The Resource Backgrounds of arithmetic and geometry : an introduction, Radu Miron, Dan Branzei, (electronic resource/)
Backgrounds of arithmetic and geometry : an introduction, Radu Miron, Dan Branzei, (electronic resource/)
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The item Backgrounds of arithmetic and geometry : an introduction, Radu Miron, Dan Branzei, (electronic resource/) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Old Colony Library Network.This item is available to borrow from 2 library branches.
Resource Information
The item Backgrounds of arithmetic and geometry : an introduction, Radu Miron, Dan Branzei, (electronic resource/) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Old Colony Library Network.
This item is available to borrow from 2 library branches.
 Summary
 The book is an introduction to the foundations of mathematics. The use of the constructive method in arithmetic and the axiomatic method in geometry gives a unitary understanding of the backgrounds of geometry, of its development and of its organic link with the study of real numbers and algebraic structures
 Language
 eng
 Extent
 1 online resource (access may be restricted)
 Contents

 Ch. I. Elements of set theory. 1. Set algebra. 2. Binary relations and functions. 3. Cardinal numbers. 4. Ordinal numbers
 ch. II. Arithmetic. 1. The set N of natural numbers. 2. The set Z of integers. 3. Divisibility in the ring of integers. 4. The set of rational numbers. 5. The set R of real numbers. 6. The set C of complex numbers
 ch. III. Axiomatic theories. 1. Deductive systems. 2. The metatheory of an axiomatic theory. 3. Peanos axiomatics of arithmetic. 4. The relation of order on the Set N of natural numbers. 5. The metatheoretical analysis of the axiomatic system of natural numbers
 ch. IV. Algebraic bases of geometry. 1. Almost linear spaces. 2. Real linear spaces. 3. Real almost affine spaces. 4. Real affine spaces. 5. Euclidean spaces
 ch. V. The bases of Euclidean geometry. 1. Group I of axioms. 2. Group II of axioms. 3. The orientation of the straight line. 4. Group III of axioms. 5. Group IV of axioms. 6. Group V of axioms. 7. The metatheory of Hilberts axiomatics
 ch. VI. Birkhoffs axiomatic system. 1. The general framework. 2. Axioms and their principal consequences. 3. Elements of metatheory
 ch. VII. Geometrical transformations. 1. Generalities. 2. Isometries. 3. Symmetries. 4. Vectors. 5. Translations. 6. Rotations. 7. Homotheties. 8. Inversions
 ch. VIII. The Erlangen program. 1. Klein spaces. 2. Plane affine geometry. 3. The real projective plane. 4. Plane projective geometry. 5. The hyperbolic plane. 6. Complements of absolute geometry. 7. Plane hyperbolic geometry. 8. Hyperbolic trigonometry
 ch. IX. Bachmanns axiomatic system / Francise Rado. 1. The isometries of the absolute plane. 2. The embedding of the absolute plane into the group of its isometries. 3. The group plane. 4. The consequences of Bachmanns axioms. 5. The theorem of perpendiculars and its applications
 Label
 Backgrounds of arithmetic and geometry : an introduction
 Title
 Backgrounds of arithmetic and geometry
 Title remainder
 an introduction
 Statement of responsibility
 Radu Miron, Dan Branzei
 Language
 eng
 Summary
 The book is an introduction to the foundations of mathematics. The use of the constructive method in arithmetic and the axiomatic method in geometry gives a unitary understanding of the backgrounds of geometry, of its development and of its organic link with the study of real numbers and algebraic structures
 Cataloging source
 N$T
 Dewey number
 512.12
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA155
 LC item number
 .M57 1995eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Series in pure mathematics
 Series volume
 v. 23
 Label
 Backgrounds of arithmetic and geometry : an introduction, Radu Miron, Dan Branzei, (electronic resource/)
