Principles of finite mathematics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Englewood Cliffs, NJ
Prentice-Hall
1977
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 455 S. Illustrationen |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV002173779 | ||
| 003 | DE-604 | ||
| 005 | 20230126 | ||
| 007 | t | ||
| 008 | 890928s1977 a||| |||| 00||| eng d | ||
| 035 | |a (OCoLC)2346104 | ||
| 035 | |a (DE-599)BVBBV002173779 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-83 |a DE-188 | ||
| 050 | 0 | |a QA39.2 | |
| 082 | 0 | |a 510 |2 19 | |
| 084 | |a SK 800 |0 (DE-625)143256: |2 rvk | ||
| 100 | 1 | |a Swift, William C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Principles of finite mathematics |c William C. Swift ; David E. Wilson |
| 264 | 1 | |a Englewood Cliffs, NJ |b Prentice-Hall |c 1977 | |
| 300 | |a X, 455 S. |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Mathématiques | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics | |
| 700 | 1 | |a Wilson, David E. |d 1929- |e Verfasser |0 (DE-588)173171613 |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001427779&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 940 | 1 | |q TUB-nveb | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001427779 | ||
Record in the Search Index
| _version_ | 1804116629228879872 |
|---|---|
| adam_text | CONIENT6
Preface ix
PORT ONE
PRO5PMUTY
1 PO66IWUT1E6 1
1 1 Basic Outcome Analysis 2
Relevant Statements and Truth Sets 3 / Strong and Weak Analyses 5
1 2 Trees 7
Models 10
1 3 Functions 14
The Set of Functions Mapping X into Y 16 I
The Multiplicative Principle 18 / The Number of Functions, in General 18
1 4 Permutations and Combinations 20
Permutations 23 / Combinations 24
1 5 Frequency Trees 28
Completing a Frequency Tree 50
V
vi Contents
2 INTUITIVE PROBABILITY 36
2 1 Ideal Frequency Trees 36
Construction of (Ideal) Frequency Trees 39
2 2 Probability Trees 44
Another Example 48
2 3 Conditional Probability 53
3 MATHEMATICAL PROBABILITY ei
3 1 The Mathematical Perspective 61
Grammar and Set Theory 63 / Analyses without Processes 65
3 2 The Formal System 69
Definition of a Probability Space 71 /
Empirical Versus Mathematical 73 / General Remarks 74
3 3 Conditional Probability and Independent Events 76
Independent Events 79
3 4 Random Variables 86
Expected Value 88
3 5 Combinations of Random Variables 92
3 6 The Standard Deviation 99
The Theoretical Setting 100
4 REPEATED TRIALS i08
4 1 Preliminary Examples 108
Another Example 111
4 2 Binomial Processes 116
4 3 Mean and Standard Deviation for a Binomial Process 121
Derivation of a1 = npq 124
4 4 The Normal Curve 128
The Adjusted Graph of a Binomial Distribution 131 /
The Normal Distribution 133
4 5 The Area Under the Normal Curve 136
4 6 Repeated Trials, in General 144
The Normal Curve Approximation 146
4 7 The Ubiquitous Normal Curve 152
56TAT16T1C6 157
5 1 Hypothesis Testing 157
The Level of Significance 159 / Variations 160 /
The General Case 163
vii Contents
5 2 Confidence intervals 166
5 3 Errors, Statistical and Logical 172
The Objective Errors 174 / Secondary Hypotheses 176
PPRT TWO
MRTRICE6
6 GAME6 PND MPTRICE6 i8i
6 1 Examples of Games 182
The Payoff Matrix 184 / Row Strategies and Expectations 185 j
Column Strategies and Expectations 187
6 2 The Problem of Game Theory 191
Optimal Strategies 192
6 3 Strictly Determined Games 199
The General Case 201
6 4 A Formal Look at Matrices 205
Multiplication of Matrices 207 /
Application to Column Strategies 211
6 5 Restatement of the Problem of Game Theory 213
The Expected Payoff 216 / The Duality Theorem 218
6 6 The Practical Analysis of Games 223
Strictly Determined Games 225 / The Analysis of 2 x 2 Games 226
6 7 Further Operations with Matrices 231
Algebraic Properties 233 j
Operational View of Matrix Multiplication 237
7 VECTORS 242
7 1 The Vectors in R2 242
Operations with Vectors 244 j Geometrical Interpretations 245
7 2 Lines and Polygons 248
Convex Polygons 251
7 3 The Analysis of 2 * n Games 258
The Optimal Column Strategy 260 / The Optimal Row Strategy 265
7 4 Functionals on R2 271
Geometrical Representation of Functionals 273
7 5 Row Strategies as Functionals 279
The Optimal Row Strategy 282
7 6 The Dual Perspective 289
7 7 Vectors and Functionals, in General 294
The Vector Space R3 296 / The Analysis of 3 x n Games 300
viii Contents
8UNKRPROGRPMMING 304
8 1 A Diet Problem 305
