Verfügbarkeit: Mathematics :: THWS Bibkatalog

Mathematics: a discrete introduction

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Bibliographische Detailangaben
1. Verfasser:	Scheinerman, Edward (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Belmont, Calif. Thomson Brooks/Cole 2006
Ausgabe:	2. ed., internat. student ed.
Schlagworte:	Informatik Mathematik Einführung
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XXVII, 561 S. Ill.
ISBN:	049501866X 0534398987

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Datensatz im Suchindex

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adam_text	CONTENTS TO THE STUDENT XV HOW TO READ A MATHEMATICS BOOK XVI EXERCISES XVII TO THE INSTRUCTOR XIX AUDIENCE AND PREREQUISITES XIX TOPICS COVERED AND NAVIGATING THE SECTIONS XIX SAMPLE COURSE OUTLINES XXI SPECIAL FEATURES XXI WHAT S NEW IN THIS SECOND EDITION XXIII ACKNOWLEDGMENTS XXV THIS NEW EDITION XXV FROM THE FIRST EDITION XXV 1 FUNDAMENTALS 1 1 JOY 1 WHY ? 1 THE AGONY AND THE ECSTASY 2 EXERCISE 2 2 DEFINITION 2 RECAP 5 EXERCISES 5 3 THEOREM 8 THE N ITURE OF TRUTH X IF-THEN 9 IF AND ONLY IT I I AND. OR. AND NOT 12 WHAT THEOREM ARE CALLED 13 VACUOUS TRUTH 14 RECAP 14 EXERC~ E 15 4 PROOF 16 A MORE INVOLVCD PROOF 70 PROVING IF-AND-ONLY-IF THEOREMS 92 PROVING EQUATIONS AND INEQUALITIES 24 RECAP 25 EXERCISES 25 5 COUNTEREXAMPLE 25 RECAP 27 EXERCISES 27 6 BOOLEAN ALGEBRA 27 MORE OPERATIONS 3 1 RECAP 32 EXERCISES 32 CHAPTER 1 SELF TEST 34 COLLECTIONS 37 7 LISTS 37 COUNTING TWO-ELEMENT LISTS 37 LONGER LISTS 40 RECAP 43 EXERCISES 43 8 FACTORIAL 45 MUCH ADO ABOUT O! 46 PRODUCT NOTATION 47 RECAP 48 EXERCISES 48 9 SETS I: INTRODUCTION, SUBSETS 49 EQUALITY OF SETS 5 1 SUBSET 53 COUNTING SUBSETS 55 POWER SET 57 RECAP 57 EXERCISES 57 10 QUANTIFIERS 58 THERE IS 58 FOR ALL 59 NEGATING QUANTIFIED STATEMENTS 60 COMBINING QUANTIFIERS 61 RECAP 62 EXERCISES 63 11 SETS II: OPERATIONS 64 UNION AND INTERSECTION 64 THE SIZE OF A UNION 66 DIFFERENCE AND SYMMETRIC DIFFERENCE 68 CARTESIAN PRODUCT 73 RECAP 74 EXERCISES 74 12 COMBINATORIAL PROOF: T W O E X A M P L E S 76 RECAP X0 EXERCISES X0 CHAPTER 2 SELF TEST 80 3 COUNTING AND RELATIONS 83 13 RELATIONS 83 PROPERTIES OF RELATIONS 86 RECAP 87 EXERCISES 87 14 EQUIVALENCE RELATIONS 89 EQUIVALENCE CLA SCS 02 RECAP 05 EXERCI C 06 15 PARTITIONS 98 O 1 1 I 1 I E 1 ; R T 100 RECAP I02 EXCRCI CS 102 16 BINOMIAL COEFFICIENTS 104 CALCULATILIG (; J 107 PASCAL S TRIANGLE 109 AFORRNULAFOR(;) 1 1 1 RECAP 113 EXCRCI C I L3 17 COUNTING MT~LTISI?TS 117 L~~LTI CL I 