Linear Geometry

Author: K. W. Gruenberg,A. J. Weir

Publisher: Springer Science & Business Media

ISBN: 1475741014

Category: Mathematics

Page: 199

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This is essentially a book on linear algebra. But the approach is somewhat unusual in that we emphasise throughout the geometric aspect of the subject. The material is suitable for a course on linear algebra for mathe matics majors at North American Universities in their junior or senior year and at British Universities in their second or third year. However, in view of the structure of undergraduate courses in the United States, it is very possible that, at many institutions, the text may be found more suitable at the beginning graduate level. The book has two aims: to provide a basic course in linear algebra up to, and including, modules over a principal ideal domain; and to explain in rigorous language the intuitively familiar concepts of euclidean, affine, and projective geometry and the relations between them. It is increasingly recognised that linear algebra should be approached from a geometric point of VIew. This applies not only to mathematics majors but also to mathematically-oriented natural scientists and engineers.

Linear geometry

Author: Karl W. Gruenberg,Alan J. Weir

Publisher: Springer

ISBN: N.A

Category: Mathematics

Page: 198

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Linear Geometry with Computer Graphics

Author: John Loustau,Meighan Dillon

Publisher: CRC Press

ISBN: 9780824788988

Category: Mathematics

Page: 458

View: 3892

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Stressing the interplay between theory and its practice, this text presents the construction of linear models that satisfy geometric postulate systems and develops geometric topics in computer graphics. It includes a computer graphics utility library of specialized subroutines on a 3.5 disk, designed for use with Turbo PASCAL 4.0 (or later version) - an effective means of computer-aided instruction for writing graphics problems.;Providing instructors with maximum flexibility that allows for the mathematics or computer graphics sections to be taught independently, this book: reviews linear algebra and notation, focusing on ideas of geometric significance that are often omitted in general purpose linear algebra courses; develops symmetric bilinear forms through classical results, including the inertia theorem, Witt's cancellation theorem and the unitary diagonalization of symmetric matrices; examines the Klein Erlanger programm, constructing models of geometries, and studying associated transformation groups; clarifies how to construct geometries from groups, encompassing topological notions; and introduces topics in computer graphics, including geometric modeling, surface rendering and transformation groups.

Linear Geometry

Author: Rafael Artzy

Publisher: N.A

ISBN: 9780486466279

Category: Mathematics

Page: 273

View: 4956

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Most linear algebra texts neglect geometry in general and linear geometry in particular. This text for advanced undergraduates and graduate students stresses the relationship between algebra and linear geometry. It begins by using the complex number plane as an introduction to a variety of transformations and their groups in the Euclidean plane, explaining algebraic concepts as they arise. A brief account of Poincaré's model of the hyperbolic plane and its transformation group follow. Succeeding chapters contain a systematic treatment of affine, Euclidean, and projective spaces over fields that emphasizes transformations and their groups, along with an outline of results involving other geometries. An examination of the foundations of geometry starts from rudimentary projective incidence planes, then gradually adjoins axioms and develops various non-Desarguesian, Desarguesian, and Pappian planes, their corresponding algebraic structures, and their collineation groups. The axioms of order, continuity, and congruence make their appearance and lead to Euclidean and non-Euclidean planes. Lists of books for suggested further reading follow the third and fourth chapters, and the Appendix provides lists of notations, axioms, and transformation groups.

Foundations of Convex Geometry

Author: W. A. Coppel

Publisher: Cambridge University Press

ISBN: 9780521639705

Category: Mathematics

Page: 222

View: 9814

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This book on the foundations of Euclidean geometry aims to present the subject from the point of view of present day mathematics, taking advantage of all the developments since the appearance of Hilbert's classic work. Here real affine space is characterised by a small number of axioms involving points and line segments making the treatment self-contained and thorough, many results being established under weaker hypotheses than usual. The treatment should be totally accessible for final year undergraduates and graduate students, and can also serve as an introduction to other areas of mathematics such as matroids and antimatroids, combinatorial convexity, the theory of polytopes, projective geometry and functional analysis.

Linear Algebra, Geometry and Transformation

Author: Bruce Solomon

Publisher: CRC Press

ISBN: 1482299305

Category: Mathematics

Page: 474

View: 669

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The Essentials of a First Linear Algebra Course and More Linear Algebra, Geometry and Transformation provides students with a solid geometric grasp of linear transformations. It stresses the linear case of the inverse function and rank theorems and gives a careful geometric treatment of the spectral theorem. An Engaging Treatment of the Interplay among Algebra, Geometry, and Mappings The text starts with basic questions about images and pre-images of mappings, injectivity, surjectivity, and distortion. In the process of answering these questions in the linear setting, the book covers all the standard topics for a first course on linear algebra, including linear systems, vector geometry, matrix algebra, subspaces, independence, dimension, orthogonality, eigenvectors, and diagonalization. A Smooth Transition to the Conceptual Realm of Higher Mathematics This book guides students on a journey from computational mathematics to conceptual reasoning. It takes them from simple "identity verification" proofs to constructive and contrapositive arguments. It will prepare them for future studies in algebra, multivariable calculus, and the fields that use them.

