adrian Albert and published by Courier Corporation. This book was released on 2015-02-18 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Text for both beginning and advanced undergraduate and graduate students covers finite planes, field planes, coordinates in an arbitrary plane, central collineations and the little Desargues' property, the fundamental theorem, and non-Desarguesian planes. 1968 edition.
Author : Mauro Beltrametti
Publisher : European Mathematical Society
ISBN 13 : 9783037190647
Total Pages : 512 pages
Book Rating : 4.1/5 (96 download)
Download or read book Lectures on Curves, Surfaces and Projective Varieties written by Mauro Beltrametti and published by European Mathematical Society. This book was released on 2009 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces, algebraic curves (with special emphasis on rational curves), linear series on algebraic curves, Cremona transformations, rational surfaces, and notable examples of special varieties like the Segre, Grassmann, and Veronese varieties. An integral part and special feature of the presentation is the inclusion of many exercises, not easy to find in the literature and almost all with complete solutions. The text is aimed at students in the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses at the advanced undergraduate or beginning graduate level, as well as interesting topics for a senior thesis. The prerequisites have been deliberately limited to basic elements of projective geometry and abstract algebra. Thus, for example, some knowledge of the geometry of subspaces and properties of fields is assumed. The book will be welcomed by teachers and students of algebraic geometry who are seeking a clear and panoramic path leading from the basic facts about linear subspaces, conics and quadrics to a systematic discussion of classical algebraic varieties and the tools needed to study them. The text provides a solid foundation for approaching more advanced and abstract literature.
Author : A. Seidenberg
Publisher : Courier Corporation
ISBN 13 : 0486154734
Total Pages : 244 pages
Book Rating : 4.4/5 (861 download)
Download or read book Lectures in Projective Geometry written by A. Seidenberg and published by Courier Corporation. This book was released on 2012-06-14 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: An ideal text for undergraduate courses, this volume takes an axiomatic approach that covers relations between the basic theorems, conics, coordinate systems and linear transformations, quadric surfaces, and the Jordan canonical form. 1962 edition.
Author : Albrecht Beutelspacher
Publisher : Cambridge University Press
ISBN 13 : 9780521483643
Total Pages : 272 pages
Book Rating : 4.4/5 (836 download)
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.
Author : M. K. Bennett
Publisher : John Wiley & Sons
ISBN 13 : 1118030826
Total Pages : 251 pages
Book Rating : 4.1/5 (18 download)
Download or read book Affine and Projective Geometry written by M. K. Bennett and published by John Wiley & Sons. This book was released on 2011-02-14 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: An important new perspective on AFFINE AND PROJECTIVEGEOMETRY This innovative book treats math majors and math education studentsto a fresh look at affine and projective geometry from algebraic,synthetic, and lattice theoretic points of view. Affine and Projective Geometry comes complete with ninetyillustrations, and numerous examples and exercises, coveringmaterial for two semesters of upper-level undergraduatemathematics. The first part of the book deals with the correlationbetween synthetic geometry and linear algebra. In the second part,geometry is used to introduce lattice theory, and the bookculminates with the fundamental theorem of projectivegeometry. While emphasizing affine geometry and its basis in Euclideanconcepts, the book: * Builds an appreciation of the geometric nature of linear algebra * Expands students' understanding of abstract algebra with itsnontraditional, geometry-driven approach * Demonstrates how one branch of mathematics can be used to provetheorems in another * Provides opportunities for further investigation of mathematicsby various means, including historical references at the ends ofchapters Throughout, the text explores geometry's correlation to algebra inways that are meant to foster inquiry and develop mathematicalinsights whether or not one has a background in algebra. Theinsight offered is particularly important for prospective secondaryteachers who must major in the subject they teach to fulfill thelicensing requirements of many states. Affine and ProjectiveGeometry's broad scope and its communicative tone make it an idealchoice for all students and professionals who would like to furthertheir understanding of things mathematical.
Author : Eric Lord
Publisher : Springer Science & Business Media
ISBN 13 : 144714631X
Total Pages : 190 pages
Book Rating : 4.4/5 (471 download)
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.
Author : Robin Hartshorne
Publisher : Ishi Press
ISBN 13 : 9784871878371
Total Pages : 190 pages
Book Rating : 4.8/5 (783 download)
Download or read book Foundations of Projective Geometry written by Robin Hartshorne and published by Ishi Press. This book was released on 2009 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first geometrical properties of a projective nature were discovered in the third century by Pappus of Alexandria. Filippo Brunelleschi (1404-1472) started investigating the geometry of perspective in 1425. Johannes Kepler (1571-1630) and Gerard Desargues (1591-1661) independently developed the pivotal concept of the "point at infinity." Desargues developed an alternative way of constructing perspective drawings by generalizing the use of vanishing points to include the case when these are infinitely far away. He made Euclidean geometry, where parallel lines are truly parallel, into a special case of an all-encompassing geometric system. Desargues's study on conic sections drew the attention of 16-years old Blaise Pascal and helped him formulate Pascal's theorem. The works of Gaspard Monge at the end of 18th and beginning of 19th century were important for the subsequent development of projective geometry. The work of Desargues was ignored until Michel Chasles chanced upon a handwritten copy in 1845. Meanwhile, Jean-Victor Poncelet had published the foundational treatise on projective geometry in 1822. Poncelet separated the projective properties of objects in individual class and establishing a relationship between metric and projective properties. The non-Euclidean geometries discovered shortly thereafter were eventually demonstrated to have models, such as the Klein model of hyperbolic space, relating to projective geometry.
Author : Christian Peskine
Publisher :
ISBN 13 :
Total Pages : 454 pages
Book Rating : 4.:/5 (48 download)
Download or read book An Algebraic Introduction to Complex Projective Geometry written by Christian Peskine and published by . This book was released on 1843 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this introduction to commutative algebra, the author choses a route that leads the reader through the essential ideas, without getting embroiled in technicalities. He takes the reader quickly to the fundamentals of complex projective geometry, requiring only a basic knowledge of linear and multilinear algebra and some elementary group theory. The author divides the book into three parts. In the first, he develops the general theory of noetherian rings and modules. He includes a certain amount of homological algebra, and he emphasizes rings and modules of fractions as preparation for working with sheaves. In the second part, he discusses polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalization lemma and Hilbert's Nullstellensatz, the author introduces affine complex schemes and their morphisms; he then proves Zariski's main theorem and Chevalley's semi-continuity theorem. Finally, the author's detailed study of Weil and Cartier divisors provides a solid background for modern intersection theory. This is an excellent textbook for those who seek an efficient and rapid introduction to the geometric applications of commutative algebra.