17 L:ORLLIILA 111R ( I: L ) I I0 KCC:TP 172 FI C~-C~ C 172 18 INCLCISIORI-EX~IIISIOI) I23 HOU TO LT~CIU ~OI-~ CL~~IO~~ 120 I)ER;R~LPC~RLENL 129 A ;HA TL! L ORILUL;~ 132 KEC:LP I32 TEE I32 CHAPTER 3 SELF TEST 133 4 MORE PROOF 135 19 CONTRADICTION 135 PROOF BY CONTRAPOSITIVE 135 REDUCTIO AD ABSURDUM 137 A MATTER OF STYLE 14 1 RECAP 141 EXERCISES 14 1 20 SMALLEST COUNTEREXAMPLE 142 WELL-ORDERING 148 RECAP 153 EXERCISES 153 AND FINALLY 154 21 INDUCTION 155 THE INDUCTION MACHINE 155 THEORETICAL UNDERPINNINGS 157 PROOF BY INDUCTION 157 PROVING EQUATIONS AND INEQUALITIES 160 OTHER EXAMPLES 162 STRONG INDUCTION 163 A MORE COMPLICATED EXAMPLE 165 A MATTER OF STYLE 168 RECAP 168 EXERCISES 168 22 RECURRENCE RELATIONS 171 FIRST-ORDER RECURRENCE RELATIONS 172 SECOND-ORDER RECURRENCE RELATIONS 175 THE CASE OF THE REPEATED ROOT 178 SEQUENCES GENERATED BY POLYNOMIALS 180 RECAP 187 EXERCISES 188 CHAPTER 4 SELF TEST 190 5 FUNCTIONS 193 23 FUNCTIONS 193 DOMAIN AND IMAGE 195 PICTURES OF FUNCTIONS 196 COUNTING FUNCTIONS 197 INVERSE FUNCTIONS 198 COUNTING FUNCTIONS, AGAIN RECAP 203 EXERCISES 203 24 THE PIGEONHOLE PRINCIPLE 205 CANTOR S THEOREM 208 RECAP 210 EXERCISES 2 10 25 COMPOSITION 211 IDENTITY FUNCTION 2 1 1 RECAP 215 EXERCISES 2 15 26 PERMUTATIONS 216 CYCLE NOTATION 2 17 CALCULATIONS WITH PERMUTATIONS 220 TRANSPOSITIONS 22 1 A GRAPHICAL APPROACH 226 RECAP 228 EXERCISES 228 27 SYMMETRY 231 SYMMETRIES OF A SQUARE 23 1 SYMNIETRIES AS PERMUTATIONS 232 COMBINING SYMMCTRIES 233 FORMAL I)ELINITION OF SYMMETR! 735 RECAP 236 EXERCISES 236 28 ASSORTED NOTATION 236 BIG OH 236 R AND (-) 239 LITTLE OH 240 FLOOR AND CEILING 241 RECAP 212 EXERCISES 242 CHAPTER 5 SELF TEST 242 6 PROBABILITY 245 30 EVEL~TS 249 CONIH~N~LIG E CRLT 251 THE R~RTHD.T! I ROHLCNI 754 RCC IP 254 EXCRC~ C 255 31 CONDITIONAL PROBABILITY AND INDEPENDENCE 257 INDEPENDENCE 259 INDEPENDENT REPEATED TRIALS 26 1 THE MONTY HALL PROBLEM 262 RECAP 263 EXERCISES 263 32 RANDOM VARIABLES 266 RANDOM VARIABLES AS EVENTS 267 INDEPENDENT RANDOM VARIABLES 269 RECAP 270 EXERCISES 270 33 EXPECTATION 271 LINEARITY OF EXPECTATION 276 PRODUCT OF RANDOM VARIABLES 279 EXPECTED VALUE AS A MEASURE OF CENTRALITY 282 VARIANCE 283 RECAP 287 EXERCISES 287 CHAPTER 6 SELF TEST 289 7 NUMBER THEORY 293 34 DIVIDING 293 DIV AND MOD 296 RECAP 297 EXERCISE5 297 35 GREATEST COMMON DIVISOR 298 CALCULATING THE GCD 299 CORRECTNE5S 30 1 HOUI:;I T ? 