"Modern Algebra" redirects here. For the area of mathematics, see Modern algebra.
Moderne Algebra is a two-volume German textbook on graduate abstract algebra by Bartel Leendert van der Waerden (1930, 1931), originally based on lectures given by Emil Artin in 1926 and by Emmy Noether (1929) from 1924 to 1928. The English translation of 1949–1950 had the title Modern algebra, though a later, extensively revised edition in 1970 had the title Algebra.
The book was one of the first textbooks to use an abstract axiomatic approach to groups, rings, and fields, and was by far the most successful, becoming the standard reference for graduate algebra for several decades. It "had a tremendous impact, and is widely considered to be the major text on algebra in the twentieth century."[1]
In 1975 van der Waerden described the sources he drew upon to write the book.[2]
Upon its publication it was soon clear that this was the way that algebra should be presented.
Its simple but austere style set the pattern for mathematical texts in other subjects, from Banach algebras to topological group theory.
[Van der Waerden's] two volumes on modern algebra ... dramatically changed the way algebra is now taught by providing a decisive example of a clear and perspicacious presentation. It is, in my view, the most influential text of algebra of the twentieth century.
Publication historyedit
Moderne Algebra has a rather confusing publication history, because it went through many different editions, several of which were extensively rewritten with chapters and major topics added, deleted, or rearranged. In addition the new editions of first and second volumes were issued almost independently and at different times, and the numbering of the English editions does not correspond to the numbering of the German editions. In 1955 the title was changed from "Moderne Algebra" to "Algebra" following a suggestion of Brandt, with the result that the two volumes of the third German edition do not even have the same title.
For volume 1, the first German edition was published in 1930, the second in 1937 (with the axiom of choice removed), the third in 1951 (with the axiom of choice reinstated, and with more on valuations).[4] The fourth edition appeared in 1955 (with the title changed to Algebra), the fifth in 1960, the sixth in 1964, the seventh in 1966, the eighth in 1971, the ninth in 1993. For volume 2, the first edition was published in 1931, the second in 1940, the third in 1955 (with the title changed to Algebra), the fourth in 1959 (extensively rewritten, with elimination theory replaced by algebraic functions of 1 variable),[5] the fifth in 1967, and the sixth in 1993. The German editions were all published by Springer.
The first English edition was published in 1949–1950 and was a translation of the second German edition. There was a second edition in 1953, and a third edition under the new title Algebra in 1970 translated from the 7th German edition of volume 1 and the 5th German edition of volume 2. The three English editions were originally published by Ungar, though the 3rd English edition was later reprinted by Springer.
van der Waerden, Bartel Leendert (1930). Moderne Algebra. Teil I. Die Grundlehren der mathematischen Wissenschaften (in German). Vol. 33. Berlin, New York: Springer-Verlag. ISBN978-3-540-56799-8. MR 0009016.
van der Waerden, Bartel Leendert (1931). Moderne Algebra. Teil II. Die Grundlehren der mathematischen Wissenschaften (in German). Vol. 34. Springer-Verlag. ISBN978-3-540-56801-8. MR 0002841.
van der Waerden, Bartel Leendert (1949). Modern Algebra. Vol I. Translated by Blum, Fred. New York, N. Y.: Frederick Ungar Publishing Co. MR 0029363.
van der Waerden, Bartel Leendert (1950). Modern Algebra. Vol II. Translated by Blum, Fred. New York, N. Y.: Frederick Ungar Publishing Co.
van der Waerden, Bartel Leendert (1970). Algebra. Vol 1. Translated by Blum, Fred; Schulenberger, John R. New York, N. Y.: Frederick Ungar Publishing Co. ISBN978-0-387-40624-4. MR 0263582. Reprinted by Springer.
van der Waerden, Bartel Leendert (1970). Algebra. Vol. 2. Translated by Schulenberger, John R. (3rd ed.). New York, N. Y.: Frederick Ungar Publishing Co. ISBN9780387406251. MR 0263583. Reprinted by Springer.
There were also Russian editions published in 1976 and 1979, and Japanese editions published in 1959 and 1967–1971.
Referencesedit
^Bernard Behan & Karl Sigmund (2008) "A Short Tale of Two Cities: Otto Schrier and the Hamburg–Vienna Connection", p. 33, Mathematical Intelligencer 30(3):27–35.
^Zelinsky, Daniel (1961). "Review of Algebra, Part 2 (4th ed. of Moderne Algebra) by B. L. van der Waerden". Bull. Amer. Math. Soc. 67: 83–86. doi:10.1090/S0002-9904-1961-10504-1.
