Discrete mathematics with proof:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley
2009
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. A85-A89) and index |
| Beschreibung: | XXIII, 806, 98 S. Ill., graph. Darst. |
| ISBN: | 9780470457931 0470457937 |
Internformat
MARC
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| 084 | |a MAT 050f |2 stub | ||
| 100 | 1 | |a Gossett, Eric |d 1950- |e Verfasser |0 (DE-588)138825718 |4 aut | |
| 245 | 1 | 0 | |a Discrete mathematics with proof |c Eric Gossett |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2009 | |
| 300 | |a XXIII, 806, 98 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references (p. A85-A89) and index | ||
| 650 | 7 | |a Algorithmes |2 ram | |
| 650 | 7 | |a Couplage, Théorie du |2 ram | |
| 650 | 7 | |a Graphes, Théorie des |2 ram | |
| 650 | 7 | |a Mathématiques - Informatique |2 ram | |
| 650 | 4 | |a Informatik | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Computer science |x Mathematics | |
| 650 | 0 | 7 | |a Diskrete Mathematik |0 (DE-588)4129143-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Diskrete Mathematik |0 (DE-588)4129143-8 |D s |
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Datensatz im Suchindex
| _version_ | 1804141152952123392 |
|---|---|
| adam_text | Titel: Discrete mathematics with proof
Autor: Gossett, Eric
Jahr: 2009
Contents
Preface xiii
Acknowledgments xx
To The Student xxii
1 Introduction 1
1.1 What Is Discrete Mathematics?........................................ 1
1.1.1 A Break from the Past ........................................ 3
1.2 The Stable Marriage Problem ........................................ 3
1.2.1 Seeking a Solution.......................................... 4
1.2.2 The Deferred Acceptance Algorithm................................. 5
1.2.3 Some Concluding Comments .................................... 7
1.3 Other Examples................................................ 7
1.3.1 A Simple Counting and Probability Example............................ 7
1.3.2 Sierpinski Curves........................................... 8
1.3.3 The Bridges of Konigsberg...................................... 9
1.3.4 Kirkman s Schoolgirls........................................ 9
1.3.5 Finite-State Machines ........................................ 10
1.3.6 The Set of Rational Numbers Is Countably Infinite......................... 11
1.4 Exercises ................................................... 13
1.5 Chapter Review................................................ 15
1.5.1 Summary............................................... 15
1.5.2 Notation ............................................... 15
2 Sets, Logic, and Boolean Algebras 17
2.1 Sets...................................................... 19
2.1.1 Definitions and Notation....................................... 19
2.1.2 Exercises............................................... 26
2.1.3 Proofs about Sets........................................... 29
2.1.4 Exercises............................................... 33
2.2 Logic in Daily Life.............................................. 34
2.2.1 General Guidelines for Analyzing Claims.............................. 34
2.2.2 Informal Fallacies .......................................... 35
2.2.3 Everyday Logic versus Symbolic Logic............................... 37
2.2.4 Exercises............................................... 37
2.3 Prepositional Logic.............................................. 38
2.3.1 Truth Tables ............................................. 39
2.3.2 The Operators NOT AND. OR. and XOR.............................. 39
2.3.3 Negations of AND, OR. and NOT.................................. 40
2.3.4 Exercises............................................... 42
2.3.5 Implication and the Biconditional.................................. 43
2.3.6 Operator Precedence......................................... 46
2.3.7 Logical Equivalence......................................... 46
2.3.8 Derived Implications......................................... 47
2.3.9 Exercises............................................... 48
VI Contents
2.4 Logical Equivalence and Rules of Inference................................. 50
2.4.1 Important Logical Equivalences and Rules of Inference....................... 53
2.4.2 Proving that a Statement is a Tautology............................... 54
2.4.3 Exercises............................................... 56
2.5 Boolean Algebras............................................... 58
2.5.1 Sets and Propositions as Boolean Algebras ............................. 60
2.5.2 Proving Additional Boolean Algebra Properties........................... 63
2.5.3 Exercises............................................... °7
2.6 Predicate Logic................................................ 68
2.6.1 Quantifiers.............................................. 69
2.6.2 Exercises............................................... 74
2.7 Quick Check Solutions............................................ 76
2.8 Chapter Review................................................ 81
2.8.1 Summary............................................... 81
2.8.2 Notation ............................................... 82
