The algebraic foundations of mathematics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass.
Addison-Wesley
1963
|
| Schriftenreihe: | Addison-Wesley ser.in introductory college mathematics.
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X,486 S. |
Internformat
MARC
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| 100 | 1 | |a Beaumont, Ross Allen |d 1914-1996 |e Verfasser |0 (DE-588)11770783X |4 aut | |
| 245 | 1 | 0 | |a The algebraic foundations of mathematics |c Ross Allen Beaumont ; Richard S. Pierce* |
| 264 | 1 | |a Reading, Mass. |b Addison-Wesley |c 1963 | |
| 300 | |a X,486 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Addison-Wesley ser.in introductory college mathematics. | |
| 650 | 4 | |a Algebra abstracta | |
| 650 | 7 | |a Algebra |2 gtt | |
| 650 | 4 | |a Algèbre | |
| 650 | 7 | |a Algèbre |2 ram | |
| 650 | 7 | |a Ensembles, Théorie des |2 ram | |
| 650 | 7 | |a Matematica |2 larpcal | |
| 650 | 7 | |a Teoria Dos Numeros |2 larpcal | |
| 650 | 4 | |a Algebra | |
| 650 | 0 | 7 | |a Lösung |g Mathematik |0 (DE-588)4120678-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lösung |g Mathematik |0 (DE-588)4120678-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Pierce, Richard Scott |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003969611&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804120496569057280 |
|---|---|
| adam_text | CONTENTS
Introduction 1
Chapter 1. Set Theory
1 1 Sets 11
1 2 The cardinal number of a set 18
1 3 The construction of sets from given sets 24
1 4 The algebra of sets 30
1 5 Further algebra of sets. General rules of operation .... 36
*l 6 Measures on sets 41
*l 7 Properties and examples of measures 48
Chapter 2. Mathematical Induction
2 1 Proof by induction 53
2 2 The binomial theorem 60
2 3 Generalizations of the induction principle 67
*2 4 The technique of induction 71
2 5 Inductive properties of the natural numbers 75
*2 6 Inductive definitions 79
Chapter 3. The Natural Numbers
3 1 The definition of numbers 82
3 2 Operations with the natural numbers 88
3 3 The ordering of the natural numbers 95
Chapter 4. The Integers
4 1 Construction of the integers 99
4 2 Rings 106
4 3 Generalized sums and products 114
4 4 Integral domains 121
4 5 The ordering of the integers 125
4 6 Properties of order 129
Chapter 5. Elementary Number Theory
5 1 The division algorithm 135
5 2 Greatest common divisor 144
5 3 The fundamental theorem of arithmetic 153
*5 4 More about primes 159
*5 5 Applications of the fundamental theorem of arithmetic . . . 165
5 6 Congruences 175
5 7 Linear congruences 181
*5 8 The theorems of Fermat and Euler 189
Chapter 6. The Rational Numbers
6 1 Basic properties of the rational numbers 200
6 2 Fields 204
6 3 The characteristic of integral domains and fields 209
ix
X CONTENTS
6 4 Equivalence relations 213
6 5 The construction of Q 218
Chapter 7. The Real Numbers
7 1 Development of the real numbers 224
7 2 The coordinate line 229
7 3 Dedekind cuts 235
7 4 Construction of the real numbers 238
7 5 The completeness of the real numbers 248
7 6 Properties of complete ordered fields 253
*7 7 Infinite sequences 258
*7 8 Infinite series 263
*7â€â€
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| any_adam_object | 1 |
| author | Beaumont, Ross Allen 1914-1996 Pierce, Richard Scott |
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| author_facet | Beaumont, Ross Allen 1914-1996 Pierce, Richard Scott |
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| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 110 |
| ctrlnum | (OCoLC)307391 (DE-599)BVBBV006280860 |
| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:43:01Z |
| institution | BVB |
| language | English |
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| physical | X,486 S. |
| psigel | HUB-ZB011200708 |
| publishDate | 1963 |
| publishDateSearch | 1963 |
| publishDateSort | 1963 |
| publisher | Addison-Wesley |
| record_format | marc |
| series2 | Addison-Wesley ser.in introductory college mathematics. |
| spelling | Beaumont, Ross Allen 1914-1996 Verfasser (DE-588)11770783X aut The algebraic foundations of mathematics Ross Allen Beaumont ; Richard S. Pierce* Reading, Mass. Addison-Wesley 1963 X,486 S. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley ser.in introductory college mathematics. Algebra abstracta Algebra gtt Algèbre Algèbre ram Ensembles, Théorie des ram Matematica larpcal Teoria Dos Numeros larpcal Algebra Lösung Mathematik (DE-588)4120678-2 gnd rswk-swf Lösung Mathematik (DE-588)4120678-2 s DE-604 Pierce, Richard Scott Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003969611&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beaumont, Ross Allen 1914-1996 Pierce, Richard Scott The algebraic foundations of mathematics Algebra abstracta Algebra gtt Algèbre Algèbre ram Ensembles, Théorie des ram Matematica larpcal Teoria Dos Numeros larpcal Algebra Lösung Mathematik (DE-588)4120678-2 gnd |
| subject_GND | (DE-588)4120678-2 |
| title | The algebraic foundations of mathematics |
| title_auth | The algebraic foundations of mathematics |
| title_exact_search | The algebraic foundations of mathematics |
| title_full | The algebraic foundations of mathematics Ross Allen Beaumont ; Richard S. Pierce* |
| title_fullStr | The algebraic foundations of mathematics Ross Allen Beaumont ; Richard S. Pierce* |
| title_full_unstemmed | The algebraic foundations of mathematics Ross Allen Beaumont ; Richard S. Pierce* |
| title_short | The algebraic foundations of mathematics |
| title_sort | the algebraic foundations of mathematics |
| topic | Algebra abstracta Algebra gtt Algèbre Algèbre ram Ensembles, Théorie des ram Matematica larpcal Teoria Dos Numeros larpcal Algebra Lösung Mathematik (DE-588)4120678-2 gnd |
| topic_facet | Algebra abstracta Algebra Algèbre Ensembles, Théorie des Matematica Teoria Dos Numeros Lösung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003969611&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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