Mathematics for the analysis of algorithms:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2008
|
| Edition: | 3. ed., reprint of the 1990 ed. |
| Series: | Modern Birkhäuser classics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Orig. publ. as vol. 1 in the series Progresss in computer science and applied logic |
| Physical Description: | VIII, 132 S. |
| ISBN: | 0817647287 9780817647285 |
Staff View
MARC
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| 100 | 1 | |a Greene, Daniel H. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematics for the analysis of algorithms |c Daniel H. Greene ; Donald E. Knuth |
| 250 | |a 3. ed., reprint of the 1990 ed. | ||
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2008 | |
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Record in the Search Index
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| adam_text | Contents
1.
Binomial
Identities
.................... 1
1.1
Summary of Useful Identities
.............. 1
1.2
Deriving the Identities
................. 3
1.3
Inverse Relations
.................... 5
1.4
Operator Calculus
................... 8
1.5
Hypergeometric Series
................. 9
1.6
Identities with the Harmonic Numbers
.......... 10
2.
Recurrence Relations
................... 11
2.1
Linear Recurrence Relations
............... 11
2.1.1
Finite History
................... 12
2.1.1.1
Constant Coefficients
.............. 12
2.1.1.2
Variable Coefficients
............... 14
2.1.2
Pull History
.................... 17
2.1.2.1
Differencing
.................. 17
2.1.2.2
By Repertoire
................. 17
2.2
Nonlinear Recurrence Relations
............. 21
2.2.1
Relations with Maximum or Minimum Functions
.... 21
2.2.2
Continued Fractions and Hidden Linear Recurrences
. . 25
2.2.3
Doubly Exponential Sequences
............ 27
3.
Operator Methods
..................... 31
3.1
The Cookie Monster
.................. 31
3.2
Coalesced Hashing
................... 34
3.3
Open Addressing: Uniform Hashing
............ 38
3.4
Open Addressing: Secondary Clustering
.......... 39
vili
CONTENTS
4.
Asymptotic Analysis
....................42
4.1
Basic Concepts
.....................42
4.1.1
Notation
...................... 43
4.1.2
Bootstrapping
................... 43
4.1.3
Dissecting
..................... 44
4.1.4
Limits of Limits
.................. 45
4.1.5
Summary of Useful Asymptotic Expansions
...... 47
4.1.6
An Example from Factorization Theory
........ 48
4.2
Stieltjes
Integration and Asymptotics
........... 55
4.2.1
О
-notation and Integrals
............... 57
4.2.2
Euler*s Summation Formula
............. 58
4.2.3
An Example from Number Theory
.......... 60
4.3
Asymptotics from Generating Functions
.......... 65
4.3.1
Darboux s Method
.................65
4.3.2
Residue Calculus
..................68
4.3.3
The Saddle Point Method
..............70
Bibliography
.........................77
Appendices
..........................81
A. Schedule of Lectures,
1980................81
B. Homework Assignments
.................83
C. Midterm Exam I and Solutions
..............84
D. Final Exam I and Solutions
...............95
E. Midterm Exam II and Solutions
............ 101
F. Final Exam II and Solutions
.............. 107
G. Midterm Exam III and Solutions
............
Ill
H. Final Exam III and Solutions
.............. 116
I. A Qualifying Exam Problem and Solution
........ 124
Index
........................... 129
|
| adam_txt |
Contents
1.
Binomial
Identities
. 1
1.1
Summary of Useful Identities
. 1
1.2
Deriving the Identities
. 3
1.3
Inverse Relations
. 5
1.4
Operator Calculus
. 8
1.5
Hypergeometric Series
. 9
1.6
Identities with the Harmonic Numbers
. 10
2.
Recurrence Relations
. 11
2.1
Linear Recurrence Relations
. 11
2.1.1
Finite History
. 12
2.1.1.1
Constant Coefficients
. 12
2.1.1.2
Variable Coefficients
. 14
2.1.2
Pull History
. 17
2.1.2.1
Differencing
. 17
2.1.2.2
By Repertoire
. 17
2.2
Nonlinear Recurrence Relations
. 21
2.2.1
Relations with Maximum or Minimum Functions
. 21
2.2.2
Continued Fractions and Hidden Linear Recurrences
. . 25
2.2.3
Doubly Exponential Sequences
. 27
3.
