Relational mathematics /:
A modern, comprehensive overview providing an easy introduction for applied scientists who are not versed in mathematics.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
[2011]
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
v. 132. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | A modern, comprehensive overview providing an easy introduction for applied scientists who are not versed in mathematics. |
| Beschreibung: | 1 online resource (xiii, 567 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781107089372 9781107101241 1107101247 1107089379 9780511778810 0511778813 9781107095687 1107095689 1107103673 9781107103672 1107092434 9781107092433 |
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| 100 | 1 | |a Schmidt, Gunther, |d 1939- |e author. |1 https://id.oclc.org/worldcat/entity/E39PBJd3PK7TRppVkdp4Ybvj4q |0 http://id.loc.gov/authorities/names/n82090755 | |
| 245 | 1 | 0 | |a Relational mathematics / |c Gunther Schmidt. |
| 264 | 1 | |a Cambridge ; |a New York : |b Cambridge University Press, |c [2011] | |
| 264 | 4 | |c ©2011 | |
| 300 | |a 1 online resource (xiii, 567 pages) : |b illustrations | ||
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| 490 | 1 | |a Encyclopedia of mathematics and its applications ; |v 132 | |
| 504 | |a Includes bibliographical references and index. | ||
| 520 | 8 | |a A modern, comprehensive overview providing an easy introduction for applied scientists who are not versed in mathematics. | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover; Half Title; Series Page; Title; Copyright; Contents; Notes on illustrations; Preface; 1 Introduction; PART I: REPRESENTATIONS OF RELATIONS; 2 Sets, subsets, and elements; 2.1 Set representation; 2.2 Element representation; 2.3 Subset representation; 3 Relations; 3.1 Relation representation; 3.2 Relations describing graphs; 3.3 Relations generated by cuts; 3.4 Relations generated randomly; 3.5 Function representation; 3.6 Permutation representation; 3.7 Partition representation; PART II: OPERATIONS AND CONSTRUCTIONS; 4 Algebraic operations on relations; 4.1 Typing relations. | |
| 505 | 8 | |a 4.2 Boolean operations4.3 Relational operations proper; 4.4 Composite operations; 5 Order and function: the standard view; 5.1 Functions; 5.2 Mappings and points; 5.3 Order and strictorder; 5.4 Equivalence and quotient; 5.5 Transitive closure; 5.6 Congruences; 5.7 Homomorphisms; 6 Relations and vectors; 6.1 Domain and codomain; 6.2 Rectangular zones; 6.3 Independent pair of sets and covering pair of sets; 6.4 Reducing vectors; 6.5 Progressively infinite subsets; 6.6 Stable and absorbant sets; 7 Domain construction; 7.1 Domains of ground type; 7.2 Direct product; 7.3 Direct sum. | |
| 505 | 8 | |a 7.4 Quotient domain7.5 Subset extrusion; 7.6 Direct power; 7.7 Domain permutation; 7.8 Remarks on further constructions; 7.9 Equivalent representations; PART III ALGEBRA; 8 Relation algebra; 8.1 Laws of relation algebra; 8.2 Visualizing the algebraic laws; 8.3 Elementary properties of relations; 8.4 Cancellation properties of residuals and cones; 8.5 Cancellation properties of the symmetric quotient; 8.6 Tarski rule and Point Axiom; 9 Orders and lattices; 9.1 Maxima and minima; 9.2 Bounds and cones; 9.3 Least and greatest elements; 9.4 Greatest lower and least upper bounds; 9.5 Lattices. | |
| 505 | 8 | |a 10 Rectangles, fringes, inverses10.1 Non-enlargeable rectangles; 10.2 Independent pairs and covering pairs of sets; 10.3 Fringes; 10.4 Difunctional relations; 10.5 Ferrers relations; 10.6 Block-transitive relations; 10.7 Inverses; 11 Concept analysis; 11.1 Row and column spaces; 11.2 Factorizations; 11.3 Concept lattices; 11.4 Closure and contact; 11.5 Completion of an ordering; PART IV APPLICATIONS; 12 Orderings: an advanced view; 12.1 Additional properties of orderings; 12.2 The hierarchy of orderings; 12.3 Block-transitive strictorders; 12.4 Order extensions. | |
| 505 | 8 | |a 12.5 Relating preference and utility12.6 Intervalorders and interval graphs; 13 Preference and indifference; 13.1 Duality; 13.2 Modelling indifference; 13.3 Modelling thresholds; 13.4 Preference structures; 14 Aggregating preferences; 14.1 Modelling preferences; 14.2 Introductory example; 14.3 Relational measures; 14.4 Relational integration; 14.5 Defining relational measures; 14.6 De Morgan triples; 15 Relational graph theory; 15.1 Reducibility and irreducibility; 15.2 Homogeneous difunctional relations; 15.3 Subsets characterized by relational properties; 16 Standard Galois mechanisms. | |