2.8.3 Fundamental Properties ....................................... 83
2.8.4 Additional Review Material..................................... 84
3 Proof 85
3.1 Introduction to Mathematical Proof...................................... 85
3.1.1 Mathematics and Proof: The Big Picture .............................. 86
3.1.2 Mathematical Objects Related to Proofs............................... 87
3.1.3 Exercises............................................... 91
3.2 Elementary Number Theory: Fuel for Practice................................ 92
3.2.1 The Integers and Other Number Systems.............................. 92
3.2.2 Divisibility.............................................. 93
3.2.3 Primes ................................................ 95
3.2.4 The Well-Ordering Principle..................................... 96
3.2.5 Congruence. Factorials. Floor and Ceiling Functions........................ 98
3.2.6 Exercises............................................... 99
3.3 Proof Strategies................................................ 100
3.3.1 Trivial Proof............................................. 100
3.3.2 Direct Proof.............................................. 101
3.3.3 Indirect Proof: Proving the Contrapositive.............................. 103
3.3.4 Proof by Contradiction........................................ 103
3.3.5 Proof by Cases............................................ 105
3.3.6 Implications with Existential Quantifiers .............................. 105
3.3.7 Implications with Universal Quantifiers............................... 106
3.3.8 Proofs Involving the Biconditional and
Logical Equivalence......................................... 108
3.3.9 Some Important Examples...................................... 109
3.3.10 Exercises............................................... 111
3.4 Applications of Elementary Number Theory................................. 113
3.4.1 The Euclidean Algorithm: Calculating gcd(a.fr) .......................... 113
3.4.2 Hashing................................................ 1 }6
3.4.3 Pseudorandom Numbers....................................... 117
3.4.4 Linear Congruence and the Chinese Remainder Theorem...................... 119
3.4.5 Fermat s Little Theorem and Fermat s Last Theorem........................ 124
3.4.6 Encryption.............................................. 126
3.4.7 Exercises............................................. 130
Contents VI1
3.5 Mathematical Induction............................................ 132
3.5.1 The Principle of Mathematical Induction .............................. 132
3.5.2 Complete Induction.......................................... 139
3.5.3 Interesting Mathematical Induction Problems............................ 141
3.5.4 The Well-Ordering Principle. Mathematical Induction, and Complete Induction.......... 146
3.5.5 Multidimensional Induction..................................... 148
3.5.6 Exercises............................................... 151
3.6 Creating Proofs: Hints and Suggestions ................................... 153
3.6.1 A Few Very General Suggestions .................................. 153
3.6.2 Some Specific Tactics ........................................ 156
3.6.3 Exercises............................................... 161
3.7 Quick Check Solutions............................................ 162
3.8 Chapter Review................................................ 167
3.8.1 Summary............................................... 167
3.8.2 Notation ............................................... 168
3.8.3 Additional Review Material ..................................... 168
Algorithms 169
4.1 Expressing Algorithms............................................ 170
4.1.1 Flow of Control............................................ 170
4.1.2 Flow of Information ......................................... 176
4.1.3 Exercises............................................... 179
4.2 Measuring Algorithm Efficiency....................................... 180
4.2.1 Big-0 and Its Cousins........................................ 181
4.2.2 Practical Big-0 Tools ........................................ 185
4.2.3 Exercises............................................... 193
4.2.4 Big-0 in Action: Searching a List.................................. 195
4.2.5 Exercises............................................... 200
4.3 Pattern Matching............................................... 202
4.3.1 The Obvious Algorithm ....................................... 202
4.3.2 KMP: Knuth-Morris-Pratt...................................... 204
4.3.3 BM: Boyer-Moore.......................................... 206
4.3.4 Exercises............................................... 213
4.4 The Halting Problem............................................. 214
4.4.1 Setting the Stage........................................... 214
4.4.2 The Halting Problem......................................... 215
4.5 Quick Check Solutions............................................ 217
4.6 Chapter Review................................................ 222
4.6.1 Summary............................................... 222
4.6.2 Notation ............................................... 223
4.6.3 Big-0 Shortcuts ........................................... 224
