Application-oriented algebra: an introduction to discrete mathematics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Harper & Row
1977
|
| Schriftenreihe: | The IEP series in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 362 S. Ill., graph. Darst. |
| ISBN: | 0700225048 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV006503891 | ||
| 003 | DE-604 | ||
| 005 | 19991130 | ||
| 007 | t | ||
| 008 | 930210s1977 ad|| |||| 00||| eng d | ||
| 020 | |a 0700225048 |9 0-7002-2504-8 | ||
| 035 | |a (OCoLC)7760051 | ||
| 035 | |a (DE-599)BVBBV006503891 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-739 |a DE-83 |a DE-188 | ||
| 050 | 0 | |a QA154.2 | |
| 082 | 0 | |a 512 | |
| 084 | |a SK 200 |0 (DE-625)143223: |2 rvk | ||
| 100 | 1 | |a Fisher, James L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Application-oriented algebra |b an introduction to discrete mathematics |c James L. Fisher |
| 264 | 1 | |a New York [u.a.] |b Harper & Row |c 1977 | |
| 300 | |a XVIII, 362 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a The IEP series in mathematics | |
| 650 | 4 | |a Algebra | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004137182&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-004137182 | ||
Datensatz im Suchindex
| _version_ | 1804120766774509568 |
|---|---|
| adam_text | Contents
Preface ix
Note to the Reader xm
List of Symbols
Chapter 1
Basic Concepts 1
1.1 Sets 1
2 Binary Relations 3
13 Partially Ordered Sets 5
1.4 Equivalence Relations 8
1.5 Functions 11
1.6 Induction 14
1.7 Algorithms 18
Chapter 2
Partially Ordered Sets 23
2.1 Introduction 25
2.2 Hasse Diagrams 27
23 Subposets, Isomorphisms, and Order Preserving Maps 31
v
vi Contents
•2.4 Weak Orders 37
•2.5 Semiorders 40
*2.6 Interval Orders 48
•2.7 Social Choice 51
Chapter 3
Graphs 60
3.1 Introduction 60
3.2 Chains, Cycles, and Coverings 62
3.3 Subgraphs and Spanning Subgraphs 65
3.4 Trees 68
3.5 Maximal Spanning Subtrees 72
3.6 Directed Graphs 74
3.7 Rooted Trees 76
3.8 Critical Path Method 82
3.9 Flows in Networks 90
Chapter 4
Boolean Algebra 100
4.1 Introduction 100
4.2 Finite Boolean Algebras 105
4.3 Switching Circuits 107
4.4 Boolean Polynomials and Disjunctive Normal Form 111
4.5 Minimization of Boolean Polynomials 120
•4.6 Decomposition of Functions 126
Chapter 5
Finite Machines 131
5.1 Introduction 131
5.2 State Tables and State Diagrams 133
5.3 Simple Properties 135
5.4 Dynamics 137
5.5 Behavior and Minimization 144
•5.6 Construction 158
Chapter 6
Languages 163
*6.1 Introduction 163
•6.2 Context Free Languages 166
•6.3 Regular Language and Finite State Machines 174
* Asterisk indicates optional sections.
Contents vii
Chapter 7
Groups 179
7.1 Introduction 179
7.2 Semigroups 180
7.3 Groups 184
7.4 Subgroups 189
7.5 Permutation Groups 193
7.6 Homomorphisms 198
7.7 Counting Symmetries 204
•7.8 Monoids and Machines 216
*7.9 Quotient Groups 224
Chapter 8
Modular Arithmetic 228
8.1 Introduction 228
8.2 The Integers 229
8.3 The Euclidean Algorithm 233
8.4 The Chinese Remainder Theorem 236
8.5 The Integers Modulo n 243
8.6 Euclidean Domains 248
8.7 Modules 254
•8.8 Rings and Homomorphisms 264
Chapter 9
Coding Theory 268
9.1 Introduction 268
9.2 Cryptography 269
93 Matrix Encodings 278
•9.4 Scrambled Codes 284
95 The Hamming Metric 294
9.6 Binary Group Codes 297
•9.7 Equivalent Codes 303
•9.8 Addressing Systems for Graphs 307
Chapter 10
Finite Fields 320
10.1 Introduction 320
10.2 Structure of Finite Fields 321
10J Existence of Finite Fields 328
* Asterisk indicates optional sections.
viii Contents
•10.4 Latin Squares 335
10.5 Fields of Fractions 338
10.6 Polynomial Codes 339
10.7 BCH Codes 340
Chapter 11
Universal Algebra 349
Index 357
* Asterisk indicates optional sections.
|
| any_adam_object | 1 |
| author | Fisher, James L. |
| author_facet | Fisher, James L. |
| author_role | aut |
| author_sort | Fisher, James L. |
| author_variant | j l f jl jlf |
| building | Verbundindex |
| bvnumber | BV006503891 |
| callnumber-first | Q - Science |
| callnumber-label | QA154 |
| callnumber-raw | QA154.2 |
| callnumber-search | QA154.2 |
| callnumber-sort | QA 3154.2 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 200 |
| ctrlnum | (OCoLC)7760051 (DE-599)BVBBV006503891 |
| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01178nam a2200325 c 4500</leader><controlfield tag="001">BV006503891</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19991130 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">930210s1977 ad|| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0700225048</subfield><subfield code="9">0-7002-2504-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)7760051</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV006503891</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-739</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA154.2</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 200</subfield><subfield code="0">(DE-625)143223:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Fisher, James L.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Application-oriented algebra</subfield><subfield code="b">an introduction to discrete mathematics</subfield><subfield code="c">James L. Fisher</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Harper & Row</subfield><subfield code="c">1977</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVIII, 362 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">The IEP series in mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebra</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004137182&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-004137182</subfield></datafield></record></collection> |
| id | DE-604.BV006503891 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:47:18Z |
| institution | BVB |
| isbn | 0700225048 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004137182 |
| oclc_num | 7760051 |
| open_access_boolean | |
| owner | DE-739 DE-83 DE-188 |
| owner_facet | DE-739 DE-83 DE-188 |
| physical | XVIII, 362 S. Ill., graph. Darst. |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Harper & Row |
| record_format | marc |
| series2 | The IEP series in mathematics |
| spelling | Fisher, James L. Verfasser aut Application-oriented algebra an introduction to discrete mathematics James L. Fisher New York [u.a.] Harper & Row 1977 XVIII, 362 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier The IEP series in mathematics Algebra HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004137182&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fisher, James L. Application-oriented algebra an introduction to discrete mathematics Algebra |
| title | Application-oriented algebra an introduction to discrete mathematics |
| title_auth | Application-oriented algebra an introduction to discrete mathematics |
| title_exact_search | Application-oriented algebra an introduction to discrete mathematics |
| title_full | Application-oriented algebra an introduction to discrete mathematics James L. Fisher |
| title_fullStr | Application-oriented algebra an introduction to discrete mathematics James L. Fisher |
| title_full_unstemmed | Application-oriented algebra an introduction to discrete mathematics James L. Fisher |
| title_short | Application-oriented algebra |
| title_sort | application oriented algebra an introduction to discrete mathematics |
| title_sub | an introduction to discrete mathematics |
| topic | Algebra |
| topic_facet | Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004137182&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT fisherjamesl applicationorientedalgebraanintroductiontodiscretemathematics |