Concrete mathematics: a foundation for computer science
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass. [u.a.]
Addison-Wesley
1994
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 604 - 656 Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XIII, 657 S. graph. Darst. |
| ISBN: | 9780201558029 0201558025 |
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Record in the Search Index
| _version_ | 1804124044312707072 |
|---|---|
| adam_text | Contents
1 Recurrent Problems 1
1.1 The Tower of Hanoi 1
1.2 Lines in the Plane 4
1.3 The Josephus Problem 8
Exercises 17
2 Sums 21
2.1 Notation 21
2.2 Sums and Recurrences 25
2.3 Manipulation of Sums 30
2.4 Multiple Sums 34
2.5 General Methods 41
2.6 Finite and Infinite Calculus 47
2.7 Infinite Sums 56
Exercises 62
3 Integer Functions 67
3.1 Floors and Ceilings 67
3.2 Floor/Ceiling Applications 70
3.3 Floor/Ceiling Recurrences 78
3.4 mod : The Binary Operation 81
3.5 Floor/Ceiling Sums 86
Exercises 95
4 Number Theory ^__ 102
4.1 Divisibility 102
4.2 Primes 105
4.3 Prime Examples 107
4.4 Factorial Factors 111
4.5 Relative Primality 115
4.6 mod : The Congruence Relation 123
4.7 Independent Residues 126
4.8 Additional Applications 129
4.9 Phi and Mu 133
Exercises 144
5 Binomial Coefficients 153
5.1 Basic Identities 153
5.2 Basic Practice 172
5.3 Tricks of the Trade 186
CONTENTS xiii
5.4 Generating Functions 196
5.5 Hypergeometric Functions 204
5.6 Hypergeometric Transformations 216
5.7 Partial Hypergeometric Sums 223
5.8 Mechanical Summation 229
Exercises 242
6 Special Numbers 257
6.1 Stirling Numbers 257
6.2 Eulerian Numbers 267
6.3 Harmonic Numbers 272
6.4 Harmonic Summation 279
6.5 Bernoulli Numbers 283
6.6 Fibonacci Numbers 290
6.7 Continuants 301
Exercises 309
7 Generating Functions 320
7.1 Domino Theory and Change 320
7.2 Basic Maneuvers 331
7.3 Solving Recurrences 337
7.4 Special Generating Functions 350
7.5 Convolutions 353
7.6 Exponential Generating Functions 364
7.7 Dirichlet Generating Functions 370
Exercises 371
8 Discrete Probability 381
8.1 Definitions 381
8.2 Mean and Variance 387
8.3 Probability Generating Functions 394
8.4 Flipping Coins 401
8.5 Hashing 411
Exercises 427
9 Asymptotics . . 439
9.1 A Hierarchy 440
9.2 O Notation 443
9.3 O Manipulation 450
9.4 Two Asymptotic Tricks 463
9.5 Euler s Summation Formula 469
9.6 Final Summations 476
Exercises 489
A Answers to Exercises 497
B Bibliography __—. 604
C Credits for Exercises 632
Index 637
List of Tables 657
|
| any_adam_object | 1 |
| author | Graham, Ronald L. 1935-2020 Knuth, Donald Ervin 1938- Patashnik, Oren 1954- |
| author_GND | (DE-588)132783843 (DE-588)121578437 (DE-588)133718042 |
| author_facet | Graham, Ronald L. 1935-2020 Knuth, Donald Ervin 1938- Patashnik, Oren 1954- |
| author_role | aut aut aut |
| author_sort | Graham, Ronald L. 1935-2020 |
| author_variant | r l g rl rlg d e k de dek o p op |
| building | Verbundindex |
| bvnumber | BV009697708 |
| callnumber-first | Q - Science |
| callnumber-label | QA39 |
| callnumber-raw | QA39.2 |
| callnumber-search | QA39.2 |
| callnumber-sort | QA 239.2 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 110 ST 110 |
| classification_tum | DAT 542f MAT 100f |
| ctrlnum | (OCoLC)29357079 (DE-599)BVBBV009697708 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 2. ed. |
| format | Book |
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| genre | 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4143389-0 Aufgabensammlung gnd-content 3\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Einführung Aufgabensammlung Lehrbuch |
| id | DE-604.BV009697708 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:39:24Z |
| institution | BVB |
| isbn | 9780201558029 0201558025 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006414480 |
| oclc_num | 29357079 |
| open_access_boolean | |
| owner | DE-29T DE-739 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-20 DE-11 DE-188 DE-83 DE-N32 DE-473 DE-BY-UBG |
| owner_facet | DE-29T DE-739 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-20 DE-11 DE-188 DE-83 DE-N32 DE-473 DE-BY-UBG |
| physical | XIII, 657 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Addison-Wesley |
| record_format | marc |
