Asymptopia:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2014]
|
| Schriftenreihe: | Student mathematical library
volume 71 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis: Seite 179-180 |
| Beschreibung: | XIV, 183 Seiten Diagramme |
| ISBN: | 9781470409043 |
Internformat
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| 650 | 7 | |a Combinatorics ... Graph theory ... Random graphs |2 msc | |
| 650 | 7 | |a Computer science ... Algorithms ... Analysis of algorithms |2 msc | |
| 650 | 7 | |a Number theory ... Elementary number theory ... Primes |2 msc | |
| 650 | 7 | |a Probability theory and stochastic processes ... Combinatorial probability ... Combinatorial probability |2 msc | |
| 650 | 4 | |a Combinatorial analysis | |
| 650 | 4 | |a Combinatorial enumeration problems | |
| 650 | 4 | |a Asymptotic expansions | |
| 650 | 4 | |a Ramsey numbers |x Asymptotic theory | |
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Datensatz im Suchindex
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| adam_text | Contents Preface ix A Reader’s Guide xiii Chapter 0. An Infinity of Primes 1 Chapter 1. Stirling’s Formula 5 §1.1 . Asymptotic Estimation of an Integral §1.2 . Approximating Sums by Trapezoids 13 §1.3 . Combining Forces to Estimate the Error 16 §1.4 . Estimating the Integral More Accurately 18 §1.5 . An Application to Random Walks 21 Chapter 2. 5 Big Oh, Little Oh, and All That 27 §2.1 . The Language of Asymptotics 28 §2.2 . ... and How to Use It 29 §2.3 . Little Oh One 31 §2.4 . Little Fleas and Littler Fleas: The Strange Hierarchy of Asymptopia 31 §2.5 . Little Oh One in the Exponent 33 §2.6 . Inverting Functions 34 §2.7 . Taylor Series 35 v
Contents vi Chapter 3. Integration in Asymptopia 37 §3.1. The Gaussian Tail 38 §3.2. High Trigonometric Powers 40 §3.3. An Easy Integral 43 §3.4. Integrals with logs 44 Chapter 4. Horn Integrals to Sums 47 §4-1. Approximating Sums by Integrals 48 §4.2. The Harmonic Numbers 51 Chapter 5. Asymptotics of Binomial Coefficients 57 §5.1. к Relatively Small 57 §5.2. Some Exercises 60 §5.3. к Linear in n 63 §5.4. At and Near the Middle Binomial Coefficient 66 §5.5. The Binomial Distribution 68 §5.6. The Binomial Tail 68 Chapter 6. Unicyclic Graphs 71 §6.1. Rooted Trees 72 §6-2. Rooted Trees to Prüfer Sequences 73 §6.3. Prüfer Sequences to Rooted Trees 79 §6-4. Proof of Bijection 82 §6.5. Rooted Forests 83 §6.6. Prüfer Sequences to Rooted Forests 83 §6-7. ... and Back Again 86 §6.8. An Exact Formula for Unicyclic Graphs 88 §6.9. Counting Unicyclic Graphs in Asymptopia 90 Ramsey Numbers 93 §7.1. Initial Erdős Argument 93 §7.2. Deletion 94 §7-3. Lovász Local Lemma 95 Chapter 7.
Contents vii §7.4 . Computations for R(k, k) 96 §7.5 . Asymmetrical Ramsey Numbers 98 §7.6 . Application to R(3,1) Chapter 8. Large Deviations 100 103 §8.1 . The Chernoff Bound 103 §8.2 . The Gaussian Tail 105 §8.3 . The Gaussian Paradigm I 105 §8.4 . Heads Minus Tails 107 §8.5 . ... and the Central Limit Theorem 109 §8.6 . The Binomial Distribution 109 §8.7 . The Gaussian Paradigm II 111 Primes Chapter 9. 115 §9.1 . Fun with Primes 116 §9.2 . Prime Number Theorem—Lower Bound 118 §9.3 . Prime Number Theorem—Upper Bound 119 §9.4 . Prime Number Theorem with Constant 120 §9.5 . Telescoping 123 Asymptotic Geometry 125 Chapter 10. §10.1 . Small Triangles 125 §10.2 . The Convex Hull of n RandomPoints 129 Chapter 11. Algorithms 137 §11.1 . Recurrences 137 §11.2 . Multiplying Large Numbers 141 §11.3 . Multiplying Large Matrices 142 §11.4 . Merge Sort 144 §11.5 . The Sorting Game 145 §11.6 . Quicksort 148 Potpourri 151 Chapter 12. §12.1. The Law of the Iterated Logarithm 151
Contents viii §12.2 . The Amazing Poisson Distribution 159 §12.3 . The Coupon Collector Problem 165 §12.4 . The Threshold of Connectivity 167 §12.5 . Tower and Log Star 170 Really Big Numbers! 173 Chapter 13. Bibliography 179 Index 181
|
