Numbers:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | German English |
| Veröffentlicht: |
New York [u.a.]
Springer
1995
|
| Ausgabe: | Corr. 3. print. |
| Schriftenreihe: | Graduate texts in mathematics
123 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XVIII, 391 S. graph. Darst. |
| ISBN: | 3540974970 0387974970 |
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Datensatz im Suchindex
| _version_ | 1804125652511621120 |
|---|---|
| adam_text | H.-D. EBBINGHAUS H. HERMES F. HIRZEBRUCH M. KOECHER K. MAINZER J.
NEUKIRCH A. PRESTEL R. REMMERT NUMBERS WITH AN INTRODUCTION BY K.
LAMOTKE TRANSLATED BY H.L.S. ORDE EDITED BY J.H. EWING WITH 24
ILLUSTRATIONS SPRINGER CONTENTS PREFACE TO THE ENGLISH EDITION V PREFACE
TO SECOND EDITION VII PREFACE TO FIRST EDITION IX INTRODUCTION, K.
LAMOTKE 1 PART A. FROM THE NATURAL NUMBERS, TO THE COMPLEX NUMBERS, TO
THE P-ADICS 7 CHAPTER 1. NATURAL NUMBERS, INTEGERS, AND RATIONAL
NUMBERS. K. MAINZER - 9 §1. HISTORICAL 9 1. EGYPTIANS AND BABYLONIANS.
2. GREECE. 3. INDO-ARABIC ARITHMETICAL PRATICE. 4. MODERN TIMES §2.
NATURAL NUMBERS 14 1. DEFINITION OF THE NATURAL NUMBERS. 2. THE
RECURSION THEOREM AND THE UNIQUENESS OF N. 3. ADDITION, MULTIPLICATION
AND ORDERING OF THE NATURAL NUMBERS. 4. PEANO S AXIOMS §3. THE INTEGERS
19 1. THE ADDITIVE GROUP Z. 2. THE INTEGRAL DOMAIN 7L. 3. THE ORDER
RELATION IN Z §4. THE RATIONAL NUMBERS 22 1. HISTORICAL. 2. THE FIELD Q.
3. THE ORDERING OF REFERENCES 23 CHAPTER 2. REAL NUMBERS. K . MAINZER
27 §1. HISTORICAL 27 1. HIPPASUS AND THE PENTAGON. 2. EUDOXUS AND THE
THEORY OF PROPORTION. 3. IRRATIONAL NUMBERS IN MODERN MATHEMATICS. 4.
THE FORMULATION OF MORE PRECISE DEFINITIONS IN THE NINETEENTH CENTURY
§2. DEDEKIND CUTS 36 1. THE SET R OF CUTS. 2. THE ORDER RELATION IN M.
XII CONTENTS 3. ADDITION IN E. 4. MULTIPLICATION IN M. §3. FUNDAMENTAL
SEQUENCES 39 1. HISTORICAL REMARKS. 2. CAUCHY S CRITERION FOR
CONVERGENCE. 3. THE RING OF FUNDAMENTAL SEQUENCES. 4. THE RESIDUE CLASS
FIELD F/N OF FUNDAMENTAL SEQUENCES MODULO THE NULL SEQUENCE. 5. THE
COMPLETELY ORDERED RESIDUE CLASS FIELD F/N §4. NESTING OF INTERVALS 43
1. HISTORICAL REMARKS. 2. NESTED INTERVALS AND COMPLETENESS §5.
AXIOMATIC DEFINITION OF REAL NUMBERS 46 1. THE NATURAL NUMBERS, THE
INTEGERS, AND THE RATIONAL NUMBERS IN THE REAL NUMBER FIELD. 2.
COMPLETENESS THEOREM. 3. EXISTENCE AND UNIQUENESS OF THE REAL NUMBERS
REFERENCES 51 CHAPTER 3. COMPLEX NUMBERS. R. REMMERT 55 §1. GENESIS OF
THE COMPLEX NUMBERS 56 1. CARDANO (1501-1576). 2. BOMBELLI (1526-1572).
3. DESCARTES (1596-1650), NEWTON (1643-1727) AND LEIBNIZ (1646-1716). 4.
EULER (1707-1783). 5. WALLIS (1616-1703), WESSEL (1745-1818) AND ARGAND
(1768-1822). 6. GAUSS (1777-1855). 7. CAUCHY (1789-1857). 8. HAMILTON
(1805-1865). 9. LATER DEVELOPMENTS §2. THE FIELD C 65 1. DEFINITION BY
PAIRS OF REAL NUMBERS. 2. THE IMAGINARY UNIT I. 3. GEOMETRIC
REPRESENTATION. 4. IMPOSSIBILITY OF ORDERING THE FIELD C. 5.