| spelling | Graham, Ronald L. 1935-2020 Verfasser (DE-588)132783843 aut Concrete mathematics a foundation for computer science Ronald L. Graham ; Donald E. Knuth ; Oren Patashnik 2. ed. Reading, Mass. [u.a.] Addison-Wesley 1994 XIII, 657 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 604 - 656 Hier auch später erschienene, unveränderte Nachdrucke Ciencias computacionales - Matemáticas Informatique - Mathématiques ram Matemáticas Mathématiques ram Software gtt Wiskundige methoden gtt Informatik Mathematik Computer science Mathematics Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf Arithmetik (DE-588)4002919-0 gnd rswk-swf Informatik (DE-588)4026894-9 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Computer (DE-588)4070083-5 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Grundlage (DE-588)4158388-7 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4143389-0 Aufgabensammlung gnd-content 3\p (DE-588)4123623-3 Lehrbuch gnd-content Zahlentheorie (DE-588)4067277-3 s DE-604 Analysis (DE-588)4001865-9 s Diskrete Mathematik (DE-588)4129143-8 s Arithmetik (DE-588)4002919-0 s 4\p DE-604 Mathematik (DE-588)4037944-9 s Datenverarbeitung (DE-588)4011152-0 s 5\p DE-604 Informatik (DE-588)4026894-9 s 6\p DE-604 Grundlage (DE-588)4158388-7 s 7\p DE-604 Computer (DE-588)4070083-5 s 8\p DE-604 Knuth, Donald Ervin 1938- Verfasser (DE-588)121578437 aut Patashnik, Oren 1954- Verfasser (DE-588)133718042 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006414480&sequence=000002&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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 7\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 8\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Graham, Ronald L. 1935-2020 Knuth, Donald Ervin 1938- Patashnik, Oren 1954- Concrete mathematics a foundation for computer science Ciencias computacionales - Matemáticas Informatique - Mathématiques ram Matemáticas Mathématiques ram Software gtt Wiskundige methoden gtt Informatik Mathematik Computer science Mathematics Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd Arithmetik (DE-588)4002919-0 gnd Informatik (DE-588)4026894-9 gnd Datenverarbeitung (DE-588)4011152-0 gnd Computer (DE-588)4070083-5 gnd Mathematik (DE-588)4037944-9 gnd Grundlage (DE-588)4158388-7 gnd Zahlentheorie (DE-588)4067277-3 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4129143-8 (DE-588)4002919-0 (DE-588)4026894-9 (DE-588)4011152-0 (DE-588)4070083-5 (DE-588)4037944-9 (DE-588)4158388-7 (DE-588)4067277-3 (DE-588)4001865-9 (DE-588)4151278-9 (DE-588)4143389-0 (DE-588)4123623-3 |
| title | Concrete mathematics a foundation for computer science |
| title_auth | Concrete mathematics a foundation for computer science |
| title_exact_search | Concrete mathematics a foundation for computer science |
| title_full | Concrete mathematics a foundation for computer science Ronald L. Graham ; Donald E. Knuth ; Oren Patashnik |
| title_fullStr | Concrete mathematics a foundation for computer science Ronald L. Graham ; Donald E. Knuth ; Oren Patashnik |
| title_full_unstemmed | Concrete mathematics a foundation for computer science Ronald L. Graham ; Donald E. Knuth ; Oren Patashnik |
| title_short | Concrete mathematics |
| title_sort | concrete mathematics a foundation for computer science |
| title_sub | a foundation for computer science |
| topic | Ciencias computacionales - Matemáticas Informatique - Mathématiques ram Matemáticas Mathématiques ram Software gtt Wiskundige methoden gtt Informatik Mathematik Computer science Mathematics Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd Arithmetik (DE-588)4002919-0 gnd Informatik (DE-588)4026894-9 gnd Datenverarbeitung (DE-588)4011152-0 gnd Computer (DE-588)4070083-5 gnd Mathematik (DE-588)4037944-9 gnd Grundlage (DE-588)4158388-7 gnd Zahlentheorie (DE-588)4067277-3 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Ciencias computacionales - Matemáticas Informatique - Mathématiques Matemáticas Mathématiques Software Wiskundige methoden Informatik Mathematik Computer science Mathematics Mathematics Diskrete Mathematik Arithmetik Datenverarbeitung Computer Grundlage Zahlentheorie Analysis Einführung Aufgabensammlung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006414480&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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