| 546 | |a English. | ||
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| contents | Cover; Half Title; Series Page; Title; Copyright; Contents; Notes on illustrations; Preface; 1 Introduction; PART I: REPRESENTATIONS OF RELATIONS; 2 Sets, subsets, and elements; 2.1 Set representation; 2.2 Element representation; 2.3 Subset representation; 3 Relations; 3.1 Relation representation; 3.2 Relations describing graphs; 3.3 Relations generated by cuts; 3.4 Relations generated randomly; 3.5 Function representation; 3.6 Permutation representation; 3.7 Partition representation; PART II: OPERATIONS AND CONSTRUCTIONS; 4 Algebraic operations on relations; 4.1 Typing relations. 4.2 Boolean operations4.3 Relational operations proper; 4.4 Composite operations; 5 Order and function: the standard view; 5.1 Functions; 5.2 Mappings and points; 5.3 Order and strictorder; 5.4 Equivalence and quotient; 5.5 Transitive closure; 5.6 Congruences; 5.7 Homomorphisms; 6 Relations and vectors; 6.1 Domain and codomain; 6.2 Rectangular zones; 6.3 Independent pair of sets and covering pair of sets; 6.4 Reducing vectors; 6.5 Progressively infinite subsets; 6.6 Stable and absorbant sets; 7 Domain construction; 7.1 Domains of ground type; 7.2 Direct product; 7.3 Direct sum. 7.4 Quotient domain7.5 Subset extrusion; 7.6 Direct power; 7.7 Domain permutation; 7.8 Remarks on further constructions; 7.9 Equivalent representations; PART III ALGEBRA; 8 Relation algebra; 8.1 Laws of relation algebra; 8.2 Visualizing the algebraic laws; 8.3 Elementary properties of relations; 8.4 Cancellation properties of residuals and cones; 8.5 Cancellation properties of the symmetric quotient; 8.6 Tarski rule and Point Axiom; 9 Orders and lattices; 9.1 Maxima and minima; 9.2 Bounds and cones; 9.3 Least and greatest elements; 9.4 Greatest lower and least upper bounds; 9.5 Lattices. 10 Rectangles, fringes, inverses10.1 Non-enlargeable rectangles; 10.2 Independent pairs and covering pairs of sets; 10.3 Fringes; 10.4 Difunctional relations; 10.5 Ferrers relations; 10.6 Block-transitive relations; 10.7 Inverses; 11 Concept analysis; 11.1 Row and column spaces; 11.2 Factorizations; 11.3 Concept lattices; 11.4 Closure and contact; 11.5 Completion of an ordering; PART IV APPLICATIONS; 12 Orderings: an advanced view; 12.1 Additional properties of orderings; 12.2 The hierarchy of orderings; 12.3 Block-transitive strictorders; 12.4 Order extensions. 12.5 Relating preference and utility12.6 Intervalorders and interval graphs; 13 Preference and indifference; 13.1 Duality; 13.2 Modelling indifference; 13.3 Modelling thresholds; 13.4 Preference structures; 14 Aggregating preferences; 14.1 Modelling preferences; 14.2 Introductory example; 14.3 Relational measures; 14.4 Relational integration; 14.5 Defining relational measures; 14.6 De Morgan triples; 15 Relational graph theory; 15.1 Reducibility and irreducibility; 15.2 Homogeneous difunctional relations; 15.3 Subsets characterized by relational properties; 16 Standard Galois mechanisms. |
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| id | ZDB-4-EBA-ocn847526851 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:21:27Z |
| institution | BVB |
| isbn | 9781107089372 9781107101241 1107101247 1107089379 9780511778810 0511778813 9781107095687 1107095689 1107103673 9781107103672 1107092434 9781107092433 |
| language | English |
| oclc_num | 847526851 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (xiii, 567 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Schmidt, Gunther, 1939- author. https://id.oclc.org/worldcat/entity/E39PBJd3PK7TRppVkdp4Ybvj4q http://id.loc.gov/authorities/names/n82090755 Relational mathematics / Gunther Schmidt. Cambridge ; New York : Cambridge University Press, [2011] ©2011 1 online resource (xiii, 567 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier text file rda Encyclopedia of mathematics and its applications ; 132 Includes bibliographical references and index. A modern, comprehensive overview providing an easy introduction for applied scientists who are not versed in mathematics. Print version record. Cover; Half Title; Series Page; Title; Copyright; Contents; Notes on illustrations; Preface; 1 Introduction; PART I: REPRESENTATIONS OF RELATIONS; 2 Sets, subsets, and elements; 2.1 Set representation; 2.2 Element representation; 2.3 Subset representation; 3 Relations; 3.1 Relation representation; 3.2 Relations describing graphs; 3.3 Relations generated by cuts; 3.4 Relations generated randomly; 3.5 Function representation; 3.6 Permutation representation; 3.7 Partition representation; PART II: OPERATIONS AND CONSTRUCTIONS; 4 Algebraic operations on relations; 4.1 Typing relations. 