REPRESENTATION BY MEANS OF 2 X 2 REAL MATRICES §3. ALGEBRAIC PROPERTIES
OF THE FIELD C 71 1. THE CONJUGATION C-»C,ZI-+Z.2. THE FIELD
AUTOMORPHISMS OF C. 3. THE NATURAL SCALAR PRODUCT RE(U Z) AND EUCLIDEAN
LENGTH Z . 4. PRODUCT RULE AND THE TWO SQUARES THEOREM. 5. QUADRATIC
ROOTS AND QUADRATIC EQUATIONS. 6. SQUARE ROOTS AND NTH ROOTS §4.
GEOMETRIC PROPERTIES OF THE FIELD C 78 1. THE IDENTITY {W, Z) 2 + (IW,
Z) 2 = |H 2 I 2 I 2 - 2 - COSINE THEOREM AND THE TRIANGLE INEQUALITY. 3.
NUMBERS ON STRAIGHT LINES AND CIRCLES. CROSS-RATIO. 4. CYCLIC
QUADRILATERALS AND CROSS- RATIO. 5. PTOLEMY S THEOREM. 6. WALLACE S
LINE. §5. THE GROUPS O(C) ..AND 50(2) 85 1. DISTANCE PRESERVING MAPPINGS
OF C. 2. THE GROUP O(C). 3. THE GROUP SO(2) AND THE ISOMORPHISM S 1 -*
50(2). CONTENTS XIII 4. RATIONAL PARAMETRIZATION OF PROPERLY ORTHOGONAL
2X2 MATRICES. §6. POLAR COORDINATES AND NTH ROOTS 89 1. POLAR
COORDINATES. 2. MULTIPLICATION OF COMPLEX NUMBERS IN POLAR COORDINATES.
3. DE MOIVRE S FORMULA. 4. ROOTS IN UNITY. CHAPTER 4- THE FUNDAMENTAL
THEOREM OF ALGEBRA. R. REMMERT 97 §1. ON THE HISTORY OF THE FUNDAMENTAL
THEOREM 98 1. GIRARD (1595-1632) AND DESCARTES (1596-1650). 2. LEIBNIZ
(1646-1716). 3. EULER (1707-1783). 4. D ALEMBERT (1717-1783). 5.
LAGRANGE (1736-1813) AND LAPLACE (1749-1827). 6. GAUSS S CRITIQUE. 7.
GAUSS S FOUR PROOFS. 8. ARGAND (1768-1822) AND CAUCHY (1798-1857). 9.
THE FUNDAMENTAL THEOREM OF ALGEBRA: THEN AND NOW. 10. BRIEF BIOGRAPHICAL
NOTES ON CARL FRIEDRICH GAUSS §2. PROOF OF THE FUNDAMENTAL THEOREM BASED
ON ARGAND 111 1. CAUCHY S MINIMUM THEOREM. 2. PROOF OF THE FUNDAMENTAL
THEOREM. 3. PROOF OF ARGAND S INEQUALITY. 4. VARIANT OF THE PROOF. 5.
CONSTRUCTIVE PROOFS OF THE FUNDAMENTAL THEOREM. §3. APPLICATION OF THE
FUNDAMENTAL THEOREM 115 1. FACTORIZATION LEMMA. 2. FACTORIZATION OF
COMPLEX POLYNOMIALS. 3. FACTORIZATION OF REAL POLYNOMIALS. 4. EXISTENCE
OF EIGENVALUES. 5. PRIME POLYNOMIALS IN C[Z] AND R[X]. 6. UNIQUENESS OF
C. 7. THE PROSPECTS FOR HYPERCOMPLEX NUMBERS. APPENDIX. PROOF OF THE
FUNDAMENTAL THEOREM, AFTER LAPLACE 120 1. RESULTS USED. 2. PROOF. 3.
HISTORICAL NOTE CHAPTER 5. WHAT IS TT?R. REMMERT 123 §1. ON THE HISTORY
OF IR 124 1. DEFINITION BY MEASURING A CIRCLE. 2. PRACTICAL APPROXI-
MATIONS. 3. SYSTEMATIC APPROXIMATION. 4. ANALYTICAL FORMULAE. 5.