302 AN IMPORTANT THEORCM 304 RCCAP 307 EXCRCI ES 307 36 MODULAR ARITHMETIC 309 A NEW CONTEXT FOR BA IC OPERATION 309 MODULAR ADDITION AND MULTIPLICATION 3 10 MODULAR SUBTRACTION 3 1 1 MODULAR DIVI ION 3 13 A NOTE ON NOTATION 3 18 RECAP 318 EXERCISES 3 18 37 THE CHINESE REMAINDER THEOREM 320 SOLVING ONE EQUATION 320 SOLVING TWO EQUATIONS 322 RECAP 324 EXERCISES 324 38 FACTORING 325 INFINITELY MANY PRIMES 327 A FORMULA FOR GREATEST COMMON DIVISOR 328 IRRATIONALITY OF & 329 RECAP 331 EXERCISES 33 1 CHAPTER 7 SELF TEST 335 8 ALGEBRA 337 39 GROUPS 337 OPERATIONS 337 PROPERTIES OF OPERATIONS 338 GROUPS 340 EXAMPLES 342 RECAP 345 EXERCISES 345 40 GROUP ISOMORPHISM 347 THE SAME ? 347 CYCLIC GROUPS 349 RECAP 352 EXERCISES 352 41 SUBGROUPS 353 LAGRANGE S THEOREM 356 RECAP 359 EXERCISE5 359 42 FCRMAT S L-LTTLT. TTIEOITIN 367 FLR T PROOF 762 SECOND PROOF 361 TH~RD PROOF 366 EULER ~ THEOREM 767 PR~MAL~TY TE5T1NG 368 RECAP 369 EUERC~CE 369 43 PUBLIC KEY CRYPTOYRDPTIY I IR~TRC~CLOCTIC~RI 370 THE PROBLEM PRNATE CORNMUNLCAT~ON IN PUHLLC 770 FACTORLNP 370 WORDS TO NUMBERS 37 1 CRYPTOGRAPHY AND THE LAW 373 RECAP 373 EXERCISES 373 44 PUBLIC KEY CRYPTOGRAPHY II: RABIN S METHOD 373 SQUARE ROOTS MODULO N 374 THE ENCRYPTION AND DECRYPTION PROCEDURES 378 RECAP 379 EXERCISES 379 45 PUBLIC KEY CRYPTOGRAPHY ILL: RSA 380 THE RSA ENCRYPTION AND DECRYPTION FUNCTIONS 38 1 SECURITY 383 RECAP 384 EXERCISES 384 CHAPTER 8 SELF TEST 385 9 GRAPHS 389 46 FUNDAMENTALS OF GRAPH THEORY 389 MAP COLORING 389 THREE UTILITIES 391 SEVEN BRIDGES 391 WHAT IS A GRAPH? 392 ADJACENCY 393 A MATTER OF DEGREE 394 FURTHER NOTATION AND VOCABULARY 396 RECAP 397 EXERCISES 397 47 SUBGRAPHS 399 INDUCED AND SPANNING SUBGRAPHS 400 CLIQUES AND INDEPENDENT SETS 402 COMPLEMENTS 403 RECAP 404 EXERCISE5 404 48 CONNECTION 406 WALKS 406 PATHS 407 DISCONNECTION 4 10 RECAP 41 1 EXERCISES 4 1 1 49 TREES 413 CYCLES 413 FORESTS AND TREES 413 PROPERTIES OF TREES 4 14 LEAVES 416 SPANNING TREES 4 1 8 RECAP 419 EXERCISES 420 50 EULERIAN GRAPHS 421 NECESSARY CONDITIONS 422 MAIN THEOREMS 423 UNFINISHED BUSINESS 425 RECAP 426 EXERCISES 426 51 COLORING 427 CORE CONCEPTS 427 BIPARTITE GRAPHS 429 THE EASE OF TWO-COLORING AND THE DIFFICULTY OF THREE-COLORING 433 RECAP 434 EXERCISES 434 52 PLANAR GRAPHS 435 DA~LGEROUS CURVES 435 EMBEDDING 436 EULER S FORMULA 437 NONPLANAR GRAPHS 440 COLORING PLANAR GRAPHS 441 RECAP 444 EXERCISES 444 CHAPTER 9 SELF TEST 446 10 PARTIALLY ORDERED SETS 449 53 FUNDAMENTALS OF PART~ALLY ORDERED SETS 449 WHAT IS ,I POXT 4-49 NOTATION ,~ND LD,LNYUAPR 451 RCCAP 454 EXCRC~SC 455 54 MAX AND MLN 455 RECAP 457 EXERCISES 457 55 LINEAR ORDERS 458 RECAP 460 EXERCISES 461 56 LINEAR EXTENSIONS 