The Resource An Algebraic Approach to Geometry : Geometric Trilogy II, by Francis Borceux, (electronic resource)
An Algebraic Approach to Geometry : Geometric Trilogy II, by Francis Borceux, (electronic resource)
Resource Information
The item An Algebraic Approach to Geometry : Geometric Trilogy II, by Francis Borceux, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item An Algebraic Approach to Geometry : Geometric Trilogy II, by Francis Borceux, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 This is a unified treatment of the various algebraic approaches to geometric spaces. The study of algebraic curves in the complex projective plane is the natural link between linear geometry at an undergraduate level and algebraic geometry at a graduate level, and it is also an important topic in geometric applications, such as cryptography. 380 years ago, the work of Fermat and Descartes led us to study geometric problems using coordinates and equations. Today, this is the most popular way of handling geometrical problems. Linear algebra provides an efficient tool for studying all the first degree (lines, planes, ...) and second degree (ellipses, hyperboloids, ...) geometric figures, in the affine, the Euclidean, the Hermitian and the projective contexts. But recent applications of mathematics, like cryptography, need these notions not only in real or complex cases, but also in more general settings, like in spaces constructed on finite fields. And of course, why not also turn our attention to geometric figures of higher degrees? Besides all the linear aspects of geometry in their most general setting, this book also describes useful algebraic tools for studying curves of arbitrary degree and investigates results as advanced as the Bezout theorem, the Cramer paradox, topological group of a cubic, rational curves etc. Hence the book is of interest for all those who have to teach or study linear geometry: affine, Euclidean, Hermitian, projective; it is also of great interest to those who do not want to restrict themselves to the undergraduate level of geometric figures of degree one or two
 Language
 eng
 Extent
 XVII, 430 pages 117 illustrations
 Contents

 Introduction
 Preface
 1.The Birth of Analytic Geometry
 2.Affine Geometry
 3.More on Real Affine Spaces
 4.Euclidean Geometry
 5.Hermitian Spaces
 6.Projective Geometry
 7.Algebraic Curves
 Appendices:A.Polynomials Over a Field
 B.Polynomials in Several Variables
 C.Homogenous Polynomials
 D.Resultants
 E.Symmetric Polynomials
 F.Complex Numbers
 G.Quadratic Forms
 H.Dual Spaces
 Index
 Bibliography
 Isbn
 9783319017334
 Label
 An Algebraic Approach to Geometry : Geometric Trilogy II
 Title
 An Algebraic Approach to Geometry
 Title remainder
 Geometric Trilogy II
 Statement of responsibility
 by Francis Borceux
 Language
 eng
 Summary
 This is a unified treatment of the various algebraic approaches to geometric spaces. The study of algebraic curves in the complex projective plane is the natural link between linear geometry at an undergraduate level and algebraic geometry at a graduate level, and it is also an important topic in geometric applications, such as cryptography. 380 years ago, the work of Fermat and Descartes led us to study geometric problems using coordinates and equations. Today, this is the most popular way of handling geometrical problems. Linear algebra provides an efficient tool for studying all the first degree (lines, planes, ...) and second degree (ellipses, hyperboloids, ...) geometric figures, in the affine, the Euclidean, the Hermitian and the projective contexts. But recent applications of mathematics, like cryptography, need these notions not only in real or complex cases, but also in more general settings, like in spaces constructed on finite fields. And of course, why not also turn our attention to geometric figures of higher degrees? Besides all the linear aspects of geometry in their most general setting, this book also describes useful algebraic tools for studying curves of arbitrary degree and investigates results as advanced as the Bezout theorem, the Cramer paradox, topological group of a cubic, rational curves etc. Hence the book is of interest for all those who have to teach or study linear geometry: affine, Euclidean, Hermitian, projective; it is also of great interest to those who do not want to restrict themselves to the undergraduate level of geometric figures of degree one or two
 Cataloging source
 ITFiEUI
 http://library.link/vocab/creatorDate
 1948
 http://library.link/vocab/creatorName
 Borceux, Francis
 Image bit depth
 0
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink (Online service)
 Series statement
 Springer eBooks
 http://library.link/vocab/subjectName

 Mathematics
 Geometry
 Label
 An Algebraic Approach to Geometry : Geometric Trilogy II, by Francis Borceux, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 Introduction  Preface  1.The Birth of Analytic Geometry  2.Affine Geometry  3.More on Real Affine Spaces  4.Euclidean Geometry  5.Hermitian Spaces  6.Projective Geometry  7.Algebraic Curves  Appendices:A.Polynomials Over a Field  B.Polynomials in Several Variables  C.Homogenous Polynomials  D.Resultants  E.Symmetric Polynomials  F.Complex Numbers  G.Quadratic Forms  H.Dual Spaces  Index  Bibliography
 Control code
 9783319017334
 Dimensions
 unknown
 Extent
 XVII, 430 pages 117 illustrations
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319017334
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319017334
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)876298552
 Label
 An Algebraic Approach to Geometry : Geometric Trilogy II, by Francis Borceux, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 Introduction  Preface  1.The Birth of Analytic Geometry  2.Affine Geometry  3.More on Real Affine Spaces  4.Euclidean Geometry  5.Hermitian Spaces  6.Projective Geometry  7.Algebraic Curves  Appendices:A.Polynomials Over a Field  B.Polynomials in Several Variables  C.Homogenous Polynomials  D.Resultants  E.Symmetric Polynomials  F.Complex Numbers  G.Quadratic Forms  H.Dual Spaces  Index  Bibliography
 Control code
 9783319017334
 Dimensions
 unknown
 Extent
 XVII, 430 pages 117 illustrations
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319017334
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319017334
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)876298552
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/AnAlgebraicApproachtoGeometryGeometric/EnGk8gFxbA/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/AnAlgebraicApproachtoGeometryGeometric/EnGk8gFxbA/">An Algebraic Approach to Geometry : Geometric Trilogy II, by Francis Borceux, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>