BALTZER S DEFINITION. 6. LANDAU AND HIS CONTEMPORARY CRITICS §2. THE
EXPONENTIAL HOMOMORPHISM EXP:C -+ C X 131 1. THE ADDITION THEOREM. 2.
ELEMENTARY CONSEQUENCES. 3. EPIMORPHISM THEOREM. 4. THE KERNEL OF THE
EXPONENTIAL HOMOMORPHISM. DEFINITION OF IT. APPENDIX. ELEMENTARY PROOF
OF LEMMA 3. §3. CLASSICAL CHARACTERIZATIONS OF N 137 1. DEFINITIONS OF
COSZ AND SINZ. 2. ADDITION THEOREM. XIV CONTENTS 3. THE NUMBER JT AND
THE ZEROS OF COS Z AND SINZ. 4. THE NUMBER IR AND THE PERIODS OF EXPZ,
COSZ AND SIN 2. 5. THE INEQUALITY SIN Y 0 FOR 0 Y JT AND THE
EQUATION E * = I. 6. THE POLAR COORDINATE EPIMORPHISM P:L * * S 1 . 7.
THE NUMBER T T AND THE CIRCUMFERENCE AND AREA OF A CIRCLE. §4. CLASSICAL
FORMULAE FOR JR 142 1. LEIBNIZ S SERIES FOR N. 2. VIETA S PRODUCT
FORMULA FOR JR. 3. EULER S PRODUCT FOR THE SINE AND WALLIS S PRODUCT FOR
JR. 4. EULER S SERIES FOR 7R 2 , TT 4 , .... 5. THE WEIERSTRASS
DEFINITION OF TT. 6. THE IRRATIONALITY OF T T AND ITS CONTINUED FRACTION
EXPANSION. 7. TRANSCENDENCE OF JR. CHAPTER 6. THE P-ADICNUMBERS. J .
NEUKIRCH 155 §1. NUMBERS AS FUNCTIONS 155 §2. THE ARITHMETIC
SIGNIFICANCE OF THE P-ADIC NUMBERS 162 §3. THE ANALYTICAL NATURE OF
P-ADIC NUMBERS 166 §4. THE P-ADIC NUMBERS 173 REFERENCES 177 PART B.
REAL DIVISION ALGEBRAS 179 INTRODUCTION, M. KOECHER, R. REMMERT 181
REPERTORY. BASIC CONCEPTS FROM THE THEORY OF ALGEBRAS, M. KOECHER, R.
REMMERT 183 1. REAL ALGEBRAS. 2. EXAMPLES OF REAL ALGEBRAS. 3.
SUBALGEBRAS AND ALGEBRA HOMOMORPHISMS. 4. DETERMINATION OF ALL ONE-
DIMENSIONAL ALGEBRAS. 5. DIVISION ALGEBRAS. 6. CONSTRUCTION OF ALGEBRAS
BY MEANS OF BASES CHAPTER 7. HAMILTON S QUATERNIONS. M. KOECHER, R.
REMMERT 189 INTRODUCTION 189 §1. THE QUATERNION ALGEBRA H ** 194 1. THE
ALGEBRA H OF THE QUATERNIONS. 2. THE MATRIX ALGEBRA U AND THE
ISOMORPHISM F:E-»W. 3. THE IMAGINARY SPACE OF H. 4. QUATERNION PRODUCT,
VECTOR PRODUCT AND SCALAR PRODUCT. 5. NONCOMMUTATIVITY OF M. THE CENTER.