461 SORTING 465 LINEAR EXTENSIONS OF INFINITE POSETS 467 RECAP 468 EXERCISES 468 57 DIMENSION 469 REALIZERS 469 DIMENSION 47 1 EMBEDDING 473 RECAP 476 EXERCISES 476 58 LATTICES 477 MEET AND JOIN 477 LATTICES 479 RECAP 481 EXERCISES 482 CHAPTER 10 SELF TEST 483 APPENDICES 487 A LOTS OF HINTS AND COMMENTS; SOME ANSWERS 487 B SOLUTIONS TO SELF TESTS 515 CHAPTER 1 515 CHAPTER 2 516 CHAPTER 3 5 18 CHAPTER 4 520 CHAPTER 5 524 CHAPTER 6 526 CHAPTER 7 530 CHAPTER 8 532 CHAPTER 9 535 CHAPTER L0 539 C GLOSSARY 544 D FUNDAMENTALS 552 NUMBERS 552 OPERATIONS 552 ORDERING 553 COMPLEX NUMBERS 553 SUBSTITUTION 553 INDEX 555
adam_txt	CONTENTS TO THE STUDENT XV HOW TO READ A MATHEMATICS BOOK XVI EXERCISES XVII TO THE INSTRUCTOR XIX AUDIENCE AND PREREQUISITES XIX TOPICS COVERED AND NAVIGATING THE SECTIONS XIX SAMPLE COURSE OUTLINES XXI SPECIAL FEATURES XXI WHAT'S NEW IN THIS SECOND EDITION XXIII ACKNOWLEDGMENTS XXV THIS NEW EDITION XXV FROM THE FIRST EDITION XXV 1 FUNDAMENTALS 1 1 JOY 1 WHY'? 1 THE AGONY AND THE ECSTASY 2 EXERCISE 2 2 DEFINITION 2 RECAP 5 EXERCISES 5 3 THEOREM 8 THE N'ITURE OF TRUTH X IF-THEN 9 IF AND ONLY IT I I AND. OR. AND NOT 12 WHAT THEOREM\ ARE CALLED 13 VACUOUS TRUTH 14 RECAP 14 EXERC~\E\ 15 4 PROOF 16 A MORE INVOLVCD PROOF 70 PROVING IF-AND-ONLY-IF THEOREMS 92 PROVING EQUATIONS AND INEQUALITIES 24 RECAP 25 EXERCISES 25 5 COUNTEREXAMPLE 25 RECAP 27 EXERCISES 27 6 BOOLEAN ALGEBRA 27 MORE OPERATIONS 3 1 RECAP 32 EXERCISES 32 CHAPTER 1 SELF TEST 34 COLLECTIONS 37 7 LISTS 37 COUNTING TWO-ELEMENT LISTS 37 LONGER LISTS 40 RECAP 43 EXERCISES 43 8 FACTORIAL 45 MUCH ADO ABOUT O! 46 PRODUCT NOTATION 47 RECAP 48 EXERCISES 48 9 SETS I: INTRODUCTION, SUBSETS 49 EQUALITY OF SETS 5 1 SUBSET 53 COUNTING SUBSETS 55 POWER SET 57 RECAP 57 EXERCISES 57 10 QUANTIFIERS 58 THERE IS 58 FOR ALL 59 NEGATING QUANTIFIED STATEMENTS 60 COMBINING QUANTIFIERS 61 RECAP 62 EXERCISES 63 11 SETS II: OPERATIONS 64 UNION AND INTERSECTION 64 THE SIZE OF A UNION 66 DIFFERENCE AND SYMMETRIC DIFFERENCE 68 CARTESIAN PRODUCT 73 RECAP 74 EXERCISES 74 12 COMBINATORIAL PROOF: T W O E X A M P L E S 76 RECAP X0 EXERCISES X0 CHAPTER 2 SELF TEST 80 3 COUNTING AND RELATIONS 83 13 RELATIONS 83 PROPERTIES OF RELATIONS 86 RECAP 87 EXERCISES 87 14 EQUIVALENCE RELATIONS 89 EQUIVALENCE CLA\SCS 02 RECAP 05 EXERCI\C\ 06 15 PARTITIONS 98 O 1 1 I 1 I E 1 ; R T 100 RECAP I02 EXCRCI\CS 102 16 BINOMIAL COEFFICIENTS 104 CALCULATILIG (; J 107 PASCAL'S TRIANGLE 109 AFORRNULAFOR(;) 1 1 1 RECAP 113 EXCRCI\C\ I L3 17 COUNTING MT~LTISI?TS 117 \L~~LTI\CL\ I 17 L:ORLLIILA\ 111R ( I: L ) I I0 KCC:TP 172 FI\C~-C~\C\ 172 18 INCLCISIORI-EX~IIISIOI) I23 HOU TO LT~CIU\~OI-~ \CL~~IO~~ 120 I)ER;R~LPC~RLENL\ 129 A ;HA\TL! L'ORILUL;~ 132 KEC:LP I32 TEE\\ I32 CHAPTER 3 SELF TEST 133 4 MORE PROOF 135 19 CONTRADICTION 135 PROOF BY CONTRAPOSITIVE 135 REDUCTIO AD ABSURDUM 137 A MATTER OF STYLE 14 1 RECAP 141 EXERCISES 14 1 20 SMALLEST COUNTEREXAMPLE 142 WELL-ORDERING 148 RECAP 153 EXERCISES 153 AND FINALLY 154 21 INDUCTION 155 THE INDUCTION MACHINE 155 THEORETICAL UNDERPINNINGS 157 PROOF BY INDUCTION 157 PROVING EQUATIONS AND INEQUALITIES 160 OTHER EXAMPLES 162 STRONG INDUCTION 163 A MORE COMPLICATED EXAMPLE 165 A MATTER OF STYLE 168 RECAP 168 EXERCISES 168 22 RECURRENCE RELATIONS 171 FIRST-ORDER RECURRENCE RELATIONS 172 SECOND-ORDER RECURRENCE RELATIONS 175 THE CASE OF THE REPEATED ROOT 178 SEQUENCES GENERATED BY POLYNOMIALS 180 RECAP 187 EXERCISES 188 CHAPTER 4 SELF TEST 190 5 FUNCTIONS 193 23 FUNCTIONS 193 DOMAIN AND IMAGE 195 PICTURES OF FUNCTIONS 196 COUNTING FUNCTIONS 197 INVERSE FUNCTIONS 198 COUNTING FUNCTIONS, AGAIN RECAP 203 EXERCISES 203 24 THE PIGEONHOLE PRINCIPLE 205 CANTOR'S THEOREM 208 RECAP 210 EXERCISES 2 10 25 COMPOSITION 211 IDENTITY FUNCTION 2 1 1 RECAP 215 EXERCISES 2 15 26 PERMUTATIONS 216 CYCLE NOTATION 2 17 CALCULATIONS WITH PERMUTATIONS 220 TRANSPOSITIONS 22 1 A GRAPHICAL APPROACH 226 RECAP 228 EXERCISES 228 27 SYMMETRY 231 SYMMETRIES OF A SQUARE 23 1 SYMNIETRIES AS PERMUTATIONS 232 COMBINING SYMMCTRIES 233 FORMAL I)ELINITION OF SYMMETR! '735 RECAP 236 EXERCISES 236 28 ASSORTED NOTATION 236 BIG OH 236 R AND (-) 239 LITTLE OH 240 FLOOR AND CEILING 241 RECAP 212 EXERCISES 242 CHAPTER 5 SELF TEST 242 6 PROBABILITY 245 30 EVEL~TS 249 CONIH~N~LIG E\CRLT\ 251 THE R~RTHD.T! I'ROHLCNI 754 RCC'IP 254 EXCRC~\C\ 255 31 CONDITIONAL PROBABILITY AND INDEPENDENCE 257 INDEPENDENCE 259 INDEPENDENT REPEATED TRIALS 26 1 THE MONTY HALL PROBLEM 262 RECAP 263 EXERCISES 263 32 RANDOM VARIABLES 266 RANDOM VARIABLES AS EVENTS 267 INDEPENDENT RANDOM VARIABLES 269 RECAP 270 EXERCISES 270 33 EXPECTATION 271 LINEARITY OF EXPECTATION 276 PRODUCT OF RANDOM VARIABLES 279 EXPECTED VALUE AS A MEASURE OF CENTRALITY 282 VARIANCE 283 RECAP 287 EXERCISES 287 CHAPTER 6 SELF TEST 289 7 NUMBER THEORY 293 34 DIVIDING 293 DIV AND MOD 296 RECAP 297 EXERCISE5 297 35 GREATEST COMMON DIVISOR 298 CALCULATING THE GCD 299 CORRECTNE5S 30 1 HOUI:;I\T'? 