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Introduction To Projective Geometry And Modern Algebra
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Book Synopsis Projective Geometry and Modern Algebra by : Lars Kadison
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.
Book Synopsis The Four Pillars of Geometry by : John Stillwell
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
Book Synopsis Introduction to Algebraic Geometry by : Steven Dale Cutkosky
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.
Book Synopsis Lectures in Projective Geometry by : A. Seidenberg
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 :Jürgen Richter-Gebert Publisher :Springer Science & Business Media ISBN 13 :3642172865 Total Pages :573 pages Book Rating :4.6/5 (421 download)
Book Synopsis Perspectives on Projective Geometry by : Jürgen Richter-Gebert
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.
Book Synopsis Lectures on Curves, Surfaces and Projective Varieties by : Mauro Beltrametti
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.
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.
Book Synopsis Algebraic Geometry by : Robin Hartshorne
Download or read book Algebraic Geometry written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Book Synopsis Algebraic Projective Geometry by : John Greenlees Semple
Download or read book Algebraic Projective Geometry written by John Greenlees Semple and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reissued in the Oxford Classic Texts in the Physical Sciences series, this book provides a clear and systematic introduction to projective geometry, building on concepts from linear algebra.
Book Synopsis Projective Geometry by : Albrecht Beutelspacher
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.
Book Synopsis A Modern View of Geometry by : Leonard M. Blumenthal
Download or read book A Modern View of Geometry written by Leonard M. Blumenthal and published by Courier Dover Publications. This book was released on 2017-04-19 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elegant exposition of postulation geometry of planes offers rigorous, lucid treatment of coordination of affine and projective planes, set theory, propositional calculus, affine planes with Desargues and Pappus properties, more. 1961 edition.
Book Synopsis Foundations of Projective Geometry by : Robin Hartshorne
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.
Book Synopsis Modern Algebra (Abstract Algebra) by :
Download or read book Modern Algebra (Abstract Algebra) written by and published by Krishna Prakashan Media. This book was released on with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Classical Algebraic Geometry by : Igor V. Dolgachev
Download or read book Classical Algebraic Geometry written by Igor V. Dolgachev and published by Cambridge University Press. This book was released on 2012-08-16 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.
Book Synopsis An Introduction to Finite Projective Planes by : Abraham Adrian Albert
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.
Book Synopsis The Real Projective Plane by : H.S.M. Coxeter
Download or read book The Real Projective Plane written by H.S.M. Coxeter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Along with many small improvements, this revised edition contains van Yzeren's new proof of Pascal's theorem (§1.7) and, in Chapter 2, an improved treatment of order and sense. The Sylvester-Gallai theorem, instead of being introduced as a curiosity, is now used as an essential step in the theory of harmonic separation (§3.34). This makes the logi cal development self-contained: the footnotes involving the References (pp. 214-216) are for comparison with earlier treatments, and to give credit where it is due, not to fill gaps in the argument. H.S.M.C. November 1992 v Preface to the Second Edition Why should one study the real plane? To this question, put by those who advocate the complex plane, or geometry over a general field, I would reply that the real plane is an easy first step. Most of the prop erties are closely analogous, and the real field has the advantage of intuitive accessibility. Moreover, real geometry is exactly what is needed for the projective approach to non· Euclidean geometry. Instead of introducing the affine and Euclidean metrics as in Chapters 8 and 9, we could just as well take the locus of 'points at infinity' to be a conic, or replace the absolute involution by an absolute polarity.
Book Synopsis Lectures on Analytic and Projective Geometry by : Dirk J. Struik
Download or read book Lectures on Analytic and Projective Geometry written by Dirk J. Struik and published by Courier Corporation. This book was released on 2011-10-24 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate text develops the geometry of plane and space, leading up to conics and quadrics, within the context of metrical, affine, and projective transformations. 1953 edition.
