Discrete mathematics: elementary and beyond
"This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2003
|
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of discrete mathematics, mostly from the areas of combinatorics and graph theory, with a little number theory, probability, and combinatorial geometry. Wherever possible, the authors use proofs and problem solving to help students understand the solutions to problems. In addition, there are numerous examples, figures, and exercises spread throughout the book."--BOOK JACKET. |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | IX, 290 S. Ill., graph. Darst. |
| ISBN: | 0387955844 0387955852 9780387955841 9780387955858 9798644588923 |
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| 490 | 0 | |a Undergraduate texts in mathematics | |
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| 520 | 1 | |a "This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of discrete mathematics, mostly from the areas of combinatorics and graph theory, with a little number theory, probability, and combinatorial geometry. Wherever possible, the authors use proofs and problem solving to help students understand the solutions to problems. In addition, there are numerous examples, figures, and exercises spread throughout the book."--BOOK JACKET. | |
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| 650 | 4 | |a Informatik | |
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Datensatz im Suchindex
| _version_ | 1804129431115005952 |
|---|---|
| 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 |
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| callnumber-label | QA39 |
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| callnumber-search | QA39.3 |
| callnumber-sort | QA 239.3 |
| callnumber-subject | QA - Mathematics |
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| classification_tum | DAT 540f |
| ctrlnum | (OCoLC)50494481 (DE-599)BVBBV014683661 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
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| indexdate | 2024-07-09T19:05:01Z |
| institution | BVB |
| isbn | 0387955844 0387955852 9780387955841 9780387955858 9798644588923 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009959270 |
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| physical | IX, 290 S. Ill., graph. Darst. |
| publishDate | 2003 |
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| spelling | Lovász, László 1948- Verfasser (DE-588)108767337 aut Discrete mathematics elementary and beyond L. Lovász ; J. Pelikán ; K. Vesztergombi New York [u.a.] Springer 2003 IX, 290 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Hier auch später erschienene, unveränderte Nachdrucke "This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of discrete mathematics, mostly from the areas of combinatorics and graph theory, with a little number theory, probability, and combinatorial geometry. Wherever possible, the authors use proofs and problem solving to help students understand the solutions to problems. In addition, there are numerous examples, figures, and exercises spread throughout the book."--BOOK JACKET. 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 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 |
| 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 |
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