Discrete mathematics: elementary and beyond
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [und 7 andere]
Springer
[2003]
|
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| 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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Record in the Search Index
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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 |
| any_adam_object | 1 |
| author | Lovász, László 1948- Pelikán, József Vesztergombi, Katalin |
| author_GND | (DE-588)108767337 (DE-588)110869931 |
| author_facet | Lovász, László 1948- Pelikán, József Vesztergombi, Katalin |
| author_role | aut aut aut |
| author_sort | Lovász, László 1948- |
| author_variant | l l ll j p jp k v kv |
| building | Verbundindex |
| bvnumber | BV014683661 |
| callnumber-first | Q - Science |
| callnumber-label | QA39 |
| callnumber-raw | QA39.3 |
| callnumber-search | QA39.3 |
| callnumber-sort | QA 239.3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 110 SK 170 SK 890 |
| classification_tum | DAT 540f |
| ctrlnum | (OCoLC)50494481 (DE-599)BVBBV014683661 |
| 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 | Informatik Mathematik |
| format | Book |
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| indexdate | 2025-03-28T17:07:57Z |
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| isbn | 0387955844 0387955852 9780387955841 9780387955858 9798644588923 |
| language | English |
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| physical | ix, 290 Seiten Illustrationen, Diagramme |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in mathematics |
| spelling | Lovász, László 1948- Verfasser (DE-588)108767337 aut Discrete mathematics elementary and beyond L. Lovász ; J. Pelikán ; K. Vesztergombi New York [und 7 andere] Springer [2003] © 2003 ix, 290 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Hier auch später erschienene, unveränderte Nachdrucke Combinatieleer gtt Combinatória larpcal Informatique - Mathématiques Mathématiques Informatik Mathematik Computer science Mathematics Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf Diskrete Mathematik (DE-588)4129143-8 s DE-604 Pelikán, József Verfasser aut Vesztergombi, Katalin Verfasser (DE-588)110869931 aut Erscheint auch als Online-Ausgabe 978-0-387-21777-2 DNB Datenaustausch application/pdf 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 Inhaltsverzeichnis |
| 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 |
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