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Title:	Discrete mathematics elementary and beyond
From:	L. Lovász ; J. Pelikán ; K. Vesztergombi
Person:	Lovász, László 1948- Verfasser aut Pelikán, József Vesztergombi, Katalin
Main Authors:	Lovász, László 1948- (Author), Pelikán, József (Author), Vesztergombi, Katalin (Author)
Format:	Book
Language:	English
Published:	New York [und 7 andere] Springer [2003]
Series:	Undergraduate texts in mathematics
Subjects:	Combinatieleer Combinatória Informatique - Mathématiques Mathématiques Informatik Mathematik Computer science > Mathematics Mathematics Diskrete Mathematik
Online Access:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009959270&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	ix, 290 Seiten Illustrationen, Diagramme
ISBN:	0387955844 0387955852 9780387955841 9780387955858 9798644588923

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adam_text	L. LOVASZ J . PELIKA N K. VESZTERGOMB I DISCRETE MATHEMATICS ELEMENTARY AND BEYOND WITH 95 ILLUSTRATION S SPRINGER CONTENTS PREFACE V LET'S COUNT! 1 1.1 A PARTY 1 1.2 SETS AND THE LIKE ' 4 1.3 THE NUMBER OF SUBSETS 9 1.4 THE APPROXIMATE NUMBER OF SUBSETS 14 1.5 SEQUENCES 15 1.6 PERMUTATIONS 17 1.7 THE NUMBER OF ORDERED SUBSETS 19 1.8 THE NUMBER OF SUBSETS OF A GIVEN SIZE 20 COMBINATORIAL TOOLS 25 2.1 INDUCTION ' 25 2.2 COMPARING AND ESTIMATING NUMBERS 30 2.3 INCLUSION-EXCLUSION 32 2.4 PIGEONHOLES 34 2.5 THE TWIN PARADOX AND THE GOOD OLD LOGARITHM 37 BINOMIAL COEFFICIENTS AND PASCAL'S TRIANGLE 4 3 3.1 THE BINOMIAL THEOREM 43 3.2 DISTRIBUTING PRESENTS 45 3.3 ANAGRAMS .YY '. 46 3.4 DISTRIBUTING MONEY 48 VIII CONTENTS 3.5 PASCAL' S TRIANGL E 49 3.6 IDENTITIE S IN PASCAL' S TRIANGL E 50 3.7 A BIRD'S-EY E VIEW OF PASCAL' S TRIANGLE 54 3.8 AN EAGLE'S-EY E VIEW: FIN E DETAILS 57 4 FIBONACC I NUMBER S 6 5 4.1 FIBONACCI' S EXERCIS E 65 4.2 LOT S OF IDENTITIE S 68 4.3 A FORMULA FOR TH E FIBONACC I NUMBERS 71 5 COMBINATORIA L PROBABILIT Y 7 7 5.1 EVENT S AN D PROBABILITIE S 77 5.2 INDEPENDEN T REPETITIO N OF A N EXPERIMEN T 79 5.3 TH E LAW OF LARG E NUMBER S 80 5.4 TH E LAW OF SMAL L NUMBER S AN D TH E LAW OF VERY LARGE NUM BER S 83 6 INTEGERS , DIVISORS , AN D PRIME S 8 7 6.1 DIVISIBILITY OF INTEGER S 87 6.2 PRIME S AN D THEI R HISTOR Y 88 6.3 FACTORIZATIO N INT O PRIME S 90 6.4 O N TH E SE T OF PRIME S 93 6.5 FERMAT' S "LITTLE " THEORE M 97 6.6 TH E EUCLIDEA N ALGORITH M 99 6.7 CONGRUENCE S 105 6.8 STRANG E NUMBER S ' 107 6.9 NUMBE R THEOR Y AN D COMBINATORIC S 114 6.10 HOW T O TES T WHETHE R A NUMBE R IS A PRIME ? 117 7 GRAPH S 12 5 7.1 EVEN AN D OD D DEGREE S 125 7.2 PATHS , CYCLES , AN D CONNECTIVIT Y 130 7.3 EULERIA N WALK S AN D HAMILTONIA N CYCLES 135 8 TREE S 14 1 8.1 HOW T O DEFINE TREE S YY 141 8.2 HOW T O GRO W TREE S 143 8.3 HOW T O COUN T TREES ? 