Mathematics of choice or how to count without counting:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Random House
1965
|
| Ausgabe: | 3. print. |
| Schriftenreihe: | New mathematical library.
15. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 202 S.: graph.Darst. |
Internformat
MARC
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| 245 | 1 | 0 | |a Mathematics of choice or how to count without counting |
| 250 | |a 3. print. | ||
| 264 | 1 | |a New York, NY |b Random House |c 1965 | |
| 300 | |a XI, 202 S.: graph.Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a New mathematical library. |v 15. | |
| 650 | 4 | |a Analyse combinatoire | |
| 650 | 7 | |a Analyse combinatoire |2 ram | |
| 650 | 7 | |a Combinatieleer |2 gtt | |
| 650 | 4 | |a Combinatorial analysis | |
| 650 | 0 | 7 | |a Kombinatorische Analysis |0 (DE-588)4164746-4 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804122900373962752 |
|---|---|
| adam_text | Contents
Preface xi
Chapter 1 Introductory Questions 1
Chapter 2 Permutations and Combinations 7
2.1 The Multiplication Principle 8
2.2 Factorials 10
2.3 Permutations 12
2.4 Zero Factorial 16
2.5 Combinations 18
2.6 Permutations of Things in a Circle 23
2.7 Summary 25
Chapter 3 Combinations and Binomial Coefficients 27
3.1 A Path Problem 27
3.2 Permutations of Things Not All Alike 28
3.3 Pascal s Formula for C(n, r) 31
3.4 The Binomial Expansion 34
3.5 The Multinomial Expansion 38
3.6 Pascal s Triangle 41
3.7 The Number of Subsets of a Set 42
3.8 Sums of Powers of Natural Numbers 44
3.9 Summary 48
Chapter 4 Some Special Distributions 50
4.1 Fibonacci Numbers 50
4.2 Linear Equations with Unit Coefficients 54
4.3 Combinations with Repetitions 59
4.4 Equations with Restricted Solutions 60
4.5 Summary 65
Chapter 5 The Inclusion-Exclusion Principle; Probability 67
5.1 A General Result 67
vii
5.2 Applications to Equations and to Combinations
with Repetitions 72
5.3 Derangements 78
5.4 Combinatorial Probability 82
5.5 Summary 88
Chapter 6 Partitions of an Integer 91
6.1 Graphs of Partitions 92
6.2 The Number of Partitions 96
6.3 Summary 99
Chapter 7 Generating Polynomials 100
7.1 Partitions and Products of Polynomials 102
7.2 Change for a Dollar Bill 106
7.3 Summary 108
Chapter 8 Distribution of Objects Not All Alike 109
8.1 Objects Different, Boxes Different 110
8.2 Objects Different, Boxes Alike (Partitions of a
Set) 112
8.3 Objects Mixed, Boxes Different 114
8.4 Summary 118
Chapter 9 Configuration Problems 120
9.1 The Pigeonhole Principle 120
9.2 Chromatic Triangles 122
9.3 Separations of the Plane 124
9.4 Summary 128
Chapter 10 Mathematical Induction 129
10.1 The Principle of Mathematical Induction 130
10.2 Notation for Sums and Products 133
10.3 Summary 139
Chapter 11 Interpretations of a Non-Associative Product 140
11.1 A Recursion Relation 141
11.2 The Development of an Explicit Formula 143
11.3 Proof of the Conjecture 148
11.4 A Formula for Fin) 150
11.5 Summary 152
Miscellaneous Problems 153
Answers and Solutions 160
Bibliography 199
Index 201
viii
|
| any_adam_object | 1 |
| author | Niven, Ivan 1915-1999 |
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| author_facet | Niven, Ivan 1915-1999 |
| author_role | aut |
| author_sort | Niven, Ivan 1915-1999 |
| author_variant | i n in |
| building | Verbundindex |
| bvnumber | BV008567621 |
| callnumber-first | Q - Science |
| callnumber-label | QA164 |
| callnumber-raw | QA164 |
| callnumber-search | QA164 |
| callnumber-sort | QA 3164 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 170 |
| ctrlnum | (OCoLC)536506 (DE-599)BVBBV008567621 |
| dewey-full | 512.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.5 |
| dewey-search | 512.5 |
| dewey-sort | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. print. |
| format | Book |
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| genre | 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content |
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| id | DE-604.BV008567621 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:21:13Z |
| institution | BVB |
| language | English |
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| physical | XI, 202 S.: graph.Darst. |
| publishDate | 1965 |
| publishDateSearch | 1965 |
| publishDateSort | 1965 |
| publisher | Random House |
| record_format | marc |
| series | New mathematical library. |
| series2 | New mathematical library. |
| spelling | Niven, Ivan 1915-1999 Verfasser (DE-588)115101217 aut Mathematics of choice or how to count without counting 3. print. New York, NY Random House 1965 XI, 202 S.: graph.Darst. txt rdacontent n rdamedia nc rdacarrier New mathematical library. 15. Analyse combinatoire Analyse combinatoire ram Combinatieleer gtt Combinatorial analysis Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Kombinatorik (DE-588)4031824-2 s DE-604 Kombinatorische Analysis (DE-588)4164746-4 s 2\p DE-604 New mathematical library. 15. (DE-604)BV001888260 15 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005631079&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 |
| spellingShingle | Niven, Ivan 1915-1999 Mathematics of choice or how to count without counting New mathematical library. Analyse combinatoire Analyse combinatoire ram Combinatieleer gtt Combinatorial analysis Kombinatorische Analysis (DE-588)4164746-4 gnd Kombinatorik (DE-588)4031824-2 gnd |
| subject_GND | (DE-588)4164746-4 (DE-588)4031824-2 (DE-588)4143389-0 |
| title | Mathematics of choice or how to count without counting |
| title_auth | Mathematics of choice or how to count without counting |
| title_exact_search | Mathematics of choice or how to count without counting |
| title_full | Mathematics of choice or how to count without counting |
| title_fullStr | Mathematics of choice or how to count without counting |
| title_full_unstemmed | Mathematics of choice or how to count without counting |
| title_short | Mathematics of choice or how to count without counting |
| title_sort | mathematics of choice or how to count without counting |
| topic | Analyse combinatoire Analyse combinatoire ram Combinatieleer gtt Combinatorial analysis Kombinatorische Analysis (DE-588)4164746-4 gnd Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Analyse combinatoire Combinatieleer Combinatorial analysis Kombinatorische Analysis Kombinatorik Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005631079&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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