Operator Methods
. 31
3.1
The Cookie Monster
. 31
3.2
Coalesced Hashing
. 34
3.3
Open Addressing: Uniform Hashing
. 38
3.4
Open Addressing: Secondary Clustering
. 39
vili
CONTENTS
4.
Asymptotic Analysis
.42
4.1
Basic Concepts
.42
4.1.1
Notation
. 43
4.1.2
Bootstrapping
. 43
4.1.3
Dissecting
. 44
4.1.4
Limits of Limits
. 45
4.1.5
Summary of Useful Asymptotic Expansions
. 47
4.1.6
An Example from Factorization Theory
. 48
4.2
Stieltjes
Integration and Asymptotics
. 55
4.2.1
О
-notation and Integrals
. 57
4.2.2
Euler*s Summation Formula
. 58
4.2.3
An Example from Number Theory
. 60
4.3
Asymptotics from Generating Functions
. 65
4.3.1
Darboux's Method
.65
4.3.2
Residue Calculus
.68
4.3.3
The Saddle Point Method
.70
Bibliography
.77
Appendices
.81
A. Schedule of Lectures,
1980.81
B. Homework Assignments
.83
C. Midterm Exam I and Solutions
.84
D. Final Exam I and Solutions
.95
E. Midterm Exam II and Solutions
. 101
F. Final Exam II and Solutions
. 107
G. Midterm Exam III and Solutions
.
Ill
H. Final Exam III and Solutions
. 116
I. A Qualifying Exam Problem and Solution
. 124
Index
. 129 |
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| author | Greene, Daniel H. Knuth, Donald Ervin 1938- |
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| author_sort | Greene, Daniel H. |
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| bvnumber | BV023041733 |
| classification_rvk | ST 130 ST 134 ST 150 |
| ctrlnum | (OCoLC)845158054 (DE-599)DNB985584939 |
| 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 |
| discipline_str_mv | Informatik Mathematik |
| edition | 3. ed., reprint of the 1990 ed. |
| format | Book |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:20:51Z |
| indexdate | 2024-07-09T21:09:38Z |
| institution | BVB |
| isbn | 0817647287 9780817647285 |
| language | English |
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| physical | VIII, 132 S. |
| publishDate | 2008 |
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| spelling | Greene, Daniel H. Verfasser aut Mathematics for the analysis of algorithms Daniel H. Greene ; Donald E. Knuth 3. ed., reprint of the 1990 ed. Boston [u.a.] Birkhäuser 2008 VIII, 132 S. txt rdacontent n rdamedia nc rdacarrier Modern Birkhäuser classics Orig. publ. as vol. 1 in the series Progresss in computer science and applied logic Algorithmus (DE-588)4001183-5 gnd rswk-swf Algorithmentheorie (DE-588)4200409-3 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Algorithmus (DE-588)4001183-5 s Mathematik (DE-588)4037944-9 s DE-604 Datenverarbeitung (DE-588)4011152-0 s Algorithmentheorie (DE-588)4200409-3 s 1\p DE-604 Knuth, Donald Ervin 1938- Verfasser (DE-588)121578437 aut Erscheint auch als Online-Ausgabe 978-0-8176-4729-2 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016245254&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 |
| spellingShingle | Greene, Daniel H. Knuth, Donald Ervin 1938- Mathematics for the analysis of algorithms Algorithmus (DE-588)4001183-5 gnd Algorithmentheorie (DE-588)4200409-3 gnd Datenverarbeitung (DE-588)4011152-0 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4200409-3 (DE-588)4011152-0 (DE-588)4037944-9 |
| title | Mathematics for the analysis of algorithms |
| title_auth | Mathematics for the analysis of algorithms |
| title_exact_search | Mathematics for the analysis of algorithms |
| title_exact_search_txtP | Mathematics for the analysis of algorithms |
| title_full | Mathematics for the analysis of algorithms Daniel H. Greene ; Donald E. Knuth |
| title_fullStr | Mathematics for the analysis of algorithms Daniel H. Greene ; Donald E. Knuth |
| title_full_unstemmed | Mathematics for the analysis of algorithms Daniel H. Greene ; Donald E. Knuth |
| title_short | Mathematics for the analysis of algorithms |
| title_sort | mathematics for the analysis of algorithms |
| topic | Algorithmus (DE-588)4001183-5 gnd Algorithmentheorie (DE-588)4200409-3 gnd Datenverarbeitung (DE-588)4011152-0 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Algorithmus Algorithmentheorie Datenverarbeitung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016245254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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