A course in discrete mathematical structures:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Imperial College Press
2012
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 626 S. Ill., graph. Darst. |
| ISBN: | 1848166966 9781848166967 1848167075 9781848167070 |
Internformat
MARC
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| 100 | 1 | |a Vermani, Lekh R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A course in discrete mathematical structures |c L. R. Vermani ; Shalini Vermani |
| 264 | 1 | |a London |b Imperial College Press |c 2012 | |
| 300 | |a XIV, 626 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-027002386 | ||
Datensatz im Suchindex
| _version_ | 1804151740395683840 |
|---|---|
| adam_text | CONTENTS
Preface xiii
1. Sets 1
1.1 Preliminaries ............................................. 1
1.2 Algebra, of Sets........................................... 4
1.3 Venn Diagrams.............................................. 9
1.4 Power Set................................................. 10
1.5 Countable Sets............................................ 11
1.6 Some Special Maps (Functions)............................. 17
1.6.1 The characteristic function....................... 21
1.7 Partitions of Sets........................................ 22
1.8 The Minsefc and Maxset Normal Forms....................... 24
1.9 Multisets................................................. 31
2. Propositional Calculus and Logic
2.1 Propositions..........................................
2.2 Compositions of Propositions..........................
2.3 Truth Tables and Applications.........................
2.4 Some Further Applications of Logic....................
2.5 Functionally Complete Set of Connectives..............
2.6 The Connectives NAND and NOR..........................
41
41
43
45
55
63
64
3. More on Sets 69
3.1 The Principle of Inclusion and Exclusion.............. 69
3.2 The Pigeonhole Principle.............................. 81
3.2.1 Some typical applications
of the pigeonhole principle................... 82
Vll
A Course in Discrete Mathematical Structures
viii
3.3 Binary Relations...................................... 89
3.3.1 Relations....................................... 89
3.3.2 Equivalence relations........................... 89
3.3.3 Union, intersection and inverse of relations . . . 91
3.3.4 Composition of relations........................ 93
3.3.5 The matrix of a relation........................ 95
3.3.6 Closure operations on relations................. 98
4. Some Counting Techniques 107
4.1 The Principle of Mathematical Induction................ 107
4.2 Strong Induction....................................... 114
4.3 Arithmetic. Geometric and Arithmetic-Geometric
Series................................................. 131
4.4 Permutations and Combinations.......................... 144
4.4.1 Rules of product and sum ...................... 144
4.4.2 Permutations................................... 147
4.4.3 The arrangements of objects that are not
all distinct................................... 149
4.4.4 Combinations................................... 152
4.4.5 Generation of permutations
and combinations............................... 156
5. Recurrence Relations 167
5.1 Partial Fractions..................................... 167
5.1.1 Rational functions............................. 167
5.1.2 Partial fractions.............................. 168
5.1.3 Procedure for resolving into partial
fractions..................................... 170
5.1.4 Some solved examples........................... 173
5.2 Recurrence Relations: Preliminaries................... 180
5.2.1 Homogeneous solutions.......................... 183
5.2.2 Particular solutions........................... 187
5.2.3 Solution by the method of generating
functions..................................... 193
5.2.4 Some typical examples.......................... 197
5.2.5 Recurrence relations reducible to linear
recurrence relations.......................... 205
ix
213
213
216
221
241
241
261
265
271
281
298
309
313
316
319
325
325
343
343
350
362
376
376
384
388
395
400
416
443
443
449
451
455
457
Contents
Partially Ordered Sets
6.1 Preliminaries .........................
6.2 Hasse Diagrams.........................
6.3 Chains and Antichains in Posets........
Graphs
7.1 Preliminaries and Graph Terminology . .
7.1.1 Some typical examples..........
7.2 Paths and Circuits.....................
7.3 Shortest Path in Weighted Graphs ....
7.4 Eulerian Paths and Circuits............
7.5 Hamiltonian Paths and Circuits.........
7.6 Planar Graphs..........................
7.6.1 Applications...................
7.6.2 Some further examples..........
7.6.3 Graph colouring................
7.7 Matrix Representations of Graphs.......
7.7.1 Adjacency matrix...............
Trees
8.1 Introduction and Elementary Properties .
8.2 Rooted Trees...........................
