A Course in Constructive Algebra
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1988
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| Schriftenreihe: | Universitext
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| Schlagworte: | |
| Online-Zugang: | Volltext |
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| 500 | |a The constructive approach to mathematics has enjoyed a renaissance, caused in large part by the appearance of Errett Bishop's book Foundations of constructive analysis in 1967, and by the subtle influences of the proliferation of powerful computers. Bishop demonstrated that pure mathematics can be developed from a constructive point of view while maintaining a continuity with classical terminology and spirit; much more of classical mathematics was preserved than had been thought possible, and no classically false theorems resulted, as had been the case in other constructive schools such as intuitionism and Russian constructivism. The computers created a widespread awareness of the intuitive notion of an effecti ve procedure, and of computation in principle, in addition to stimulating the study of constructive algebra for actual implementation, and from the point of view of recursive function theory. In analysis, constructive problems arise instantly because we must start with the real numbers, and there is no finite procedure for deciding whether two given real numbers are equal or not (the real numbers are not discrete) . The main thrust of constructive mathematics was in the direction of analysis, although several mathematicians, including Kronecker and van der waerden, made important contributions to constructive algebra. Heyting, working in intuitionistic algebra, concentrated on issues raised by considering algebraic structures over the real numbers, and so developed a handmaiden of analysis rather than a theory of discrete algebraic structures | ||
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Datensatz im Suchindex
| DE-BY-TUM_katkey | 2066299 |
|---|---|
| _version_ | 1820813449661251584 |
| any_adam_object | |
| author | Mines, Ray |
| author_facet | Mines, Ray |
| author_role | aut |
| author_sort | Mines, Ray |
| author_variant | r m rm |
| building | Verbundindex |
| bvnumber | BV042419290 |
| classification_rvk | SK 200 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)725288540 (DE-599)BVBBV042419290 |
| 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 |
| doi_str_mv | 10.1007/978-1-4419-8640-5 |
| format | Electronic eBook |
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| id | DE-604.BV042419290 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-24T04:23:19Z |
| institution | BVB |
| isbn | 9781441986405 9780387966403 |
| issn | 0172-5939 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027854707 |
| oclc_num | 725288540 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XI, 344 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Springer New York |
| record_format | marc |
| series2 | Universitext |
| spellingShingle | Mines, Ray A Course in Constructive Algebra Mathematics Algebra Mathematik Konstruktive Mathematik (DE-588)4165105-4 gnd Algebra (DE-588)4001156-2 gnd Konstruktive Algebra (DE-588)4195681-3 gnd |
| subject_GND | (DE-588)4165105-4 (DE-588)4001156-2 (DE-588)4195681-3 |
| title | A Course in Constructive Algebra |
| title_auth | A Course in Constructive Algebra |
| title_exact_search | A Course in Constructive Algebra |
| title_full | A Course in Constructive Algebra by Ray Mines, Fred Richman, Wim Ruitenburg |
| title_fullStr | A Course in Constructive Algebra by Ray Mines, Fred Richman, Wim Ruitenburg |
| title_full_unstemmed | A Course in Constructive Algebra by Ray Mines, Fred Richman, Wim Ruitenburg |
| title_short | A Course in Constructive Algebra |
| title_sort | a course in constructive algebra |
| topic | Mathematics Algebra Mathematik Konstruktive Mathematik (DE-588)4165105-4 gnd Algebra (DE-588)4001156-2 gnd Konstruktive Algebra (DE-588)4195681-3 gnd |
| topic_facet | Mathematics Algebra Mathematik Konstruktive Mathematik Konstruktive Algebra |
| url | https://doi.org/10.1007/978-1-4419-8640-5 |
| work_keys_str_mv | AT minesray acourseinconstructivealgebra AT richmanfred acourseinconstructivealgebra AT ruitenburgwim acourseinconstructivealgebra |