Episodes in the history of modern algebra: (1800 - 1950)
Algebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians...
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2007
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Algebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians call "modern algebra" is even shorter still. The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenth-century work of Charles Babbage on functional equations to Alexandre Grothendieck's mid-twentieth-century metaphor of a "rising sea" in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries. Among the specific algebraic ideas considered are the concept of divisibility and the introduction of non-commutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century. The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics. Co-published with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners. |
| Beschreibung: | VIII, 336 S. 26 cm |
| ISBN: | 0821843435 |
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| 520 | 3 | |a Algebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians call "modern algebra" is even shorter still. The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenth-century work of Charles Babbage on functional equations to Alexandre Grothendieck's mid-twentieth-century metaphor of a "rising sea" in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries. Among the specific algebraic ideas considered are the concept of divisibility and the introduction of non-commutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century. The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics. Co-published with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners. | |
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| adam_text | INHALTSVERZEICHNIS
ORTIZ, EDUARDO L.
BABBAGE AND FRENCH IDEOLOGIE: FUNCTIONAL EQUATIONS, LANGUAGE, AND THE
ANALYTICAL METHOD
S. 13-
DESPEAUX, SLOAN EVANS
VERY FULL OF SYMBOLS: DUNCAN F. GREGORY, THE CALCULUS OF OPERATIONS, AND
THE CAMBRIDGE MATHEMATICAL JOURNAL
S. 49-
NEUMANN, OLAF
DIVISIBILITY THEORIES IN THE EARLY HISTORY OF COMMUTATIVE ALGEBRA AND
THE FOUNDATIONS OF ALGEBRAIC GEOMETRY
S. 73-
EDWARDS, HAROLD M.
KRONECKERS FUNDAMENTAL THEOREM OF GENERAL ARITHMETIC
S. 107-
FREI, GUENTHER
DEVELOPMENTS IN THE THEORY OF ALGEBRAS OVER NUMBER FIELDS: A NEW
FOUNDATION FOR THE HASSE NORM RESIDUE SYMBOL AND NEW APPROACHES TO BOTH
THE ARTIN RECIPROCITY LAW AND CLASS FIELD THEORY
S. 117-
SCHWERMER, JOACHIM
MINKOWSKI, HENSEL, AND HASSE: ON THE BEGINNINGS OF THE LOCAL-GLOBAL
PRINCIPLE
S. 153-
FENSTER, DELLA DUMBAUGH
RESEARCH IN ALGEBRA AT THE UNIVERSITY OF CHICAGO: LEONARD EUGENE DICKSON
AND A. ADRIAN ALBERT
S. 179-
CURTIS, CHARLES W.
EMMY NOETHERS 1932 ICM LECTURE ON NONCOMMUTATIVE METHODS IN ALGEBRAIC
NUMBER THEORY
S. 199-
CORRY, LEO
FROM ALGEBRA (1895) TO MODERNE ALGEBRA (1930): CHANGING CONCEPTIONS OF A
DISCIPLINEA GUIDED TOUR USING THE JAHRBUCH UEBER DIE FORTSCHRITTE DER
MATHEMATIK
S. 221-
SCHAPPACHER, NORBERT
A HISTORICAL SKETCH OF B. L. VAN DER WAERDENS WORK IN ALGEBRAIC
GEOMETRY: 19261946
S. 245-
SLEMBEK, SILKE
ON THE ARITHMETIZATION OF ALGEBRAIC GEOMETRY
S. 285-
MCLARTY, COLIN
THE RISING SEA: GROTHENDIECK ON SIMPLICITY AND GENERALITY
S. 301-
INHALTSVERZEICHNIS ALS PDF
2000- OESTERR. BIBLIOTHEKENVERBUND & SERVICE GMBH [HTML 4.0 /
GENERATED: 2008.01.17]
|
| adam_txt |
INHALTSVERZEICHNIS
ORTIZ, EDUARDO L.
BABBAGE AND FRENCH IDEOLOGIE: FUNCTIONAL EQUATIONS, LANGUAGE, AND THE
ANALYTICAL METHOD
S. 13-
DESPEAUX, SLOAN EVANS
VERY FULL OF SYMBOLS: DUNCAN F. GREGORY, THE CALCULUS OF OPERATIONS, AND
THE CAMBRIDGE MATHEMATICAL JOURNAL
S. 49-
NEUMANN, OLAF
DIVISIBILITY THEORIES IN THE EARLY HISTORY OF COMMUTATIVE ALGEBRA AND
THE FOUNDATIONS OF ALGEBRAIC GEOMETRY
S. 73-
EDWARDS, HAROLD M.