8.3 Tree Searching or Traversing a Tree ....
8.4 Applications of Trees..................
8.4.1 Prefix codes...................
8.4.2 Binary search trees............
8.4.3 On counting trees..............
8.4.4 Some further examples..........
8.5 Spanning Trees and Cut-Sets ...........
8.6 Minimal/Minimiim/Shortest Spanning Tree
Groups
9.1 Groups: Preliminaries..................
9.2 Subgroups..............................
9.2.1 Lagrange’s theorem.............
9.3 Quotient Groups........................
9.4 Symmetric Groups.......................
A Course in Discrete Mathematical Structures
Rings 467
10.1 Rings................................................. 467
10.2 Polynomial Rings...................................... 470
10.3 Quotient Rings and Homomorphisms...................... 474
Fields arid Vector Spaces 481
11.1 Fields ............................................... 481
11.1.1 Field extensions and minimal polynomial .... 484
11.1.2 Characteristic of a field..................... 485
11.1.3 Splitting field ............................... 485
11.2 Vector Spaces......................................... 491
11.2.1 Basis of a vector space........................ 494
11.2.2 Subspaces and quotient spaces...................498
11.2.3 Linear transformations......................... 504
Lattices and Boolean Algebra 509
12.1 Lattices.............................................. 509
12.2 Lattices as Algebraic Systems......................... 515
12.3 Sublattices and Homomorphisms......................... 521
12.4 Distributive and Modular Lattices......................525
12.5 Complemented Lattices................................. 541
12.6 Boolean Algebras...................................... 545
12.7 Boolean Polynomials and Boolean Functions..............554
12.8 Switching (or Logical) Circuits ...................... 567
Matrices. Systems of Linear Equations and Eigen Values 577
13.1 Linear System of Equations............................ 577
13.1.1 Rank of a matrix .............................. 577
13.1.2 Linear system of equations..................... 578
13.2 Elementary Row Operations, Gaussian Elimination ... 581
13.2.1 Elementary row operations...................... 581
13.2.2 Gaussian elimination in matrix form............ 583
13.2.3 Gaussian elimination method.................... 585
13.2.4 Direct methods for the solution of linear
system of equations........................... 591
Contents
xi
13.2.5 Method of factorization.......................... 594
13.2.6 Some additional examples ........................ 598
13.3 Eigen Values............................................... 600
13.3.1 Eigen values and eigen vectors................... 603
Bibliography 613
Index 615
|
| any_adam_object | 1 |
| author | Vermani, Lekh R. Vermani, Shalini |
| author_facet | Vermani, Lekh R. Vermani, Shalini |
| author_role | aut aut |
| author_sort | Vermani, Lekh R. |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.6 |
| dewey-search | 511.6 |
| dewey-sort | 3511.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-10T00:59:37Z |
| institution | BVB |
| isbn | 1848166966 9781848166967 1848167075 9781848167070 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027002386 |
| oclc_num | 808630186 |
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| spelling | Vermani, Lekh R. Verfasser aut A course in discrete mathematical structures L. R. Vermani ; Shalini Vermani London Imperial College Press 2012 XIV, 626 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computermathematik (DE-588)4788218-9 gnd rswk-swf Informatik (DE-588)4026894-9 gnd rswk-swf Informatik (DE-588)4026894-9 s Computermathematik (DE-588)4788218-9 s DE-604 Vermani, Shalini Verfasser aut Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027002386&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vermani, Lekh R. Vermani, Shalini A course in discrete mathematical structures Computermathematik (DE-588)4788218-9 gnd Informatik (DE-588)4026894-9 gnd |
| subject_GND | (DE-588)4788218-9 (DE-588)4026894-9 |
| title | A course in discrete mathematical structures |
| title_auth | A course in discrete mathematical structures |
| title_exact_search | A course in discrete mathematical structures |
| title_full | A course in discrete mathematical structures L. R. Vermani ; Shalini Vermani |
| title_fullStr | A course in discrete mathematical structures L. R. Vermani ; Shalini Vermani |
| title_full_unstemmed | A course in discrete mathematical structures L. R. Vermani ; Shalini Vermani |
| title_short | A course in discrete mathematical structures |
| title_sort | a course in discrete mathematical structures |
| topic | Computermathematik (DE-588)4788218-9 gnd Informatik (DE-588)4026894-9 gnd |
| topic_facet | Computermathematik Informatik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027002386&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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