6. THE ENDOMORPHISMS OF THE E-VECTOR SPACE H. 7. QUATERNION
MULTIPLICATION AND VECTOR ANALYSIS. 8. THE FUNDAMENTAL THEOREM OF
ALGEBRA FOR QUATERNIONS. §2. THE ALGEBRA H AS A EUCLIDEAN VECTOR SPACE
206 1. CONJUGATION AND THE LINEAR FORM ME. 2. PROPERTIES OF CONTENTS XV
THE SCALAR PRODUCT. 3. THE FOUR SQUARES THEOREM . 4. PRESERVATION OF
LENGTH, AND OF THE CONJUGACY RELATION UNDER AUTOMORPHISMS. 5. THE GROUP
S 3 OF QUATERNIONS OF LENGTH 1. 6. THE SPECIAL UNITARY GROUP SU(2) AND
THE ISOMORPHISM 5 3 -+ SU(2). §3. THE ORTHOGONAL GROUPS 0(3), 0(4) AND
QUATERNIONS 213 1. ORTHOGONAL GROUPS. 2. THE GROUP 0(H). CAYLEY S
THEOREM. 3. THE GROUP O(IMH). HAMILTON S THEOREM. 4. THE EPIMORPHISMS S
3 -» 50(3) AND S 3 X 5 3 -+ 5O(4). 5. AXIS OF ROTATION AND ANGLE OF
ROTATION. 6. EULER S PARAMETRIC REPRESENTATION OF 50(3). CHAPTER 8. THE
ISOMORPHISM THEOREMS OF FROBENIUS, HOPF AND GELFAND-MAZUR. M. KOECHER,
R. REMMERT 221 INTRODUCTION . 221 §1. HAMILTONIAN TRIPLES IN ALTERNATIVE
ALGEBRAS 223 1. THE PURELY IMAGINARY ELEMENTS OF AN ALGEBRA. 2.
HAMILTONIAN TRIPLE. 3. EXISTENCE OF HAMILTONIAN TRIPLES IN ALTERNATIVE
ALGEBRAS. 4. ALTERNATIVE ALGEBRAS. §2. FROBENIUS S THEOREM 227 1.
FROBENIUS S LEMMA. 2. EXAMPLES OF QUADRATIC ALGEBRAS. 3. QUATERNIONS
LEMMA. 4. THEOREM OF FROBENIUS (1877) §3. HOPF S THEOREM 230 1.
TOPOLOGIZATION OF REAL ALGEBRAS. 2. THE QUADRATIC MAPPING A * A, X I-*
X 2 . HOPF S LEMMA. 3. HOPF S THEOREM. 4. THE ORIGINAL PROOF BY HOPF. 5.
DESCRIPTION OF ALL 2-DIMENSIONAL ALGEBRAS WITH UNIT ELEMENT §4. THE
GELFAND-MAZUR THEOREM 238 1. BANACH ALGEBRAS. 2. THE BINOMIAL SERIES. 3.
LOCAL INVERSION THEOREM. 4. THE MULTIPLICATIVE GROUP A* . 5. THE
GELFAND-MAZUR THEOREM. 6. STRUCTURE OF NORMED ASSOCIATIVE DIVISION
ALGEBRAS. 7. THE SPECTRUM. 8. HISTORICAL REMARKS ON THE GELFAND-MAZUR
THEOREM. 9. FURTHER DEVELOPMENTS CHAPTER 9. CAYLEY NUMBERS OR
ALTERNATIVE DIVISION ALGEBRAS. M. KOECHER, R. REMMERT 249 §1.
ALTERNATIVE QUADRATIC ALGEBRAS 250 1. QUADRATIC ALGEBRAS. 2. THEOREM ON
THE BILINEAR FORM. 3. THEOREM ON THE CONJUGATION MAPPING. 4. THE TRIPLE
PRODUCT IDENTITY. 5.. THE EUCLIDEAN VECTOR SPACE A AND THE ORTHOGONAL
GROUP O(A) §2. EXISTENCE AND PROPERTIES OF OCTONIONS 256 1. CONSTRUCTION
OF THE QUADRATIC ALGEBRA OF OCTONIONS. XVI CONTENTS 2. THE IMAGINARY
SPACE, LINEAR FORM, BILINEAR FORM, AND CONJUGATION OF O. 3. 0 AS AN
ALTERNATIVE DIVISION ALGEBRA. 4. THE EIGHT-SQUARES THEOREM. 5. THE
EQUATION = H 0 HP. 6. MULTIPLICATION TABLE FOR §3. UNIQUENESS OF THE
CAYLEY ALGEBRA 261 1. DUPLICATION THEOREM. 2. UNIQUENESS OF THE CAYLEY
ALGEBRA (ZORN 1933). 3. DESCRIPTION OF BY ZORN S VECTOR MATRICES
CHAPTER 10. COMPOSITION ALGEBRAS. HURWITZ S THEOREM- VECTOR-PRODUCT
ALGEBRAS. M. KOECHER, R. REMMERT 265 §1. COMPOSITION ALGEBRAS 267 1.
HISTORICAL REMARKS ON THE THEORY OF COMPOSITION. 2. EXAMPLES. 3.