A Production Scheduling Problem 308
8 2 Restatement of the Diet Problem 314
The Graphical Attack 318
8 3 The Duality Theorem 326
8 4 Finding the Solutions 336
Another Example 341
8 5 Proof and Interpretation of the Duality Theorem 348
The Evaluation Question 352
8 6 Games and Linear Programming 360
Remarks 366
8 7 Linear Mappings 371
Composition of Linear Mappings 376
QPHNPLPPPUCPTION 383
9 1 Markov Processes 383
The General Case 387
9 2 Gambler s Ruin 390
A Theoretical Attack 392 / The General Problem 395
Solutions for Odd Numbered Exercises 405
Index 451
|
| any_adam_object | 1 |
| author | Swift, William C. Wilson, David E. 1929- |
| author_GND | (DE-588)173171613 |
| author_facet | Swift, William C. Wilson, David E. 1929- |
| author_role | aut aut |
| author_sort | Swift, William C. |
| author_variant | w c s wc wcs d e w de dew |
| building | Verbundindex |
| bvnumber | BV002173779 |
| 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 800 |
| ctrlnum | (OCoLC)2346104 (DE-599)BVBBV002173779 |
| 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 | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01231nam a2200349 c 4500</leader><controlfield tag="001">BV002173779</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230126 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">890928s1977 a||| |||| 00||| eng d</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)2346104</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV002173779</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA39.2</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 800</subfield><subfield code="0">(DE-625)143256:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Swift, William C.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Principles of finite mathematics</subfield><subfield code="c">William C. Swift ; David E. Wilson</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Englewood Cliffs, NJ</subfield><subfield code="b">Prentice-Hall</subfield><subfield code="c">1977</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 455 S.</subfield><subfield code="b">Illustrationen</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathématiques</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wilson, David E.</subfield><subfield code="d">1929-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)173171613</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001427779&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">TUB-nveb</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-001427779</subfield></datafield></record></collection> |
| id | DE-604.BV002173779 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:41:33Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001427779 |
| oclc_num | 2346104 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-83 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-83 DE-188 |
| physical | X, 455 S. Illustrationen |
| psigel | TUB-nveb |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Prentice-Hall |
| record_format | marc |
| spelling | Swift, William C. Verfasser aut Principles of finite mathematics William C. Swift ; David E. Wilson Englewood Cliffs, NJ Prentice-Hall 1977 X, 455 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Mathématiques Mathematik Mathematics Wilson, David E. 1929- Verfasser (DE-588)173171613 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001427779&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Swift, William C. Wilson, David E. 1929- Principles of finite mathematics Mathématiques Mathematik Mathematics |
| title | Principles of finite mathematics |
| title_auth | Principles of finite mathematics |
| title_exact_search | Principles of finite mathematics |
| title_full | Principles of finite mathematics William C. Swift ; David E. Wilson |
| title_fullStr | Principles of finite mathematics William C. Swift ; David E. Wilson |
| title_full_unstemmed | Principles of finite mathematics William C. Swift ; David E. Wilson |
| title_short | Principles of finite mathematics |
| title_sort | principles of finite mathematics |
| topic | Mathématiques Mathematik Mathematics |
| topic_facet | Mathématiques Mathematik Mathematics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001427779&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT swiftwilliamc principlesoffinitemathematics AT wilsondavide principlesoffinitemathematics |