Affine And Projective Geometry PDF Download
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| Author | : M. K. Bennett |
| Publisher | : John Wiley & Sons |
| Total Pages | : 251 |
| Release | : 2011-02-14 |
| Genre | : Mathematics |
| ISBN | : 1118030826 |
Download Affine and Projective Geometry Book in PDF, ePub and Kindle
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provetheorems in another * Provides opportunities for further investigation of mathematicsby various means, including historical references at the ends ofchapters Throughout, the text explores geometry's correlation to algebra inways that are meant to foster inquiry and develop mathematicalinsights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 | : Ernst Snapper |
| Publisher | : Elsevier |
| Total Pages | : 456 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483269337 |
Download Metric Affine Geometry Book in PDF, ePub and Kindle
Metric Affine Geometry focuses on linear algebra, which is the source for the axiom systems of all affine and projective geometries, both metric and nonmetric. This book is organized into three chapters. Chapter 1 discusses nonmetric affine geometry, while Chapter 2 reviews inner products of vector spaces. The metric affine geometry is treated in Chapter 3. This text specifically discusses the concrete model for affine space, dilations in terms of coordinates, parallelograms, and theorem of Desargues. The inner products in terms of coordinates and similarities of affine spaces are also elaborated. The prerequisites for this publication are a course in linear algebra and an elementary course in modern algebra that includes the concepts of group, normal subgroup, and quotient group. This monograph is suitable for students and aspiring geometry high school teachers.
| Author | : Albrecht Beutelspacher |
| Publisher | : Cambridge University Press |
| Total Pages | : 272 |
| Release | : 1998-01-29 |
| Genre | : Mathematics |
| ISBN | : 9780521483643 |
Download Projective Geometry Book in PDF, ePub and Kindle
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 | : Ivan Cheltsov |
| Publisher | : Springer |
| Total Pages | : 509 |
| Release | : 2014-06-11 |
| Genre | : Mathematics |
| ISBN | : 3319056816 |
Download Automorphisms in Birational and Affine Geometry Book in PDF, ePub and Kindle
The main focus of this volume is on the problem of describing the automorphism groups of affine and projective varieties, a classical subject in algebraic geometry where, in both cases, the automorphism group is often infinite dimensional. The collection covers a wide range of topics and is intended for researchers in the fields of classical algebraic geometry and birational geometry (Cremona groups) as well as affine geometry with an emphasis on algebraic group actions and automorphism groups. It presents original research and surveys and provides a valuable overview of the current state of the art in these topics. Bringing together specialists from projective, birational algebraic geometry and affine and complex algebraic geometry, including Mori theory and algebraic group actions, this book is the result of ensuing talks and discussions from the conference “Groups of Automorphisms in Birational and Affine Geometry” held in October 2012, at the CIRM, Levico Terme, Italy. The talks at the conference highlighted the close connections between the above-mentioned areas and promoted the exchange of knowledge and methods from adjacent fields.
| Author | : Reinhold Baer |
| Publisher | : Courier Corporation |
| Total Pages | : 338 |
| Release | : 2012-06-11 |
| Genre | : Mathematics |
| ISBN | : 0486154661 |
Download Linear Algebra and Projective Geometry Book in PDF, ePub and Kindle
Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. 1952 edition.
| Author | : Elmer G. Rees |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 119 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642617778 |
Download Notes on Geometry Book in PDF, ePub and Kindle
In recent years, geometry has played a lesser role in undergraduate courses than it has ever done. Nevertheless, it still plays a leading role in mathematics at a higher level. Its central role in the history of mathematics has never been disputed. It is important, therefore, to introduce some geometry into university syllabuses. There are several ways of doing this, it can be incorporated into existing courses that are primarily devoted to other topics, it can be taught at a first year level or it can be taught in higher level courses devoted to differential geometry or to more classical topics. These notes are intended to fill a rather obvious gap in the literature. It treats the classical topics of Euclidean, projective and hyperbolic geometry but uses the material commonly taught to undergraduates: linear algebra, group theory, metric spaces and complex analysis. The notes are based on a course whose aim was two fold, firstly, to introduce the students to some geometry and secondly to deepen their understanding of topics that they have already met. What is required from the earlier material is a familiarity with the main ideas, specific topics that are used are usually redone.
| Author | : Lars Kadison |
| Publisher | : Birkhäuser Boston |
| Total Pages | : 228 |
| Release | : 1996-01-26 |
| Genre | : Mathematics |
| ISBN | : 0817639004 |
Download Projective Geometry and Modern Algebra Book in PDF, ePub and Kindle
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 | : Katsumi Nomizu |
| Publisher | : Cambridge University Press |
| Total Pages | : 286 |
| Release | : 1994-11-10 |
| Genre | : Mathematics |
| ISBN | : 9780521441773 |
Download Affine Differential Geometry Book in PDF, ePub and Kindle
This is a self-contained and systematic account of affine differential geometry from a contemporary viewpoint, not only covering the classical theory, but also introducing the modern developments that have happened over the last decade. In order both to cover as much as possible and to keep the text of a reasonable size, the authors have concentrated on the significant features of the subject and their relationship and application to such areas as Riemannian, Euclidean, Lorentzian and projective differential geometry. In so doing, they also provide a modern introduction to the last. Some of the important geometric surfaces considered are illustrated by computer graphics, making this a physically and mathematically attractive book for all researchers in differential geometry, and for mathematical physicists seeking a quick entry into the subject.
| Author | : Johannes Ueberberg |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 259 |
| Release | : 2011-08-26 |
| Genre | : Mathematics |
| ISBN | : 3642209726 |
Download Foundations of Incidence Geometry Book in PDF, ePub and Kindle
Incidence geometry is a central part of modern mathematics that has an impressive tradition. The main topics of incidence geometry are projective and affine geometry and, in more recent times, the theory of buildings and polar spaces. Embedded into the modern view of diagram geometry, projective and affine geometry including the fundamental theorems, polar geometry including the Theorem of Buekenhout-Shult and the classification of quadratic sets are presented in this volume. Incidence geometry is developed along the lines of the fascinating work of Jacques Tits and Francis Buekenhout. The book is a clear and comprehensible introduction into a wonderful piece of mathematics. More than 200 figures make even complicated proofs accessible to the reader.
| Author | : Dirk J. Struik |
| Publisher | : Courier Corporation |
| Total Pages | : 304 |
| Release | : 2014-03-05 |
| Genre | : Mathematics |
| ISBN | : 0486173526 |
Download Lectures on Analytic and Projective Geometry Book in PDF, ePub and Kindle
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.
