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/)

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
Creator
Contributor
Subject
Genre
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
Member of
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/)
Link
http://library.quincycollege.edu:2048/login?url=http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=532581
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 261-282) 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/)
Link
http://library.quincycollege.edu:2048/login?url=http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=532581
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 261-282) 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

Library Locations

    • Massasoit Community College Brockton CampusBorrow it
      1 Massasoit Blvd., Brockton, MA, 02301, US
      42.07562679999999 -70.99027629999999
    • Quincy College Library Borrow it
      1250 Hancock St. 3rd Fl Rm#347, Quincy, MA, 02169, US
      42.2513682 -70.9962875
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