Discrete mathematics and its applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
McGraw-Hill
1995
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 709 S. graph. Darst. |
| ISBN: | 0070539650 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV011101867 | ||
| 003 | DE-604 | ||
| 005 | 19970923 | ||
| 007 | t | ||
| 008 | 961206s1995 d||| |||| 00||| eng d | ||
| 020 | |a 0070539650 |9 0-07-053965-0 | ||
| 035 | |a (OCoLC)636074362 | ||
| 035 | |a (DE-599)BVBBV011101867 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-19 |a DE-634 |a DE-83 | ||
| 050 | 0 | |a QA39.2 | |
| 082 | 0 | |a 511 |2 20 | |
| 084 | |a SK 890 |0 (DE-625)143267: |2 rvk | ||
| 084 | |a MAT 050f |2 stub | ||
| 100 | 1 | |a Rosen, Kenneth H. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Discrete mathematics and its applications |c Kenneth H. Rosen |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York [u.a.] |b McGraw-Hill |c 1995 | |
| 300 | |a XXII, 709 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Informatique - Mathématiques |2 ram | |
| 650 | 7 | |a Mathématiques |2 ram | |
| 650 | 4 | |a Informatik | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Computer science |x Mathematics | |
| 650 | 4 | |a Mathematics | |
| 650 | 0 | 7 | |a Diskrete Mathematik |0 (DE-588)4129143-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lehrbuch |0 (DE-588)4123623-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lehrbuch |0 (DE-588)4123623-3 |D s |
| 689 | 0 | 1 | |a Diskrete Mathematik |0 (DE-588)4129143-8 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 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=007437484&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007437484 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804125591891345408 |
|---|---|
| adam_text | CONTENTS
Preface xi
To the Student xxi
1
The Foundations: Logic, Sets, and Functions 1
1.1 Logic 1
1.2 Propositional Equivalences 13
1.3 Predicates and Quantifiers 21
1.4 Sets 37
1.5 Set Operations 46
1.6 Functions 58
1.7 Sequences and Summations 71
1.8 The Growth of Functions 79
Key Terms and Results 89
Review Questions 92
Supplementary Exercises 93
Computer Projects 95
Computations and Explorations 95
Writing Projects 96
2
The Fundamentals: Algorithms, the Integers, and Matrices 97
2.1 Algorithms 98
2.2 Complexity of Algorithms 104
v
2.3 The Integers and Division 111
2.4 Integers and Algorithms 126
2.5 Applications of Number Theory 136
2.6 Matrices 150
Key Terms and Results 162
Review Questions 163
Supplementary Exercises 164
Computer Projects 166
Computations and Explorations 166
Writing Projects 167
3
Mathematical Reasoning 168
3.1 MethodsofProof 169
3.2 Mathematical Induction 183
3.3 Recursive Definitions 201
3.4 Recursive Algorithms 211
3.5 Program Correctness 217
Key Terms and Results 224
Review Questions 225
Supplementary Exercises 226
Computer Projects 229
Computations and Explorations 229
Writing Projects 230
4
Counting 231
4.1 The Basics of Counting 232
4.2 The Pigeonhole Principle 243
4.3 Permutations and Combinations 250
4.4 Discrete Probability 261
4.5 Probability Theory 268
4.6 Generalized Permutations and Combinations 282
4.7 Generating Permutations and Combinations 293
Key Terms and Concepts 298
Review Questions 300
Supplementary Exercises 301
Computer Projects 305
Computations and Explorations 305
Writing Projects 306
5
Advanced Counting Techniques 307
5.1 Recurrence Relations 307
5.2 Solving Recurrence Relations 318
5.3 Divide-and-Conquer Relations 325
5.4 Inclusion-Exclusion 332
5.5 Applications of Inclusion-Exclusion 339
Key Terms and Results 349
Review Questions 350
Supplementary Exercises 351
Computer Projects 353
Computations and Explorations 353
Writing Projects 354
6
Relations 355
6.1 Relations and Their Properties 355
6.2 n-ary Relations and Their Applications 366
6.3 Representing Relations 373
6.4 Closures of Relations 381
6.5 Equivalence Relations 393
6.6 Partial Orderings 402
Key Terms and Results 419
Review Questions 421
Supplementary Exercises 422
Computer Projects 426
Computations and Explorations 427
Writing Projects 427
7
Graphs 429
7.1 Introduction to Graphs 429
7.2 Graph Terminology 437
7.3 Representing Graphs and Graph Isomorphism 449
7.4 Connectivity 462
7.5 Euler and Hamilton Paths 472
7.6 Shortest Path Problems 488
7.7 Planar Graphs 499
7.8 Graph Coloring 509
Key Terms and Results 520
Review Questions 522
Supplementary Exercises 523
Computer Projects 528
Computations and Explorations 529
Writing Projects 529
8
Trees 531
8.1 Introduction to Trees 531
8.2 Applications of Trees 547
8.3 Tree Traversal 554
8.4 Trees and Sorting 571
8.5 Spanning Trees 580
8.6 Minimum Spanning Trees 593
Key Terms and Results 600
Review Questions 602
Supplementary Exercises 603
Computer Projects 606
Computations and Explorations 607
Writing Projects 607
9
Boolean Algebra 608
9.1 Boolean Functions 609
9.2 Representing Boolean Functions 616
9.3 Logic Gates 621
9.4 Minimization of Circuits 629
Key Terms and Results 645
Review Questions 646
Supplementary Exercises 646
Computer Projects 649
Computations and Explorations 649
Writing Projects 650
10
Modeling Computation 651
10.1 Languages and Grammars 652
10.2 Finite-State Machines with Output 663
10.3 Finite-State Machines with No Output 672
10.4 Language Recognition 682
10.5 Turing Machines 694
Key Terms and Results 703
Review Questions 704
Supplementary Exercises 705
Computer Projects 708