4.2 Boolean operations4.3 Relational operations proper; 4.4 Composite operations; 5 Order and function: the standard view; 5.1 Functions; 5.2 Mappings and points; 5.3 Order and strictorder; 5.4 Equivalence and quotient; 5.5 Transitive closure; 5.6 Congruences; 5.7 Homomorphisms; 6 Relations and vectors; 6.1 Domain and codomain; 6.2 Rectangular zones; 6.3 Independent pair of sets and covering pair of sets; 6.4 Reducing vectors; 6.5 Progressively infinite subsets; 6.6 Stable and absorbant sets; 7 Domain construction; 7.1 Domains of ground type; 7.2 Direct product; 7.3 Direct sum. 7.4 Quotient domain7.5 Subset extrusion; 7.6 Direct power; 7.7 Domain permutation; 7.8 Remarks on further constructions; 7.9 Equivalent representations; PART III ALGEBRA; 8 Relation algebra; 8.1 Laws of relation algebra; 8.2 Visualizing the algebraic laws; 8.3 Elementary properties of relations; 8.4 Cancellation properties of residuals and cones; 8.5 Cancellation properties of the symmetric quotient; 8.6 Tarski rule and Point Axiom; 9 Orders and lattices; 9.1 Maxima and minima; 9.2 Bounds and cones; 9.3 Least and greatest elements; 9.4 Greatest lower and least upper bounds; 9.5 Lattices. 10 Rectangles, fringes, inverses10.1 Non-enlargeable rectangles; 10.2 Independent pairs and covering pairs of sets; 10.3 Fringes; 10.4 Difunctional relations; 10.5 Ferrers relations; 10.6 Block-transitive relations; 10.7 Inverses; 11 Concept analysis; 11.1 Row and column spaces; 11.2 Factorizations; 11.3 Concept lattices; 11.4 Closure and contact; 11.5 Completion of an ordering; PART IV APPLICATIONS; 12 Orderings: an advanced view; 12.1 Additional properties of orderings; 12.2 The hierarchy of orderings; 12.3 Block-transitive strictorders; 12.4 Order extensions. 12.5 Relating preference and utility12.6 Intervalorders and interval graphs; 13 Preference and indifference; 13.1 Duality; 13.2 Modelling indifference; 13.3 Modelling thresholds; 13.4 Preference structures; 14 Aggregating preferences; 14.1 Modelling preferences; 14.2 Introductory example; 14.3 Relational measures; 14.4 Relational integration; 14.5 Defining relational measures; 14.6 De Morgan triples; 15 Relational graph theory; 15.1 Reducibility and irreducibility; 15.2 Homogeneous difunctional relations; 15.3 Subsets characterized by relational properties; 16 Standard Galois mechanisms. English. Computer science Mathematics. http://id.loc.gov/authorities/subjects/sh85042295 Operations research Mathematics. Informatique Mathématiques. Recherche opérationnelle Mathématiques. COMPUTERS Computer Literacy. bisacsh COMPUTERS Computer Science. bisacsh COMPUTERS Data Processing. bisacsh COMPUTERS Hardware General. bisacsh COMPUTERS Information Technology. bisacsh COMPUTERS Machine Theory. bisacsh COMPUTERS Reference. bisacsh Computer science Mathematics fast Operations research Mathematics fast has work: Relational mathematics (Text) https://id.oclc.org/worldcat/entity/E39PCGjqwbCqfq8VmKK6XhvDmb https://id.oclc.org/worldcat/ontology/hasWork Print version: Schmidt, Gunther, 1939- Relational mathematics. Cambridge ; New York : Cambridge University Press, ©2011 9780521762687 (DLC) 2011280047 (OCoLC)696115284 Encyclopedia of mathematics and its applications ; v. 132. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569353 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569353 Volltext |