4.6.4 Additional Review Material ..................................... 224
Counting 225
5.1 Permutations and Combinations ....................................... 226
5.1.1 Two Basic Counting Principles ................................... 226
5.1.2 Permutations............................................. 229
5.1.3 Permutations with Repetition..................................... 231
5.1.4 Combinations............................................. 231
5.1.5 Combinations with Repetition.................................... 234
5.1.6 Exercises............................................... 237
5.1.7 More Complex Counting Problems ................................. 239
5.1.8 Exercises............................................... 246
VI11 Contents
5.2 Combinatorial Proofs............................................. 248
5.2.1 Introduction to Combinatorial Proofs ................................ 248
5.2.2 Counting Tulips: Three Combinatorial Proofs............................ 251
5.2.3 Exercises............................................... 257
5.3 Pigeon-Hole Principle: Inclusion-Exclusion................................. 258
5.3.1 The Pigeon-Hole Principle...................................... 258
5.3.2 Inclusion-Exclusion......................................... 261
5.}J Exercises............................................... 264
5.4 Quick Check Solutions............................................ 266
5.5 Chapter Review................................................ 270
5.5.1 Summary............................................... 270
5.5.2 Notation ............................................... 271
5.5.3 Some Counting Formulas ...................................... 272
5.5.4 Additional Review Material..................................... 272
6 Finite Probability Theory 273
6.1 The Language of Probabilities........................................ 274
6.1.1 Sample Spaces. Outcomes, and Events................................ 274
6.1.2 Probabilities of Events........................................ 277
6.1.3 Exercises............................................... 281
6.2 Conditional Probabilities and Independent Events.............................. 283
6.2.1 Definitions.............................................. 283
6.2.2 Computing Probabilities....................................... 287
6.2.3 Exercises............................................... 294
6.3 Counting and Probability........................................... 297
6.3.1 Exercises............................................... 299
6.4 Expected Value................................................ 302
6.4.1 Exercises............................................... 308
6.5 The Binomial Distribution.......................................... 310
6.5.1 Exercises............................................... 315
6.6 Bayes s Theorem............................................... 316
6.6.1 Exercises............................................... 319
6.7 Quick Check Solutions............................................ 322
6.8 Chapter Review................................................ 327
6.8.1 Summary............................................... 327
6.8.2 Notation ............................................... 328
6.8.3 Additional Review Material..................................... 328
7 Recursion 329
7.1 Recursive Algorithms............................................. 332
7.1.1 General Guidelines for Creating Recursive Algorithms....................... 333
7.1.2 A Detailed Example..... ........ ............................ 334
7.1.3 When Should Recursion Be Avoided?................................ 336
7.1.4 Persian Rugs............................................. 339
7.1.5 Drawing Sierpinski Curves...................................... 342
7.1.6 Adaptive Quadrature......................................... 345
7.1.7 Exercises............................................... 349
7.2 Recurrence Relations............................................. 350
7.2.1 Solving Recurrence Relations.................................... 353
7.2.2 Linear Homogeneous Recurrence Relations with Constant Coefficients .............. 357
7.2.3 Repeated Roots............................................ 366
7.2.4 The Sordid Truth........................................... 373
7.2.5 Exercises............................................... 375
7.3 Big-0 and Recursive Algorithms: The Master Theorem.......................... 377
7.3.1 Exercises............................................... 3g9
Contents IX
7.4 Generating functions..............................................V)|
7.4.1 Exercises............................................... 401
7.5 The Josephus Problem ............................................ 402
7.5.1 Exercises............................................... 407
7.6 Quick Cheek Solutions............................................ 407
7.7 Chapter Review................................................ 414
7.7.1 Summarv............................................... 414
7.7.2 Notation ............................................... 416
7.7.3 Generating Function fable...................................... 416
7.7.4 Additional Review Material ..................................... 416