302 AN IMPORTANT THEORCM 304 RCCAP 307 EXCRCI\ES 307 36 MODULAR ARITHMETIC 309 A NEW CONTEXT FOR BA\IC OPERATION\ 309 MODULAR ADDITION AND MULTIPLICATION 3 10 MODULAR SUBTRACTION 3 1 1 MODULAR DIVI\ION 3 13 A NOTE ON NOTATION 3 18 RECAP 318 EXERCISES 3 18 37 THE CHINESE REMAINDER THEOREM 320 SOLVING ONE EQUATION 320 SOLVING TWO EQUATIONS 322 RECAP 324 EXERCISES 324 38 FACTORING 325 INFINITELY MANY PRIMES 327 A FORMULA FOR GREATEST COMMON DIVISOR 328 IRRATIONALITY OF & 329 RECAP 331 EXERCISES 33 1 CHAPTER 7 SELF TEST 335 8 ALGEBRA 337 39 GROUPS 337 OPERATIONS 337 PROPERTIES OF OPERATIONS 338 GROUPS 340 EXAMPLES 342 RECAP 345 EXERCISES 345 40 GROUP ISOMORPHISM 347 THE SAME'? 347 CYCLIC GROUPS 349 RECAP 352 EXERCISES 352 41 SUBGROUPS 353 LAGRANGE'S THEOREM 356 RECAP 359 EXERCISE5 359 42 FCRMAT S L-LTTLT. TTIEOITIN 367 FLR\T PROOF 762 SECOND PROOF 361 TH~RD PROOF 366 EULER'~ THEOREM 767 PR~MAL~TY TE5T1NG 368 RECAP 369 EUERC~CE\ 369 43 PUBLIC KEY CRYPTOYRDPTIY I IR~TRC~CLOCTIC~RI 370 THE PROBLEM PRNATE CORNMUNLCAT~ON IN PUHLLC 770 FACTORLNP 370 WORDS TO NUMBERS 37 1 CRYPTOGRAPHY AND THE LAW 373 RECAP 373 EXERCISES 373 44 PUBLIC KEY CRYPTOGRAPHY II: RABIN'S METHOD 373 SQUARE ROOTS MODULO N 374 THE ENCRYPTION AND DECRYPTION PROCEDURES 378 RECAP 379 EXERCISES 379 45 PUBLIC KEY CRYPTOGRAPHY ILL: RSA 380 THE RSA ENCRYPTION AND DECRYPTION FUNCTIONS 38 1 SECURITY 383 RECAP 384 EXERCISES 384 CHAPTER 8 SELF TEST 385 9 GRAPHS 389 46 FUNDAMENTALS OF GRAPH THEORY 389 MAP COLORING 389 THREE UTILITIES 391 SEVEN BRIDGES 391 WHAT IS A GRAPH? 392 ADJACENCY 393 A MATTER OF DEGREE 394 FURTHER NOTATION AND VOCABULARY 396 RECAP 397 EXERCISES 397 47 SUBGRAPHS 399 INDUCED AND SPANNING SUBGRAPHS 400 CLIQUES AND INDEPENDENT SETS 402 COMPLEMENTS 403 RECAP 404 EXERCISE5 404 48 CONNECTION 406 WALKS 406 PATHS 407 DISCONNECTION 4 10 RECAP 41 1 EXERCISES 4 1 1 49 TREES 413 CYCLES 413 FORESTS AND TREES 413 PROPERTIES OF TREES 4 14 LEAVES 416 SPANNING TREES 4 1 8 RECAP 419 EXERCISES 420 50 EULERIAN GRAPHS 421 NECESSARY CONDITIONS 422 MAIN THEOREMS 423 UNFINISHED BUSINESS 425 RECAP 426 EXERCISES 426 51 COLORING 427 CORE CONCEPTS 427 BIPARTITE GRAPHS 429 THE EASE OF TWO-COLORING AND THE DIFFICULTY OF THREE-COLORING 433 RECAP 434 EXERCISES 434 52 PLANAR GRAPHS 435 DA~LGEROUS CURVES 435 EMBEDDING 436 EULER'S FORMULA 437 NONPLANAR GRAPHS 440 COLORING PLANAR GRAPHS 441 RECAP 444 EXERCISES 444 CHAPTER 9 SELF TEST 446 10 PARTIALLY ORDERED SETS 449 53 FUNDAMENTALS OF PART~ALLY ORDERED SETS 449 WHAT IS ,I POXT" 4-49 NOTATION ,~ND LD,LNYUAPR 451 RCCAP 454 EXCRC~SC\ 455 54 MAX AND MLN 455 RECAP 457 EXERCISES 457 55 LINEAR ORDERS 458 RECAP 460 EXERCISES 