146 8.4 HOW T O STOR E TREE S 148 8.5 TH E NUMBE R OF UNLABELE D TREES 153 9 FINDIN G TH E OPTIMU M 15 7 9.1 FINDIN G TH E BES T TRE E 157 9.2 TH E TRAVELIN G .SALESMA N PROBLE M 161 1 0 MATCHING S I N GRAPH S 16 5 CONTENTS IX 10.1 A DANCING PROBLEM 165 10.2 ANOTHER MATCHING PROBLEM 167 10.3 THE MAIN THEOREM 169 10.4 HOW TO FIND A PERFECT MATCHING 171 11 COMBINATORIC S IN GEOMETR Y 179 11.1 INTERSECTIONS OF DIAGONALS 179 11.2 COUNTING REGIONS 181 11.3 CONVEX POLYGONS 184 12 EULER'S FORMULA 189 12:1 A PLANET UNDER ATTACK 189 12.2 PLANAR GRAPHS 192 12.3 EULER'S FORMULA FOR POLYHEDRA 194 13 COLORIN G MAP S AND GRAPH S 197 13.1 COLORING REGIONS WITH TWO COLORS 197 13.2 COLORING GRAPHS WITH TWO COLORS 199 13.3 COLORING GRAPHS WITH MANY COLORS 202 13.4 MAP COLORING AND THE FOUR COLOR THEOREM 204 14 FINIT E GEOMETRIES , CODES , LATIN SQUARES , AND OTHE R PRETT Y CREATURE S 21 1 14.1 SMALL EXOTIC WORLDS 211 14.2 FINITE AFFINE AND PROJECTIVE PLANES *. 217 14.3 BLOCK DESIGNS 220 14.4 STEINER SYSTEMS 224 14.5 LATIN SQUARES 229 14.6 CODES 232 15 A GLIMPS E OF COMPLEXIT Y AND CRYPTOGRAPH Y 23 9 15.1 A CONNECTICUT CLASS IN KING ARTHUR' S COURT 239 15.2 CLASSICAL CRYPTOGRAPHY 242 15.3 HOW TO SAVE THE LAST MOVE IN CHESS ' 244 15.4 HOW TO VERIFY A PASSWORD-WITHOUT LEARNING IT : 246 15.5 HOW TO FIND THESE PRIMES 246 15.6 PUBLIC KEY CRYPTOGRAPHY 247 16 ANSWER S T O EXERCISE S 25 1 INDE X 28 7
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author	Lovász, László 1948- Pelikán, József Vesztergombi, Katalin
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spellingShingle	Lovász, László 1948- Pelikán, József Vesztergombi, Katalin Discrete mathematics elementary and beyond Combinatieleer gtt Combinatória larpcal Informatique - Mathématiques Mathématiques Informatik Mathematik Computer science Mathematics Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd
subject_GND	(DE-588)4129143-8
title	Discrete mathematics elementary and beyond
title_auth	Discrete mathematics elementary and beyond
title_exact_search	Discrete mathematics elementary and beyond
title_full	Discrete mathematics elementary and beyond L. Lovász ; J. Pelikán ; K. Vesztergombi
title_fullStr	Discrete mathematics elementary and beyond L. Lovász ; J. Pelikán ; K. Vesztergombi
title_full_unstemmed	Discrete mathematics elementary and beyond L. Lovász ; J. Pelikán ; K. Vesztergombi
title_short	Discrete mathematics
title_sort	discrete mathematics elementary and beyond
title_sub	elementary and beyond
topic	Combinatieleer gtt Combinatória larpcal Informatique - Mathématiques Mathématiques Informatik Mathematik Computer science Mathematics Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd
topic_facet	Combinatieleer Combinatória Informatique - Mathématiques Mathématiques Informatik Mathematik Computer science Mathematics Mathematics Diskrete Mathematik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009959270&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT lovaszlaszlo discretemathematicselementaryandbeyond AT pelikanjozsef discretemathematicselementaryandbeyond AT vesztergombikatalin discretemathematicselementaryandbeyond

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