Combinatorics 417
8.1 Partitions. Occupancy Problems. Stirling Numbers ............................. 419
8.1.1 Partitions of a Positive Integer.................................... 419
8.1.2 Occupancv Problems......................................... 423
8.1.3 Stirling Numbers........................................... 427
8.1.4 Exercises............................................... 433
8.2 Latin Squares. Finite Projective Planes.................................... 435
8.2.1 Latin Squares............................................. 435
8.2.2 Finite Projective Planes........................................ 442
8.2.3 Finite Projective Planes and Latin Squares.............................. 447
8.2.4 Exercises............................................... 457
8.3 Balanced Incomplete Block Designs..................................... 460
8.3.1 Constructing Balanced Incomplete Block Designs.......................... 464
8.3.2 Exercises............................................... 471
8.4 The Knapsack Problem............................................ 472
8.4.1 Exercises............................................... 4X5
8.5 Error-Correcting Codes ........................................... 488
8.5.1 The 7-Bit Hamming Code...................................... 489
8.5.2 A Formal Look at Coding Theory.................................. 492
8.5.3 Combinatorial Aspects of Coding Theory.............................. 497
8.5.4 Exercises............................................... 500
8.6 Distinct Representatives. Ramsey Numbers ................................. 502
8.6.1 Systems of Distinct Representatives................................. 502
8.6.2 Ramsey Numbers........................................... 509
8.6.3 Exercises............................................... 516
8.7 Quick Check Solutions............................................ 518
8.8 Chapter Review................................................ 529
8.8.1 Summary............................................... 529
8.8.2 Notation ............................................... 531
8.8.3 The Fano Plane............................................ 532
8.8.4 Occupancy Problems......................................... 532
8.8.5 Additional Review Material ..................................... 532
Formal Models in Computer Science 533
9.1 Information.................................................. 533
9.1.1 A General Model of Communication ................................ 534
9.1.2 A Mathematical Definition of Information.............................. 535
9.1.3 A Summary of Other Ideas in Shannon s Paper........................... 540
9.1.4 Exercises............................................... 541
9.2 Finite-State Machines ............................................ 542
9.2.1 Finite Automata ........................................... 543
9.2.2 Finite-State Machines with Output.................................. 547
9.2.3 Exercises............................................... 551
X Contents
9.3 Formal Languages .............................................. 553
9.3.1 Regular Grammars.......................................... 554
9.3.2 Exercises............................................... 559
9.4 Regular Expressions ............................................. 560
9.4.1 Introduction to Regular Expressions................................. 560
9.4.2 Perl Extensions............................................ 566
9.4.3 Exercises............................................... 568
9.5 The Three Faces of Regular.......................................... 569
9.5.1 Optional: Completing the Proof of Kleene s Theorem........................ 576
9.5.2 Exercises............................................... 582
9.6 A Glimpse at More Advanced Topics..................................... 584
9.6.1 Context-Free Languages and Grammars............................... 584
9.6.2 Turing Machines........................................... 585
9.6.3 Exercises............................................... 590
9.7 Quick Check Solutions............................................ 591
9.8 Chapter Review................................................ 596
9.8.1 Summary............................................... 596
9.8.2 Notation ............................................... 597
9.8.3 Additional Review Material..................................... 598
10 Graphs 599
10.1 Terminology ................................................. 600
10.1.1 New Graphs from Old........................................ 603
10.1.2 Special Graph Families........................................ 605
10.1.3 Exercises............................................... 608
10.2 Connectivity and Adjacency......................................... 609
10.2.1 Connectivity ............................................. 609
10.2.2 The Adjacency Matrix........................................ 613
10.2.3 Exercises............................................... 615
10.3 Euler and Hamilton.............................................. 618
10.3.1 Euler Circuits and Euler Trails.................................... 618
10.3.2 Hamilton Cycles and Hamilton Paths ................................ 620
10.3.3 Exercises............................................... 624