KRONECKERS FUNDAMENTAL THEOREM OF GENERAL ARITHMETIC
S. 107-
FREI, GUENTHER
DEVELOPMENTS IN THE THEORY OF ALGEBRAS OVER NUMBER FIELDS: A NEW
FOUNDATION FOR THE HASSE NORM RESIDUE SYMBOL AND NEW APPROACHES TO BOTH
THE ARTIN RECIPROCITY LAW AND CLASS FIELD THEORY
S. 117-
SCHWERMER, JOACHIM
MINKOWSKI, HENSEL, AND HASSE: ON THE BEGINNINGS OF THE LOCAL-GLOBAL
PRINCIPLE
S. 153-
FENSTER, DELLA DUMBAUGH
RESEARCH IN ALGEBRA AT THE UNIVERSITY OF CHICAGO: LEONARD EUGENE DICKSON
AND A. ADRIAN ALBERT
S. 179-
CURTIS, CHARLES W.
EMMY NOETHERS 1932 ICM LECTURE ON NONCOMMUTATIVE METHODS IN ALGEBRAIC
NUMBER THEORY
S. 199-
CORRY, LEO
FROM ALGEBRA (1895) TO MODERNE ALGEBRA (1930): CHANGING CONCEPTIONS OF A
DISCIPLINEA GUIDED TOUR USING THE JAHRBUCH UEBER DIE FORTSCHRITTE DER
MATHEMATIK
S. 221-
SCHAPPACHER, NORBERT
A HISTORICAL SKETCH OF B. L. VAN DER WAERDENS WORK IN ALGEBRAIC
GEOMETRY: 19261946
S. 245-
SLEMBEK, SILKE
ON THE ARITHMETIZATION OF ALGEBRAIC GEOMETRY
S. 285-
MCLARTY, COLIN
THE RISING SEA: GROTHENDIECK ON SIMPLICITY AND GENERALITY
S. 301-
INHALTSVERZEICHNIS ALS PDF
2000- OESTERR. BIBLIOTHEKENVERBUND & SERVICE GMBH [HTML 4.0 /
GENERATED: 2008.01.17] |
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| spelling | Episodes in the history of modern algebra (1800 - 1950) Jeremy J. Gray ... ed. Providence, RI American Mathematical Society 2007 VIII, 336 S. 26 cm txt rdacontent n rdamedia nc rdacarrier Algebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians call "modern algebra" is even shorter still. The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenth-century work of Charles Babbage on functional equations to Alexandre Grothendieck's mid-twentieth-century metaphor of a "rising sea" in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries. Among the specific algebraic ideas considered are the concept of divisibility and the introduction of non-commutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century. The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics. Co-published with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners. Geschichte 1800-1950 gnd rswk-swf Algebra gtt Geschichte Algebra History Algebra (DE-588)4001156-2 gnd rswk-swf Algebra (DE-588)4001156-2 s Geschichte 1800-1950 z b DE-604 Gray, Jeremy J. 1947- Sonstige (DE-588)122175549 oth OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016067731&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Episodes in the history of modern algebra (1800 - 1950) |
| title_auth | Episodes in the history of modern algebra (1800 - 1950) |
| title_exact_search | Episodes in the history of modern algebra (1800 - 1950) |
| title_exact_search_txtP | Episodes in the history of modern algebra (1800 - 1950) |
| title_full | Episodes in the history of modern algebra (1800 - 1950) Jeremy J. Gray ... ed. |
| title_fullStr | Episodes in the history of modern algebra (1800 - 1950) Jeremy J. Gray ... ed. |
| title_full_unstemmed | Episodes in the history of modern algebra (1800 - 1950) Jeremy J. Gray ... ed. |
| title_short | Episodes in the history of modern algebra |
| title_sort | episodes in the history of modern algebra 1800 1950 |
| title_sub | (1800 - 1950) |
| topic | Algebra gtt Geschichte Algebra History Algebra (DE-588)4001156-2 gnd |
| topic_facet | Algebra Geschichte Algebra History |
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