Sets for mathematics:
Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. This book, first published in 2003, uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common ph...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2003
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| Schlagwörter: | |
| Links: | https://doi.org/10.1017/CBO9780511755460 https://doi.org/10.1017/CBO9780511755460 https://doi.org/10.1017/CBO9780511755460 |
| Zusammenfassung: | Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. This book, first published in 2003, uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure of the axiom of choice. An appendix provides an explicit introduction to necessary concepts from logic, and an extensive glossary provides a window to the mathematical landscape |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Umfang: | 1 online resource (xiii, 261 pages) |
| ISBN: | 9780511755460 |
| DOI: | 10.1017/CBO9780511755460 |
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 520 | |a Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. This book, first published in 2003, uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure of the axiom of choice. An appendix provides an explicit introduction to necessary concepts from logic, and an extensive glossary provides a window to the mathematical landscape | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Lawvere, F. W. |
| author_facet | Lawvere, F. W. |
| author_role | aut |
| author_sort | Lawvere, F. W. |
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| building | Verbundindex |
| bvnumber | BV043943324 |
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| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9780511755460 (OCoLC)849876368 (DE-599)BVBBV043943324 |
| dewey-full | 511.3/22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/22 |
| dewey-search | 511.3/22 |
| dewey-sort | 3511.3 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511755460 |
| format | Electronic eBook |
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| id | DE-604.BV043943324 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:49:20Z |
| institution | BVB |
| isbn | 9780511755460 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029352294 |
| oclc_num | 849876368 |
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| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xiii, 261 pages) |
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| publishDate | 2003 |
| publishDateSearch | 2003 |
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| publisher | Cambridge University Press |
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| spelling | Lawvere, F. W. Verfasser aut Sets for mathematics F. William Lawvere, Robert Rosebrugh Cambridge Cambridge University Press 2003 1 online resource (xiii, 261 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. This book, first published in 2003, uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure of the axiom of choice. An appendix provides an explicit introduction to necessary concepts from logic, and an extensive glossary provides a window to the mathematical landscape Set theory Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mengenlehre (DE-588)4074715-3 s 1\p DE-604 Rosebrugh, Robert 1948- Sonstige oth Erscheint auch als Druckausgabe 978-0-521-01060-3 Erscheint auch als Druckausgabe 978-0-521-80444-8 https://doi.org/10.1017/CBO9780511755460 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lawvere, F. W. Sets for mathematics Set theory Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4074715-3 |
| title | Sets for mathematics |
| title_auth | Sets for mathematics |
| title_exact_search | Sets for mathematics |
| title_full | Sets for mathematics F. William Lawvere, Robert Rosebrugh |
| title_fullStr | Sets for mathematics F. William Lawvere, Robert Rosebrugh |
| title_full_unstemmed | Sets for mathematics F. William Lawvere, Robert Rosebrugh |
| title_short | Sets for mathematics |
| title_sort | sets for mathematics |
| topic | Set theory Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Set theory Mengenlehre |
| url | https://doi.org/10.1017/CBO9780511755460 |
| work_keys_str_mv | AT lawverefw setsformathematics AT rosebrughrobert setsformathematics |