Computations and Explorations 709
Writing Projects 709
Appendixes A-0
A.l Exponential and Logarithmic Functions A-0
A.2 Pseudocode A-3
A.3 Generating Functions A-9
Suggested Readings B-0
Solutions to Odd-Numbered Exercises S-l
Index of Biographies 1-0
Index 1-1
|
| any_adam_object | 1 |
| author | Rosen, Kenneth H. |
| author_facet | Rosen, Kenneth H. |
| author_role | aut |
| author_sort | Rosen, Kenneth H. |
| author_variant | k h r kh khr |
| building | Verbundindex |
| bvnumber | BV011101867 |
| 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 890 |
| classification_tum | MAT 050f |
| ctrlnum | (OCoLC)636074362 (DE-599)BVBBV011101867 |
| dewey-full | 511 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511 |
| dewey-search | 511 |
| dewey-sort | 3511 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01699nam a2200469 c 4500</leader><controlfield tag="001">BV011101867</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19970923 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">961206s1995 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0070539650</subfield><subfield code="9">0-07-053965-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)636074362</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV011101867</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-19</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA39.2</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 890</subfield><subfield code="0">(DE-625)143267:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 050f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Rosen, Kenneth H.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Discrete mathematics and its applications</subfield><subfield code="c">Kenneth H. Rosen</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">3. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">McGraw-Hill</subfield><subfield code="c">1995</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XXII, 709 S.</subfield><subfield code="b">graph. Darst.</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="7"><subfield code="a">Informatique - Mathématiques</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Mathématiques</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Informatik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computer science</subfield><subfield code="x">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Diskrete Mathematik</subfield><subfield code="0">(DE-588)4129143-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lehrbuch</subfield><subfield code="0">(DE-588)4123623-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Lehrbuch</subfield><subfield code="0">(DE-588)4123623-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Diskrete Mathematik</subfield><subfield code="0">(DE-588)4129143-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</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=007437484&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007437484</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV011101867 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:04:00Z |
| institution | BVB |
| isbn | 0070539650 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007437484 |
| oclc_num | 636074362 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-634 DE-83 |
| owner_facet | DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-634 DE-83 |
| physical | XXII, 709 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | McGraw-Hill |
| record_format | marc |
| spelling | Rosen, Kenneth H. Verfasser aut Discrete mathematics and its applications Kenneth H. Rosen 3. ed. New York [u.a.] McGraw-Hill 1995 XXII, 709 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Informatique - Mathématiques ram Mathématiques ram Informatik Mathematik Computer science Mathematics Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf Lehrbuch (DE-588)4123623-3 gnd rswk-swf Lehrbuch (DE-588)4123623-3 s Diskrete Mathematik (DE-588)4129143-8 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007437484&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 | Rosen, Kenneth H. Discrete mathematics and its applications Informatique - Mathématiques ram Mathématiques ram Informatik Mathematik Computer science Mathematics Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd Lehrbuch (DE-588)4123623-3 gnd |
| subject_GND | (DE-588)4129143-8 (DE-588)4123623-3 |
| title | Discrete mathematics and its applications |
| title_auth | Discrete mathematics and its applications |
| title_exact_search | Discrete mathematics and its applications |
| title_full | Discrete mathematics and its applications Kenneth H. Rosen |
| title_fullStr | Discrete mathematics and its applications Kenneth H. Rosen |
| title_full_unstemmed | Discrete mathematics and its applications Kenneth H. Rosen |
| title_short | Discrete mathematics and its applications |
| title_sort | discrete mathematics and its applications |
| topic | Informatique - Mathématiques ram Mathématiques ram Informatik Mathematik Computer science Mathematics Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd Lehrbuch (DE-588)4123623-3 gnd |
| topic_facet | Informatique - Mathématiques Mathématiques Informatik Mathematik Computer science Mathematics Mathematics Diskrete Mathematik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007437484&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rosenkennethh discretemathematicsanditsapplications |