COMPOSITION ALGEBRAS WITH UNIT ELEMENT. 4. STRUCTURE THEOREM FOR
COMPOSITION ALGEBRAS WITH UNIT ELEMENT §2. MUTATION OF COMPOSITION
ALGEBRAS 272 1. MUTATION OF ALGEBRAS. 2. MUTATION THEOREM FOR FINITE-
DIMENSIONAL COMPOSITION ALGEBRAS. 3. HURWITZ S THEOREM (1898) §3.
VECTOR-PRODUCT ALGEBRAS 275 1. THE CONCEPT OF A VECTOR-PRODUCT ALGEBRA.
2. CONSTRUCTION OF VECTOR-PRO DUCT ALGEBRAS. 3. SPECIFICATION OF ALL
VECTOR- PRODUCT ALGEBRAS. 4. MALCEV-ALGEBRAS. 5. HISTORICAL REMARKS
CHAPTER 11. DIVISION ALGEBRAS AND TOPOLOGY. F. HIRZEBRUCH 281 §1. THE
DIMENSION OF A DIVISION ALGEBRA IS A POWER OF 2 281 1. ODD MAPPINGS AND
HOPF S THEOREM. 2. HOMOLOGY AND COHOMOLOGY WITH COEFFICIENTS IN F 2 . 3.
PROOF OF HOPF S THEOREM. 4. HISTORICAL REMARKS ON HOMOLOGY AND
COHOMOLOGY THEORY. 5. STIEFEL S CHARACTERISTIC HOMOLOGY CLASSES §2. THE
DIMENSION OF A DIVISION ALGEBRA IS 1, 2, 4 OR 8 290 1. THE MOD 2
INVARIANTS A(F). 2. PARALLELIZABILITY OF SPHERES AND DIVISION ALGEBRAS.
3. VECTOR BUNDLES. 4. WHITNEY S CHARACTERISTIC COHOMOLOGY CLASSES. 5.
THE RING OF VECTOR BUNDLES. 6. BOTT PERIODICITY. 7. CHARACTERISTIC
CLASSES OF DIRECT SUMS AND TENSOR PRODUCTS. 8. END OF THE PROOF. 9.
HISTORICAL REMARKS §3. ADDITIONAL REMARKS 299 1. DEFINITION OF THE. HOPF
INVARIANT. 2. THE HOPF CONSTRUCTION. 3. ADAMS S THEOREM ON THE HOPF
INVARIANTS. 4. SUMMARY. 5. ADAMS S THEOREM ABOUT VECTOR FIELDS ON
SPHERES CONTENTS XVII REFERENCES 301 PART C. INFINITESIMALS, GAMES, AND
SETS 303 CHAPTER 12. NONSTANDARD ANALYSIS. A. PRESTEL 305 §1.
INTRODUCTION 305 §2. THE NONSTANDARD NUMBER DOMAIN *E 309 1.
CONSTRUCTION OF *R. 2. PROPERTIES OF*! §3. FEATURES COMMON TO 1 AND *R
316 §4. DIFFERENTIAL AND INTEGRAL CALCULUS 321 1. DIFFERENTIATION. 2.
INTEGRATION EPILOGUE 326 REFERENCES 327 CHAPTER 13. NUMBERS AND GAMES.
H. HERMES 329 §1. INTRODUCTION 329 1. THE TRADITIONAL CONSTRUCTION OF
THE REAL NUMBERS. 2. THE CONWAY METHOD. 3. SYNOPSIS §2. CONWAY GAMES 331
1. DISCUSSION OF THE DEDEKIND POSTULATES. 2. CONWAY S MODIFICATION OF
THE DEDEKIND POSTULATES. 3. CONWAY GAMES §3. GAMES 334 1. THE CONCEPT OF
A GAME. 2. EXAMPLES OF GAMES. 3. AN INDUCTION PRINCIPLE FOR GAMES §4. ON
THE THEORY OF GAMES V 336 1. WINNING STRATEGIES. 2. POSITIVE AND
NEGATIVE GAMES. 3. A CLASSIFICATION OF GAMES §5. A PARTIALLY ORDERED
GROUP OF EQUIVALENT GAMES 339 1. THE NEGATIVE OF A GAME. 2. THE SUM OF
TWO GAMES. 3. ISOMORPHIC GAMES. 4. A PARTIAL ORDERING OF GAMES. 5.
EQUALITY OF GAMES §6. GAMES AND CONWAY GAMES 343 1. THE FUNDAMENTAL
MAPPINGS. 2. EXTENDING TO CONWAY GAMES THE DEFINITIONS OF THE RELATIONS
AND OPERATIONS DEFINED FOR GAMES. 3. EXAMPLES §7. CONWAY NUMBERS 346 1.
