Invitation to discrete mathematics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford Univ. Press
2009
|
| Edition: | 2nd ed. |
| Subjects: | |
| Online Access: | Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XVII, 443 S. Illustrationen, Diagramme |
| ISBN: | 9780198570431 9780198570424 |
Staff View
MARC
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| 100 | 1 | |a Matoušek, Jiří |d 1963-2015 |e Verfasser |0 (DE-588)124638457 |4 aut | |
| 245 | 1 | 0 | |a Invitation to discrete mathematics |c Jiří Matoušek ; Jaroslav Nešetřil |
| 250 | |a 2nd ed. | ||
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2009 | |
| 300 | |a XVII, 443 S. |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 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 |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Nešetřil, Jaroslav |d 1946- |e Sonstige |0 (DE-588)13380447X |4 oth | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0907/2008021558-b.html |3 Contributor biographical information | |
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Record in the Search Index
| _version_ | 1804143697965613056 |
|---|---|
| adam_text | Contents
Introduction
and basic concepts
1
1.1
An assortment of problems
2
1.2
Numbers and sets: notation
7
1.3
Mathematical induction and other proofs
16
1.4
Functions
25
1.5
Relations
32
1.6
Equivalences and other special types
of relations
36
Orderings
43
2.1
Orderings
and how they can be depicted
43
2.2
Orderings
and linear
orderings
48
2.3
Ordering by inclusion
52
2.4
Large implies tall or wide
55
Combinatorial counting
59
3.1
Functions and subsets
59
3.2
Permutations and factorials
64
3.3
Binomial coefficients
67
3.4
Estimates: an introduction
78
3.5
Estimates: the factorial function
85
3.6
Estimates: binomial coefficients
93
3.7
Inclusion-exclusion principle
98
3.8
The hatcheck lady
&
co.
103
Graphs: an introduction
109
4.1
The notion of a graph; isomorphism
109
4.2
Subgraphs, components, adjacency matrix
118
4.3
Graph score
125
4.4
Eulerian graphs
130
4.5
Eulerian directed graphs
138
4.6
2-connectivity
143
4.7
Triangle-free graphs: an extremal problem
148
xvi Contents
5
Trees 153
5.1 Definition
and characterizations of trees
153
5.2
Isomorphism of trees
159
5.3
Spanning trees of a graph
166
5.4
The minimum spanning tree problem
170
5.5
Jarnik s algorithm and Boruvka s algorithm
176
6
Drawing graphs in the plane
182
6.1
Drawing in the plane and on other surfaces
182
6.2
Cycles in planar graphs
190
6.3
Euler s formula i96
6.4
Coloring maps: the four-color problem
206
7
Double-counting
217
7.1
Parity arguments
217
7.2
Sperner s theorem on independent systems
226
7.3
An extremal problem: forbidden four-cycles
233
8
The number of spanning trees
239
8.1
The result
239
8.2
A proof via score
240
8.3
A proof with vertebrates
242
8.4
A proof using the
Prüfer
code
245
8.5
Proofs working with determinants
247
8.6
The simplest proof?
258
9
Finite
projective
planes
261
9.1
Definition and basic properties
261
9.2
Existence of finite
projective
planes
271
9.3
Orthogonal Latin squares
277
9.4
Combinatorial applications
281
10
Probability and probabilistic proofs
284
10.1
Proofs by counting
284
10.2
Finite probability spaces
291
10.3
Random variables and their expectation
301
10.4
Several applications
307
11
Order from disorder: Ramsey s theorem
317
11.1
A party of six
318
11.2
Ramsey s theorem for graphs
319
11.3
A lower bound for the Ramsey numbers
321
Contents xvii
12
Generating functions
325
12.1
Combinatorial applications of polynomials
325
12.2
Calculation with power series
329
12.3
Fibonacci numbers and the golden section
340
12.4
Binary trees
348
12.5
On rolling the dice
353
12.6
Random walk
354
12.7
Integer partitions
357
13
Applications of linear algebra
364
13.1
Block designs
364
13.2
Fisher s inequality
369
13.3
Covering by complete bipartite graphs
373
13.4
Cycle space of a graph
376
13.5
Circulations and cuts: cycle space revisited
380
13.6
Probabilistic checking
384
Appendix: Prerequisites from algebra
395
Bibliography
402
Hints to selected exercises
407
Index
433
|
| any_adam_object | 1 |
| author | Matoušek, Jiří 1963-2015 |
| author_GND | (DE-588)124638457 (DE-588)13380447X |
| author_facet | Matoušek, Jiří 1963-2015 |
| author_role | aut |
| author_sort | Matoušek, Jiří 1963-2015 |
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| building | Verbundindex |
| bvnumber | BV036970980 |
| callnumber-first | Q - Science |
| callnumber-label | QA39 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 890 |
| ctrlnum | (OCoLC)605035810 (DE-599)BVBBV036970980 |
| 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 | 2nd ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:51:47Z |
| institution | BVB |
| isbn | 9780198570431 9780198570424 |
| language | English |
| lccn | 2008021558 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020885732 |
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| physical | XVII, 443 S. Illustrationen, Diagramme |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Matoušek, Jiří 1963-2015 Verfasser (DE-588)124638457 aut Invitation to discrete mathematics Jiří Matoušek ; Jaroslav Nešetřil 2nd ed. Oxford Oxford Univ. Press 2009 XVII, 443 S. Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Informatik Mathematik Mathematics Computer science Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Diskrete Mathematik (DE-588)4129143-8 s DE-604 Nešetřil, Jaroslav 1946- Sonstige (DE-588)13380447X oth http://www.loc.gov/catdir/enhancements/fy0907/2008021558-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0907/2008021558-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0907/2008021558-t.html Table of contents only Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020885732&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Matoušek, Jiří 1963-2015 Invitation to discrete mathematics Informatik Mathematik Mathematics Computer science Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd |
| subject_GND | (DE-588)4129143-8 (DE-588)4123623-3 |
| title | Invitation to discrete mathematics |
| title_auth | Invitation to discrete mathematics |
| title_exact_search | Invitation to discrete mathematics |
| title_full | Invitation to discrete mathematics Jiří Matoušek ; Jaroslav Nešetřil |
| title_fullStr | Invitation to discrete mathematics Jiří Matoušek ; Jaroslav Nešetřil |
| title_full_unstemmed | Invitation to discrete mathematics Jiří Matoušek ; Jaroslav Nešetřil |
| title_short | Invitation to discrete mathematics |
| title_sort | invitation to discrete mathematics |
| topic | Informatik Mathematik Mathematics Computer science Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd |
| topic_facet | Informatik Mathematik Mathematics Computer science Mathematics Diskrete Mathematik Lehrbuch |
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