Backgrounds of arithmetic and geometry: an introduction
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1995
|
| Schriftenreihe: | Series in pure mathematics
23 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 286 S. |
| ISBN: | 9810222106 |
Internformat
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Datensatz im Suchindex
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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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| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:24:52Z |
| institution | BVB |
| isbn | 9810222106 |
| language | English |
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| physical | XI, 286 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
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| publisher | World Scientific |
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| series | Series in pure mathematics |
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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 |
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