10.4 Representation and Isomorphism ...................................... 626
10.4.1 Representation............................................ 626
10.4.2 Isomorphism............................................. 629
10.4.3 Exercises............................................... 631
10.5 The Big Theorems: Planarity. Euler, Polyhedra. Chromatic Number.................... 634
10.5.1 Planarity ............................................... 634
10.5.2 The Regular Polyhedra........................................ 639
10.5.3 Chromatic Number.......................................... 642
10.5.4 Exercises............................................... 648
10.6 Directed Graphs and Weighted Graphs.................................... 651
10.6.1 Directed Graphs ........................................... 651
10.6.2 Weighted Graphs and Shortest Paths................................. 655
10.6.3 Exercises............................................... 662
10.7 Quick Check Solutions............................................ 665
10.8 Chapter Review................................................ 670
10.8.1 Summary............................................... 670
10.8.2 Notation ............................................... 671
10.8.3 Additional Review Material ..................................... 671
Contents XI
11 Trees 673
I 1.1 Terminology. Counting............................................ 673
11.1.1 Exercises............................................... 6S0
I 1.2 Traversal. Searching, and Sorting....................................... 0X2
11.2.1 Traversing Binarv Trees....................................... o.X2
11.2.2 Binary Search Trees ......................................... 6X5
11.2.3 Sorting................................................ 6X9
11.2.4 Exercises............................................... h90
11.3 More Applications of Trees.......................................... 692
11.3.1 Parse Trees.............................................. 692
11.3.2 Huffman Compression........................................ 694
11.3.3 XML................................................. 699
11.3.4 Exercises............................................... 70S
1 1.4 Spanning Trees................................................ 711
11.4.1 Spanning Trees in Unweighted Graphs ............................... 7! I
11.4.2 Minimal Spanning Trees in Weighted Graphs............................ 717
11.4.3 Exercises............................................... 722
I 1.5 Quick Check Solutions............................................ 726
1 1.6 Chapter Review................................................ 729
11.6.1 Summary............................................... 729
11.6.2 Notation ............................................... 729
11.6.3 Additional Review Material..................................... 730
12 Functions, Relations, Databases, and Circuits 731
12.1 Functions and Relations............................................ 731
12.1.1 Functions............................................... 731
12.1.2 Relations............................................... 735
12.1.3 Exercises............................................... 737
12.2 Equivalence Relations. Partially Ordered Sets................................ 739
12.2.1 Properties that Characterize Relations................................ 739
12.2.2 Equivalence Relations and Partitions................................. 742
12.2.3 Exercises............................................... 746
12.3 W-ary Relations and Relational Databases.................................. 748
12.3.1 W-ary Relations............................................ 748
12.3.2 Relational Databases......................................... 749
12.3.3 Functional Dependence: Models and Instances........................... 751
12.3.4 Keys: Operations on Relations.................................... 752
12.3.5 Normal Forms ............................................ 757
12.3.6 Exercises............................................... 769
12.4 Boolean Functions and Boolean Expressions................................. 772
12.4.1 Boolean Functions.......................................... 773
12.4.2 Binary Functions and Disjunctive Normal Form........................... 775
12.4.3 Binary Expressions and Disjunctive Normal Form ......................... 778
12.4.4 Exercises............................................... 784
12.5 Combinatorial Circuits............................................ 7X5
12.5.1 Minimizing Binary Expressions................................... 785
12.5.2 Combinatorial Circuits and Binary Expressions........................... 789
12.5.3 Functional Completeness....................................... 793
12.5.4 Exercises............................................... 795
12.6 Quick Check Solutions............................................ 797
12.7 Chapter Review................................................ 805
12.7.1 Summary............................................... 805
12.7.2 Notation ............................................... 806
12.7.3 Additional Review Material ..................................... 806
Xll Contents
A Number Systems Al
