Discourses on algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Berlin [u.a.]
Springer
2003
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 276 S. Ill. |
| ISBN: | 9783540422532 3540422536 |
Staff View
MARC
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| 100 | 1 | |a Šafarevič, Igorʹ R. |d 1923-2017 |e Verfasser |0 (DE-588)119280337 |4 aut | |
| 240 | 1 | 0 | |a Izbrannye glavy algebry |
| 245 | 1 | 0 | |a Discourses on algebra |c Igor R. Shafarevich. Transl. from the Russian by William B. Everett |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2003 | |
| 300 | |a X, 276 S. |b Ill. | ||
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Record in the Search Index
| _version_ | 1804129421457620992 |
|---|---|
| adam_text | Contents
Preface VII
1. Integers (Topic: Numbers) 1
1. /2 Is Not Rational 1
2. The Irrationality of Other Square Roots 7
3. Decomposition into Prime Factors 15
2. Simplest Properties of Polynomials
(Topic: Polynomials) 27
4. Roots and the Divisibility of Polynomials 27
5. Multiple Roots and the Derivative 39
6. Binomial Formula 47
Supplement: Polynomials and Bernoulli Numbers 60
3. Finite Sets (Topic: Sets) 67
7. Sets and Subsets 67
8. Combinatorics 74
9. Set Algebra 86
10. The Language of Probability 96
Supplement: The Chebyshev Inequality 110
4. Prime Numbers (Topic: Numbers) 117
11. The Number of Prime Numbers is Infinite 117
12. Euler s Proof That the Number of Prime Numbers
is Infinite 121
13. Distribution of Prime Numbers 128
Supplement: The Chebyshev Inequality for w(n) 131
5. Real Numbers and Polynomials
(Topic: Numbers and Polynomials) 141
14. Axioms of the Real Numbers 141
15. Limits and Infinite Sums 146
16. Representation of Real Numbers as Decimal Fractions.... 152
17. Real Roots of Polynomials 158
Supplement: Sturm s Theorem 170
X Contents
6. Infinite Sets (Topic: Sets) 183
18. Equipotence 183
19. Continuum 190
20. Thin Sets 199
Supplement: Normal Numbers 212
7. Power Series (Topic: Polynomials) 223
21. Polynomials as Generating Functions 223
22. Power Series 233
23. Partitio Numerorum 243
Supplement 1: The Euler Pentagon Theorem 253
Supplement 2: Generating Function for
Bernoulli Numbers 264
Dates of Lives of Mathematicians Mentioned in the Text 271
Index 273
|
| any_adam_object | 1 |
| author | Šafarevič, Igorʹ R. 1923-2017 |
| author_GND | (DE-588)119280337 |
| author_facet | Šafarevič, Igorʹ R. 1923-2017 |
| author_role | aut |
| author_sort | Šafarevič, Igorʹ R. 1923-2017 |
| author_variant | i r š ir irš |
| building | Verbundindex |
| bvnumber | BV014670413 |
| classification_rvk | SK 110 SK 230 |
| ctrlnum | (OCoLC)469938777 (DE-599)BVBBV014670413 |
| 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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| id | DE-604.BV014670413 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:04:52Z |
| institution | BVB |
| isbn | 9783540422532 3540422536 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009953042 |
| oclc_num | 469938777 |
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| owner_facet | DE-20 DE-384 DE-M347 DE-19 DE-BY-UBM DE-703 DE-634 DE-11 DE-188 DE-29T |
| physical | X, 276 S. Ill. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Šafarevič, Igorʹ R. 1923-2017 Verfasser (DE-588)119280337 aut Izbrannye glavy algebry Discourses on algebra Igor R. Shafarevich. Transl. from the Russian by William B. Everett Berlin [u.a.] Springer 2003 X, 276 S. Ill. txt rdacontent n rdamedia nc rdacarrier Universitext Algèbre ram Algebra (DE-588)4001156-2 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Mengenlehre (DE-588)4074715-3 gnd rswk-swf Algebra (DE-588)4001156-2 s DE-604 Zahlentheorie (DE-588)4067277-3 s Mengenlehre (DE-588)4074715-3 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009953042&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Šafarevič, Igorʹ R. 1923-2017 Discourses on algebra Algèbre ram Algebra (DE-588)4001156-2 gnd Zahlentheorie (DE-588)4067277-3 gnd Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4067277-3 (DE-588)4074715-3 |
| title | Discourses on algebra |
| title_alt | Izbrannye glavy algebry |
| title_auth | Discourses on algebra |
| title_exact_search | Discourses on algebra |
| title_full | Discourses on algebra Igor R. Shafarevich. Transl. from the Russian by William B. Everett |
| title_fullStr | Discourses on algebra Igor R. Shafarevich. Transl. from the Russian by William B. Everett |
| title_full_unstemmed | Discourses on algebra Igor R. Shafarevich. Transl. from the Russian by William B. Everett |
| title_short | Discourses on algebra |
| title_sort | discourses on algebra |
| topic | Algèbre ram Algebra (DE-588)4001156-2 gnd Zahlentheorie (DE-588)4067277-3 gnd Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Algèbre Algebra Zahlentheorie Mengenlehre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009953042&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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