Modern Structural Analysis

Modelling Process and Guidance

Author: Iain A. MacLeod,Iain Alasdair MacLeod

Publisher: Thomas Telford

ISBN: 9780727732798

Category: Technology & Engineering

Page: 191

View: 1596

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In the past, the main difficulties in structural analysis lay in the solution process, now model development is a fundamental issue. This work sets out the basic principles for structural analysis modelling and discusses basic processes for using modern software.

Geometry of Linear 2-normed Spaces

Author: Raymond W. Freese,Yeol Je Cho

Publisher: Nova Publishers

ISBN: 9781590330197

Category: Mathematics

Page: 301

View: 2121

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To encourage researchers in mathematics to apply metric geometry, functional analysis, and topology, Freese and Cho, who are not identified, introduce 2-metric spaces and linear 2 normed spaces. They survey recent results on the relations between linear 2-normed spaces and normed linear spaces, the completion of linear 2-normed spaced, 2-inner spaces, 2-inner product spaces, strict convexity, strict 2-convexity, uniform convexity, isometry conditions, orthogonal relations, quadratic forms, and other topics. c. Book News Inc.

Linear Algebra and Geometry

Author: P. K. Suetin,Alexandra I. Kostrikin,Yu I Manin

Publisher: CRC Press

ISBN: 9789056990497

Category: Mathematics

Page: 320

View: 5801

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This advanced textbook on linear algebra and geometry covers a wide range of classical and modern topics. Differing from existing textbooks in approach, the work illustrates the many-sided applications and connections of linear algebra with functional analysis, quantum mechanics and algebraic and differential geometry. The subjects covered in some detail include normed linear spaces, functions of linear operators, the basic structures of quantum mechanics and an introduction to linear programming. Also discussed are Kahler's metic, the theory of Hilbert polynomials, and projective and affine geometries. Unusual in its extensive use of applications in physics to clarify each topic, this comprehensice volume should be of particular interest to advanced undergraduates and graduates in mathematics and physics, and to lecturers in linear and multilinear algebra, linear programming and quantum mechanics.

Linear Algebra Through Geometry

Author: Thomas Banchoff,John Wermer

Publisher: Springer Science & Business Media

ISBN: 1461243904

Category: Mathematics

Page: 308

View: 6464

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This book introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space.

Comprehensive Mathematics for Computer Scientists 1

Sets and Numbers, Graphs and Algebra, Logic and Machines, Linear Geometry

Author: Guerino Mazzola,Gérard Milmeister,Jody Weissmann

Publisher: Springer Science & Business Media

ISBN: 3540368744

Category: Computers

Page: 388

View: 6602

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Contains all the mathematics that computer scientists need to know in one place.

Additive Number Theory: Inverse Problems and the Geometry of Sumsets

Author: Melvyn B. Nathanson

Publisher: Springer Science & Business Media

ISBN: 9780387946559

Category: Mathematics

Page: 296

View: 9022

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Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer H -> 2, and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. By contrast, in an inverse problem, one starts with a sumset hA, and attempts to describe the structure of the underlying set A. In recent years there has been ramrkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plünnecke, Vosper, and others. This volume includes their results, and culminates with an elegant proof by Ruzsa of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an n-dimensional arithmetic progression.

Linear Algebra and Geometry

A Second Course

Author: Irving Kaplansky

Publisher: Courier Corporation

ISBN: 9780486432335

Category: Mathematics

Page: 143

View: 9509

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The author of this text seeks to remedy a common failing in teaching algebra: the neglect of related instruction in geometry. Focusing on inner product spaces, orthogonal similarity, and elements of geometry, this volume is illustrated with an abundance of examples, exercises, and proofs and is suitable for both undergraduate and graduate courses. 1974 edition.

Linear Algebra and Projective Geometry

Author: Reinhold Baer

Publisher: Courier Corporation

ISBN: 0486154661

Category: Mathematics

Page: 336

View: 9568

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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.

Linear Functions and Matrix Theory

Author: Bill Jacob

Publisher: Springer Science & Business Media

ISBN: 3642592775

Category: Mathematics

Page: 330

View: 7754

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Courses that study vectors and elementary matrix theory and introduce linear transformations have proliferated greatly in recent years. Most of these courses are taught at the undergraduate level as part of, or adjacent to, the second-year calculus sequence. Although many students will ultimately find the material in these courses more valuable than calculus, they often experience a class that consists mostly of learning to implement a series of computational algorithms. The objective of this text is to bring a different vision to this course, including many of the key elements called for in current mathematics-teaching reform efforts. Three of the main components of this current effort are the following: 1. Mathematical ideas should be introduced in meaningful contexts, with formal definitions and procedures developed after a clear understanding of practical situations has been achieved. 2. Every topic should be treated from different perspectives, including the numerical, geometric, and symbolic viewpoints. 3. The important ideas need to be visited repeatedly throughout the term, with students' understanding deepening each time. This text was written with these three objectives in mind. The first two chapters deal with situations requiring linear functions (at times, locally linear functions) or linear ideas in geometry for their understanding. These situations provide the context in which the formal mathematics is developed, and they are returned to with increasing sophistication throughout the text.