461 56 LINEAR EXTENSIONS 461 SORTING 465 LINEAR EXTENSIONS OF INFINITE POSETS 467 RECAP 468 EXERCISES 468 57 DIMENSION 469 REALIZERS 469 DIMENSION 47 1 EMBEDDING 473 RECAP 476 EXERCISES 476 58 LATTICES 477 MEET AND JOIN 477 LATTICES 479 RECAP 481 EXERCISES 482 CHAPTER 10 SELF TEST 483 APPENDICES 487 A LOTS OF HINTS AND COMMENTS; SOME ANSWERS 487 B SOLUTIONS TO SELF TESTS 515 CHAPTER 1 515 CHAPTER 2 516 CHAPTER 3 5 18 CHAPTER 4 520 CHAPTER 5 524 CHAPTER 6 526 CHAPTER 7 530 CHAPTER 8 532 CHAPTER 9 535 CHAPTER L0 539 C GLOSSARY 544 D FUNDAMENTALS 552 NUMBERS 552 OPERATIONS 552 ORDERING 553 COMPLEX NUMBERS 553 SUBSTITUTION 553 INDEX 555
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oclc_num	441656122
open_access_boolean
owner	DE-473 DE-BY-UBG DE-703 DE-634
owner_facet	DE-473 DE-BY-UBG DE-703 DE-634
physical	XXVII, 561 S. Ill.
publishDate	2006
publishDateSearch	2006
publishDateSort	2006
publisher	Thomson Brooks/Cole
record_format	marc
spelling	Scheinerman, Edward Verfasser (DE-588)113762938X aut Mathematics a discrete introduction Edward R. Scheinerman 2. ed., internat. student ed. Belmont, Calif. Thomson Brooks/Cole 2006 XXVII, 561 S. Ill. txt rdacontent n rdamedia nc rdacarrier Informatik (DE-588)4026894-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Informatik (DE-588)4026894-9 s Mathematik (DE-588)4037944-9 s DE-604 SWBplus Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015613383&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Scheinerman, Edward Mathematics a discrete introduction Informatik (DE-588)4026894-9 gnd Mathematik (DE-588)4037944-9 gnd
subject_GND	(DE-588)4026894-9 (DE-588)4037944-9 (DE-588)4151278-9
title	Mathematics a discrete introduction
title_auth	Mathematics a discrete introduction
title_exact_search	Mathematics a discrete introduction
title_exact_search_txtP	Mathematics a discrete introduction
title_full	Mathematics a discrete introduction Edward R. Scheinerman
title_fullStr	Mathematics a discrete introduction Edward R. Scheinerman
title_full_unstemmed	Mathematics a discrete introduction Edward R. Scheinerman
title_short	Mathematics
title_sort	mathematics a discrete introduction
title_sub	a discrete introduction
topic	Informatik (DE-588)4026894-9 gnd Mathematik (DE-588)4037944-9 gnd
topic_facet	Informatik Mathematik Einführung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015613383&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT scheinermanedward mathematicsadiscreteintroduction

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