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references (pages 261282) and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Ch. I. Elements of set theory. 1. Set algebra. 2. Binary relations and functions. 3. Cardinal numbers. 4. Ordinal numbers  ch. II. Arithmetic. 1. The set N of natural numbers. 2. The set Z of integers. 3. Divisibility in the ring of integers. 4. The set of rational numbers. 5. The set R of real numbers. 6. The set C of complex numbers  ch. III. Axiomatic theories. 1. Deductive systems. 2. The metatheory of an axiomatic theory. 3. Peanos axiomatics of arithmetic. 4. The relation of order on the Set N of natural numbers. 5. The metatheoretical analysis of the axiomatic system of natural numbers  ch. IV. Algebraic bases of geometry. 1. Almost linear spaces. 2. Real linear spaces. 3. Real almost affine spaces. 4. Real affine spaces. 5. Euclidean spaces  ch. V. The bases of Euclidean geometry. 1. Group I of axioms. 2. Group II of axioms. 3. The orientation of the straight line. 4. Group III of axioms. 5. Group IV of axioms. 6. Group V of axioms. 7. The metatheory of Hilberts axiomatics  ch. VI. Birkhoffs axiomatic system. 1. The general framework. 2. Axioms and their principal consequences. 3. Elements of metatheory  ch. VII. Geometrical transformations. 1. Generalities. 2. Isometries. 3. Symmetries. 4. Vectors. 5. Translations. 6. Rotations. 7. Homotheties. 8. Inversions  ch. VIII. The Erlangen program. 1. Klein spaces. 2. Plane affine geometry. 3. The real projective plane. 4. Plane projective geometry. 5. The hyperbolic plane. 6. Complements of absolute geometry. 7. Plane hyperbolic geometry. 8. Hyperbolic trigonometry  ch. IX. Bachmanns axiomatic system / Francise Rado. 1. The isometries of the absolute plane. 2. The embedding of the absolute plane into the group of its isometries. 3. The group plane. 4. The consequences of Bachmanns axioms. 5. The theorem of perpendiculars and its applications
 Control code
 ocn828423925
 Dimensions
 unknown
 Extent
 1 online resource (access may be restricted)
 File format
 unknown
 Form of item
 online
 Governing access note
 Access restricted to subscribing institution
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Note
 eBooks on EBSCOhost
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 Label
 Backgrounds of arithmetic and geometry : an introduction, Radu Miron, Dan Branzei, (electronic resource/)
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references (pages 261282) and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Ch. I. Elements of set theory. 1. Set algebra. 2. Binary relations and functions. 3. Cardinal numbers. 4. Ordinal numbers  ch. II. Arithmetic. 1. The set N of natural numbers. 2. The set Z of integers. 3. Divisibility in the ring of integers. 4. The set of rational numbers. 5. The set R of real numbers. 6. The set C of complex numbers  ch. III. Axiomatic theories. 1. Deductive systems. 2. The metatheory of an axiomatic theory. 3. Peanos axiomatics of arithmetic. 4. The relation of order on the Set N of natural numbers. 5. The metatheoretical analysis of the axiomatic system of natural numbers  ch. IV. Algebraic bases of geometry. 1. Almost linear spaces. 2. Real linear spaces. 3. Real almost affine spaces. 4. Real affine spaces. 5. Euclidean spaces  ch. V. The bases of Euclidean geometry. 1. Group I of axioms. 2. Group II of axioms. 3. The orientation of the straight line. 4. Group III of axioms. 5. Group IV of axioms. 6. Group V of axioms. 7. The metatheory of Hilberts axiomatics  ch. VI. Birkhoffs axiomatic system. 1. The general framework. 2. Axioms and their principal consequences. 3. Elements of metatheory  ch. VII. Geometrical transformations. 1. Generalities. 2. Isometries. 3. Symmetries. 4. Vectors. 5. Translations. 6. Rotations. 7. Homotheties. 8. Inversions  ch. VIII. The Erlangen program. 1. Klein spaces. 2. Plane affine geometry. 3. The real projective plane. 4. Plane projective geometry. 5. The hyperbolic plane. 6. Complements of absolute geometry. 7. Plane hyperbolic geometry. 8. Hyperbolic trigonometry  ch. IX. Bachmanns axiomatic system / Francise Rado. 1. The isometries of the absolute plane. 2. The embedding of the absolute plane into the group of its isometries. 3. The group plane. 4. The consequences of Bachmanns axioms. 5. The theorem of perpendiculars and its applications
 Control code
 ocn828423925
 Dimensions
 unknown
 Extent
 1 online resource (access may be restricted)
 File format
 unknown
 Form of item
 online
 Governing access note
 Access restricted to subscribing institution
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Note
 eBooks on EBSCOhost
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
Subject
Genre
Member of
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