Holdings: Backgrounds of arithmetic and geometry

Backgrounds of arithmetic and geometry: an introduction

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Bibliographic Details
Main Authors:	Miron, Radu (Author), Brânzei, Dan 1942- (Author)
Format:	Book
Language:	English
Published:	Singapore [u.a.] World Scientific 1995
Series:	Series in pure mathematics 23
Online Access:	Inhaltsverzeichnis
Physical Description:	XI, 286 S.
ISBN:	9810222106

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MARC


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adam_text	SERIES IN PURE MATHEMATICS - VOLUME 23 BACKGROUNDS OF ARITHMETIC AND GEOMETRY AN INTRODUCTION RADU MIRON DAN BRANZEI UNIVERSITY AL. I. CUZA ROMANIA WORLD SCIENTIFIC SINGAPORE * NEW JERSEY * LONDON * HONG KONG CONTENTS PREFACE CHAPTER I. ELEMENTS OF SET THEORY 1 §1. SET ALGEBRA 1 §2. BINARY RELATIONS AND FUNCTIONS 4 §3. CARDINAL NUMBERS 6 §4. ORDINAL NUMBERS 12 EXERCISES 17 CHAPTER II. ARITHMETIC 18 §1. THE SET N OF NATURAL NUMBERS 18 §2. THE SET Z OF INTEGERS 22 §3. DIVISIBILITY IN THE RING OF INTEGERS 26 §4. THE SET OF RATIONAL NUMBERS 32 §5. THE SET R OF REAL NUMBERS 37 §6. THE SET C OF COMPLEX NUMBERS 44 EXERCISES 46 CHAPTER III. AXIOMATIC THEORIES 48 §1. DEDUCTIVE SYSTEMS 48 §2. THE METATHEORY OF AN AXIOMATIC THEORY 50 §3. PEANO S AXIOMATICS OF ARITHMETIC 53 §4. THE RELATION OF ORDER ON THE SET N OF NATURAL NUMBERS 58 §5. THE METATHEORETICAL ANALYSIS OF THE AXIOMATIC SYSTEM OF NATURAL NUMBERS 59 EXERCISES 61 CHAPTER IV. ALGEBRAIC BASES OF GEOMETRY 63 §1. ALMOST LINEAR SPACES 63 §2. REAL LINEAR SPACES 69 §3. REAL ALMOST AFFINE SPACES 74 §4. REAL AFFINE SPACES 79 §5. EUCLIDEAN SPACES 82 PROBLEM 86 IX X CONTENTS CHAPTER V. THE BASES OF EUCLIDEAN GEOMETRY 87 §1. GROUP I OF AXIOMS 88 §2. GROUP II OF AXIOMS 90 §3. THE ORIENTATION OF THE STRAIGHT LINE 92 §4. GROUP III OF AXIOMS 98 §5. GROUP IV OF AXIOMS 105 §6. GROUP V OF AXIOMS ILL §7. THE METATHEORY OF HILBERT S AXIOMATICS 114 EXERCISES 120 CHAPTER VI. BIRKHOFF S AXIOMATIC SYSTEM 122 §1. THE GENERAL FRAMEWORK 122 §2. AXIOMS AND THEIR PRINCIPAL CONSEQUENCES 123 §3. ELEMENTS OF METATHEORY 131 PROBLEM 135 CHAPTER VII. GEOMETRICAL TRANSFORMATIONS 139 §1. GENERALITIES 139 §2. ISOMETRIES 140 §3. SYMMETRIES 142 §4. VECTORS 144 §5. TRANSLATIONS 149 §6. ROTATIONS 151 §7. HOMOTHETIES 156 §8. INVERSIONS 161 PROBLEMS 165 CHAPTER VM. THE ERLANGEN PROGRAM 167 §1. KLEIN SPACES 167 §2. PLANE AFFINE GEOMETRY 169 §3. THE REAL PROJECTIVE PLANE 174 §4. PLANE PROJECTIVE GEOMETRY 183 §5. THE HYPERBOLIC PLANE 190 §6. COMPLEMENTS OF ABSOLUTE GEOMETRY 204 CONTENTS XI §7. PLANE HYPERBOLIC GEOMETRY 215 §8. HYPERBOLIC TRIGONOMETRY 227 PROBLEM 235 CHAPTER IX. BACHMANN S AXIOMATIC SYSTEM (FRANCISE RAD6) 236 §1. THE ISOMETRIES OF THE ABSOLUTE PLANE 236 §2. THE EMBEDDING OF THE ABSOLUTE PLANE INTO THE GROUP OF ITS ISOMETRIES 240 §3. THE GROUP PLANE 241 §4. THE CONSEQUENCES OF BACHMANN S AXIOMS 244 §5. THE THEOREM OF PERPENDICULARS AND ITS APPLICATIONS 248 HINTS 253 BIBLIOGRAPHY 261 INDEX 283
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spelling	Miron, Radu Verfasser aut Backgrounds of arithmetic and geometry an introduction Radu Miron ; Dan Branzei Singapore [u.a.] World Scientific 1995 XI, 286 S. txt rdacontent n rdamedia nc rdacarrier Series in pure mathematics 23 Brânzei, Dan 1942- Verfasser (DE-588)1058929755 aut Series in pure mathematics 23 (DE-604)BV000016845 23 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019642259&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Miron, Radu Brânzei, Dan 1942- Backgrounds of arithmetic and geometry an introduction Series in pure mathematics
title	Backgrounds of arithmetic and geometry an introduction
title_auth	Backgrounds of arithmetic and geometry an introduction
title_exact_search	Backgrounds of arithmetic and geometry an introduction
title_full	Backgrounds of arithmetic and geometry an introduction Radu Miron ; Dan Branzei
title_fullStr	Backgrounds of arithmetic and geometry an introduction Radu Miron ; Dan Branzei
title_full_unstemmed	Backgrounds of arithmetic and geometry an introduction Radu Miron ; Dan Branzei
title_short	Backgrounds of arithmetic and geometry
title_sort	backgrounds of arithmetic and geometry an introduction
title_sub	an introduction
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019642259&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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