THE CONWAY POSTULATES (CL) AND (C2). 2. ELEMENTARY PROPERTIES OF THE
ORDER RELATION. 3. EXAMPLES §8. THE FIELD OF CONWAY NUMBERS 349 1. THE
ARITHMETIC OPERATIONS FOR NUMBERS. 2. EXAMPLES. 3. PROPERTIES OF THE
FIELD OF NUMBERS REFERENCES 353 XVIII CONTENTS CHAPTER 14- SET THEORY
AND MATHEMATICS. H.-D. EBBINGHAUS 355 INTRODUCTION 355 §1. SETS AND
MATHEMATICAL OBJECTS 358 1. INDIVIDUALS AND MORE COMPLEX OBJECTS. 2. SET
THEORETICAL DEFINITIONS OF MORE COMPLEX OBJECTS. 3. URELEMENTS AS SETS
§2. AXIOM SYSTEMS OF SET THEORY 363 1. THE RUSSELL ANTINOMY. 2.
ZERMELO S AND THE ZERMELO- FRAENKEL SET THEORY. 3. SOME CONSEQUENCES. 4.
SET THEORY WITH CLASSES §3. SOME METAMATHEMATICAL ASPECTS 372 1. THE VON
NEUMANN HIERARCHY. 2. THE AXIOM OF CHOICE. 3. INDEPENDENCE PROOFS
EPILOGUE 378 REFERENCES - 378 NAME INDEX 381 SUBJECT INDEX 387
PORTRAITS OF FAMOUS MATHEMATICIANS 393
|
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| era_facet | Geschichte |
| format | Book |
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| genre | 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content |
| genre_facet | Aufsatzsammlung |
| id | DE-604.BV011157804 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:04:58Z |
| institution | BVB |
| isbn | 3540974970 0387974970 |
| language | German English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007480311 |
| oclc_num | 24073081 |
| open_access_boolean | |
| owner | DE-703 DE-29T DE-19 DE-BY-UBM DE-521 DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-703 DE-29T DE-19 DE-BY-UBM DE-521 DE-355 DE-BY-UBR DE-11 |
| physical | XVIII, 391 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Zahlen Numbers H.-D. Ebbinghaus ... With an introd. by K. Lamotke. Transl. by H. L. S. Orde. Ed. by J. H. Ewing Corr. 3. print. New York [u.a.] Springer 1995 XVIII, 391 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 123 Literaturangaben Geschichte gnd rswk-swf Getaltheorie gtt Matematica (historia) larpcal Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlensystem (DE-588)4117700-9 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Zahlentheorie (DE-588)4067277-3 s DE-604 Zahlensystem (DE-588)4117700-9 s Geschichte z 2\p DE-604 Ebbinghaus, Heinz-Dieter 1939- Sonstige (DE-588)107046857 oth Ewing, John H. Sonstige oth Graduate texts in mathematics 123 (DE-604)BV000000067 123 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007480311&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Numbers Graduate texts in mathematics Getaltheorie gtt Matematica (historia) larpcal Number theory Zahlentheorie (DE-588)4067277-3 gnd Zahlensystem (DE-588)4117700-9 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4117700-9 (DE-588)4143413-4 |
| title | Numbers |
| title_alt | Zahlen |
| title_auth | Numbers |
| title_exact_search | Numbers |
| title_full | Numbers H.-D. Ebbinghaus ... With an introd. by K. Lamotke. Transl. by H. L. S. Orde. Ed. by J. H. Ewing |
| title_fullStr | Numbers H.-D. Ebbinghaus ... With an introd. by K. Lamotke. Transl. by H. L. S. Orde. Ed. by J. H. Ewing |
| title_full_unstemmed | Numbers H.-D. Ebbinghaus ... With an introd. by K. Lamotke. Transl. by H. L. S. Orde. Ed. by J. H. Ewing |
| title_short | Numbers |
| title_sort | numbers |
| topic | Getaltheorie gtt Matematica (historia) larpcal Number theory Zahlentheorie (DE-588)4067277-3 gnd Zahlensystem (DE-588)4117700-9 gnd |
| topic_facet | Getaltheorie Matematica (historia) Number theory Zahlentheorie Zahlensystem Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007480311&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | UT zahlen AT ebbinghausheinzdieter numbers AT ewingjohnh numbers |