| spellingShingle | Schmidt, Gunther, 1939- Relational mathematics / Encyclopedia of mathematics and its applications ; Cover; Half Title; Series Page; Title; Copyright; Contents; Notes on illustrations; Preface; 1 Introduction; PART I: REPRESENTATIONS OF RELATIONS; 2 Sets, subsets, and elements; 2.1 Set representation; 2.2 Element representation; 2.3 Subset representation; 3 Relations; 3.1 Relation representation; 3.2 Relations describing graphs; 3.3 Relations generated by cuts; 3.4 Relations generated randomly; 3.5 Function representation; 3.6 Permutation representation; 3.7 Partition representation; PART II: OPERATIONS AND CONSTRUCTIONS; 4 Algebraic operations on relations; 4.1 Typing relations. 4.2 Boolean operations4.3 Relational operations proper; 4.4 Composite operations; 5 Order and function: the standard view; 5.1 Functions; 5.2 Mappings and points; 5.3 Order and strictorder; 5.4 Equivalence and quotient; 5.5 Transitive closure; 5.6 Congruences; 5.7 Homomorphisms; 6 Relations and vectors; 6.1 Domain and codomain; 6.2 Rectangular zones; 6.3 Independent pair of sets and covering pair of sets; 6.4 Reducing vectors; 6.5 Progressively infinite subsets; 6.6 Stable and absorbant sets; 7 Domain construction; 7.1 Domains of ground type; 7.2 Direct product; 7.3 Direct sum. 7.4 Quotient domain7.5 Subset extrusion; 7.6 Direct power; 7.7 Domain permutation; 7.8 Remarks on further constructions; 7.9 Equivalent representations; PART III ALGEBRA; 8 Relation algebra; 8.1 Laws of relation algebra; 8.2 Visualizing the algebraic laws; 8.3 Elementary properties of relations; 8.4 Cancellation properties of residuals and cones; 8.5 Cancellation properties of the symmetric quotient; 8.6 Tarski rule and Point Axiom; 9 Orders and lattices; 9.1 Maxima and minima; 9.2 Bounds and cones; 9.3 Least and greatest elements; 9.4 Greatest lower and least upper bounds; 9.5 Lattices. 10 Rectangles, fringes, inverses10.1 Non-enlargeable rectangles; 10.2 Independent pairs and covering pairs of sets; 10.3 Fringes; 10.4 Difunctional relations; 10.5 Ferrers relations; 10.6 Block-transitive relations; 10.7 Inverses; 11 Concept analysis; 11.1 Row and column spaces; 11.2 Factorizations; 11.3 Concept lattices; 11.4 Closure and contact; 11.5 Completion of an ordering; PART IV APPLICATIONS; 12 Orderings: an advanced view; 12.1 Additional properties of orderings; 12.2 The hierarchy of orderings; 12.3 Block-transitive strictorders; 12.4 Order extensions. 12.5 Relating preference and utility12.6 Intervalorders and interval graphs; 13 Preference and indifference; 13.1 Duality; 13.2 Modelling indifference; 13.3 Modelling thresholds; 13.4 Preference structures; 14 Aggregating preferences; 14.1 Modelling preferences; 14.2 Introductory example; 14.3 Relational measures; 14.4 Relational integration; 14.5 Defining relational measures; 14.6 De Morgan triples; 15 Relational graph theory; 15.1 Reducibility and irreducibility; 15.2 Homogeneous difunctional relations; 15.3 Subsets characterized by relational properties; 16 Standard Galois mechanisms. Computer science Mathematics. http://id.loc.gov/authorities/subjects/sh85042295 Operations research Mathematics. Informatique Mathématiques. Recherche opérationnelle Mathématiques. COMPUTERS Computer Literacy. bisacsh COMPUTERS Computer Science. bisacsh COMPUTERS Data Processing. bisacsh COMPUTERS Hardware General. bisacsh COMPUTERS Information Technology. bisacsh COMPUTERS Machine Theory. bisacsh COMPUTERS Reference. bisacsh Computer science Mathematics fast Operations research Mathematics fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85042295 |
| title | Relational mathematics / |
| title_auth | Relational mathematics / |
| title_exact_search | Relational mathematics / |
| title_full | Relational mathematics / Gunther Schmidt. |
| title_fullStr | Relational mathematics / Gunther Schmidt. |
| title_full_unstemmed | Relational mathematics / Gunther Schmidt. |
| title_short | Relational mathematics / |
| title_sort | relational mathematics |
| topic | Computer science Mathematics. http://id.loc.gov/authorities/subjects/sh85042295 Operations research Mathematics. Informatique Mathématiques. Recherche opérationnelle Mathématiques. COMPUTERS Computer Literacy. bisacsh COMPUTERS Computer Science. bisacsh COMPUTERS Data Processing. bisacsh COMPUTERS Hardware General. bisacsh COMPUTERS Information Technology. bisacsh COMPUTERS Machine Theory. bisacsh COMPUTERS Reference. bisacsh Computer science Mathematics fast Operations research Mathematics fast |
| topic_facet | Computer science Mathematics. Operations research Mathematics. Informatique Mathématiques. Recherche opérationnelle Mathématiques. COMPUTERS Computer Literacy. COMPUTERS Computer Science. COMPUTERS Data Processing. COMPUTERS Hardware General. COMPUTERS Information Technology. COMPUTERS Machine Theory. COMPUTERS Reference. Computer science Mathematics Operations research Mathematics |
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| work_keys_str_mv | AT schmidtgunther relationalmathematics |