A.l The Natural Numbers............................................. Al
A.2 The Integers.................................................. A2
A.3 The Rational Numbers............................................ A2
A.4 The Real Numbers .............................................. A4
A.5 The Complex Numbers............................................ A4
A.6 Other Number Systems............................................ A6
A.7 Representation of Numbers.......................................... A7
B Summation Notation A10
C Logic Puzzles and Analyzing Claims A12
C.I Logic Puzzles................................................. A12
C.l.l Logic Puzzles about AND, OR. and NOT.............................. A12
C.I.2 Logic Puzzles about Implication, Biconditional, and Equivalence ................. A16
C.1.3 Exercises............................................... A18
C.2 Analyzing Claims............................................... AI8
C.2.1 Analyzing Claims that Contain Implications............................. A18
C.2.2 Analyzing Claims that Contain Quantifiers ............................. A22
C.2.3 Exercises............................................... A23
C.3 Quick Check Solutions............................................ A24
D The Golden Ratio A27
E Matrices A29
F The Greek Alphabet A33
G Writing Mathematics A34
H Solutions to Selected Exercises A36
H.l Introduction.................................................. A36
H.2 Sets, Logic, and Boolean Algebras...................................... A36
H.3 Proof ..................................................... A42
H.4 Algorithms .................................................. A47
H.5 Counting ................................................... A51
H.6 Finite Probability Theory........................................... A54
H.7 Recursion................................................... A59
H.8 Combinatorics................................................. A63
H.9 Formal Models in Computer Science..................................... A68
H.10 Graphs.............................................. ..... A71
H. 11 Trees...................................................... A75
H.l2 Functions, Relations, Databases, and Circuits................................ A78
H.l3 Appendices.................................................. A83
Bibliography Ag5
Index A90
|
| any_adam_object | 1 |
| author | Gossett, Eric 1950- |
| author_GND | (DE-588)138825718 |
| author_facet | Gossett, Eric 1950- |
| author_role | aut |
| author_sort | Gossett, Eric 1950- |
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| building | Verbundindex |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 890 |
| classification_tum | MAT 050f |
| ctrlnum | (OCoLC)294879142 (DE-599)BVBBV036090227 |
| 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 |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV036090227 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:11:20Z |
| institution | BVB |
| isbn | 9780470457931 0470457937 |
| language | English |
| lccn | 2008055959 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018980841 |
| oclc_num | 294879142 |
| open_access_boolean | |
| owner | DE-29T DE-11 DE-91G DE-BY-TUM DE-824 |
| owner_facet | DE-29T DE-11 DE-91G DE-BY-TUM DE-824 |
| physical | XXIII, 806, 98 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Wiley |
| record_format | marc |
| spelling | Gossett, Eric 1950- Verfasser (DE-588)138825718 aut Discrete mathematics with proof Eric Gossett 2. ed. Hoboken, NJ Wiley 2009 XXIII, 806, 98 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. A85-A89) and index Algorithmes ram Couplage, Théorie du ram Graphes, Théorie des ram Mathématiques - Informatique ram Informatik Mathematik Mathematics Computer science Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf Diskrete Mathematik (DE-588)4129143-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018980841&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gossett, Eric 1950- Discrete mathematics with proof Algorithmes ram Couplage, Théorie du ram Graphes, Théorie des ram Mathématiques - Informatique ram Informatik Mathematik Mathematics Computer science Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd |
| subject_GND | (DE-588)4129143-8 |
| title | Discrete mathematics with proof |
| title_auth | Discrete mathematics with proof |
| title_exact_search | Discrete mathematics with proof |
| title_full | Discrete mathematics with proof Eric Gossett |
| title_fullStr | Discrete mathematics with proof Eric Gossett |
| title_full_unstemmed | Discrete mathematics with proof Eric Gossett |
| title_short | Discrete mathematics with proof |
| title_sort | discrete mathematics with proof |
| topic | Algorithmes ram Couplage, Théorie du ram Graphes, Théorie des ram Mathématiques - Informatique ram Informatik Mathematik Mathematics Computer science Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd |
| topic_facet | Algorithmes Couplage, Théorie du Graphes, Théorie des Mathématiques - Informatique Informatik Mathematik Mathematics Computer science Mathematics Diskrete Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018980841&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gossetteric discretemathematicswithproof |