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| author | Spencer, Joel H. 1946- Florescu, Laura |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| spelling | Spencer, Joel H. 1946- (DE-588)133091546 aut Asymptopia Joel Spencer with Laura Florescu Providence, Rhode Island American Mathematical Society [2014] © 2014 XIV, 183 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Student mathematical library volume 71 Literaturverzeichnis: Seite 179-180 Combinatorics ... Instructional exposition (textbooks, tutorial papers, etc.) msc Combinatorics ... Enumerative combinatorics ... Asymptotic enumeration msc Combinatorics ... Graph theory ... Random graphs msc Computer science ... Algorithms ... Analysis of algorithms msc Number theory ... Elementary number theory ... Primes msc Probability theory and stochastic processes ... Combinatorial probability ... Combinatorial probability msc Combinatorial analysis Combinatorial enumeration problems Asymptotic expansions Ramsey numbers Asymptotic theory Combinatorics ... Instructional exposition (textbooks, tutorial papers, etc.) Combinatorics ... Enumerative combinatorics ... Asymptotic enumeration Combinatorics ... Graph theory ... Random graphs Computer science ... Algorithms ... Analysis of algorithms Number theory ... Elementary number theory ... Primes Probability theory and stochastic processes ... Combinatorial probability ... Combinatorial probability Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s Kombinatorische Analysis (DE-588)4164746-4 s DE-604 Florescu, Laura (DE-588)1052041272 aut Erscheint auch als Online-Ausgabe 978-1-4704-1661-4 Student mathematical library volume 71 (DE-604)BV013184751 71 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027331422&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Spencer, Joel H. 1946- Florescu, Laura Asymptopia Student mathematical library Combinatorics ... Instructional exposition (textbooks, tutorial papers, etc.) msc Combinatorics ... Enumerative combinatorics ... Asymptotic enumeration msc Combinatorics ... Graph theory ... Random graphs msc Computer science ... Algorithms ... Analysis of algorithms msc Number theory ... Elementary number theory ... Primes msc Probability theory and stochastic processes ... Combinatorial probability ... Combinatorial probability msc Combinatorial analysis Combinatorial enumeration problems Asymptotic expansions Ramsey numbers Asymptotic theory Combinatorics ... Instructional exposition (textbooks, tutorial papers, etc.) Combinatorics ... Enumerative combinatorics ... Asymptotic enumeration Combinatorics ... Graph theory ... Random graphs Computer science ... Algorithms ... Analysis of algorithms Number theory ... Elementary number theory ... Primes Probability theory and stochastic processes ... Combinatorial probability ... Combinatorial probability Zahlentheorie (DE-588)4067277-3 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
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| title | Asymptopia |
| title_auth | Asymptopia |
| title_exact_search | Asymptopia |
| title_full | Asymptopia Joel Spencer with Laura Florescu |
| title_fullStr | Asymptopia Joel Spencer with Laura Florescu |
| title_full_unstemmed | Asymptopia Joel Spencer with Laura Florescu |
| title_short | Asymptopia |
| title_sort | asymptopia |
| topic | Combinatorics ... Instructional exposition (textbooks, tutorial papers, etc.) msc Combinatorics ... Enumerative combinatorics ... Asymptotic enumeration msc Combinatorics ... Graph theory ... Random graphs msc Computer science ... Algorithms ... Analysis of algorithms msc Number theory ... Elementary number theory ... Primes msc Probability theory and stochastic processes ... Combinatorial probability ... Combinatorial probability msc Combinatorial analysis Combinatorial enumeration problems Asymptotic expansions Ramsey numbers Asymptotic theory Combinatorics ... Instructional exposition (textbooks, tutorial papers, etc.) Combinatorics ... Enumerative combinatorics ... Asymptotic enumeration Combinatorics ... Graph theory ... Random graphs Computer science ... Algorithms ... Analysis of algorithms Number theory ... Elementary number theory ... Primes Probability theory and stochastic processes ... Combinatorial probability ... Combinatorial probability Zahlentheorie (DE-588)4067277-3 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
| topic_facet | Combinatorics ... Instructional exposition (textbooks, tutorial papers, etc.) Combinatorics ... Enumerative combinatorics ... Asymptotic enumeration Combinatorics ... Graph theory ... Random graphs Computer science ... Algorithms ... Analysis of algorithms Number theory ... Elementary number theory ... Primes Probability theory and stochastic processes ... Combinatorial probability ... Combinatorial probability Combinatorial analysis Combinatorial enumeration problems Asymptotic expansions Ramsey numbers Asymptotic theory Zahlentheorie Kombinatorische Analysis |
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