Hahn, H.; Taussky, Olga (1932), "Literaturberichte: Moderne Algebra", Monatshefte für Mathematik und Physik, 39 (1): A11–A12, doi:10.1007/BF01699101, ISSN 0026-9255, S2CID 197662655
Hofreiter (1936), "Literaturberichte: Moderne Algebra", Monatshefte für Mathematik und Physik, 45 (1): A25–A26, doi:10.1007/BF01708057, ISSN 0026-9255, S2CID 124462638
Hofreiter (1941), "Literaturberichte: Moderne Algebra", Monatshefte für Mathematik und Physik, 49 (1): A21, doi:10.1007/BF01707351, ISSN 0026-9255
Schlote, K.-H. (2005), "Chapter 70 B. L. van der Waerden, Moderne Algebra", in Grattan-Guinness, Ivor (ed.), Landmark writings in western mathematics 1640--1940, Elsevier B. V., Amsterdam, pp. 901–916, ISBN978-0-444-50871-3, MR 2169816
Taussky, Olga (1933), "Literaturberichte: Moderne Algebra", Monatshefte für Mathematik und Physik, 40 (1): A3–A4, doi:10.1007/BF01708891, ISSN 0026-9255, S2CID 124038027
December 29, 2023
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Modern Algebra redirects here For the area of mathematics see Modern algebra Moderne Algebra is a two volume German textbook on graduate abstract algebra by Bartel Leendert van der Waerden 1930 1931 originally based on lectures given by Emil Artin in 1926 and by Emmy Noether 1929 from 1924 to 1928 The English translation of 1949 1950 had the title Modern algebra though a later extensively revised edition in 1970 had the title Algebra Moderne AlgebraAuthorBartel Leendert van der WaerdenLanguageGermanPublication date1930The book was one of the first textbooks to use an abstract axiomatic approach to groups rings and fields and was by far the most successful becoming the standard reference for graduate algebra for several decades It had a tremendous impact and is widely considered to be the major text on algebra in the twentieth century 1 In 1975 van der Waerden described the sources he drew upon to write the book 2 In 1997 Saunders Mac Lane recollected the book s influence 3 Upon its publication it was soon clear that this was the way that algebra should be presented Its simple but austere style set the pattern for mathematical texts in other subjects from Banach algebras to topological group theory Van der Waerden s two volumes on modern algebra dramatically changed the way algebra is now taught by providing a decisive example of a clear and perspicacious presentation It is in my view the most influential text of algebra of the twentieth century Publication history editModerne Algebra has a rather confusing publication history because it went through many different editions several of which were extensively rewritten with chapters and major topics added deleted or rearranged In addition the new editions of first and second volumes were issued almost independently and at different times and the numbering of the English editions does not correspond to the numbering of the German editions In 1955 the title was changed from Moderne Algebra to Algebra following a suggestion of Brandt with the result that the two volumes of the third German edition do not even have the same title For volume 1 the first German edition was published in 1930 the second in 1937 with the axiom of choice removed the third in 1951 with the axiom of choice reinstated and with more on valuations 4 The fourth edition appeared in 1955 with the title changed to Algebra the fifth in 1960 the sixth in 1964 the seventh in 1966 the eighth in 1971 the ninth in 1993 For volume 2 the first edition was published in 1931 the second in 1940 the third in 1955 with the title changed to Algebra the fourth in 1959 extensively rewritten with elimination theory replaced by algebraic functions of 1 variable 5 the fifth in 1967 and the sixth in 1993 The German editions were all published by Springer The first English edition was published in 1949 1950 and was a translation of the second German edition There was a second edition in 1953 and a third edition under the new title Algebra in 1970 translated from the 7th German edition of volume 1 and the 5th German edition of volume 2 The three English editions were originally published by Ungar though the 3rd English edition was later reprinted by Springer van der Waerden Bartel Leendert 1930 Moderne Algebra Teil I Die Grundlehren der mathematischen Wissenschaften in German Vol 33 Berlin New York Springer Verlag ISBN 978 3 540 56799 8 MR 0009016 van der Waerden Bartel Leendert 1931 Moderne Algebra Teil II Die Grundlehren der mathematischen Wissenschaften in German Vol 34 Springer Verlag ISBN 978 3 540 56801 8 MR 0002841 van der Waerden Bartel Leendert 1949 Modern Algebra Vol I Translated by Blum Fred New York N Y Frederick Ungar Publishing Co MR 0029363 van der Waerden Bartel Leendert 1950 Modern Algebra Vol II Translated by Blum Fred New York N Y Frederick Ungar Publishing Co van der Waerden Bartel Leendert 1970 Algebra Vol 1 Translated by Blum Fred Schulenberger John R New York N Y Frederick Ungar Publishing Co ISBN 978 0 387 40624 4 MR 0263582 Reprinted by Springer van der Waerden Bartel Leendert 1970 Algebra Vol 2 Translated by Schulenberger John R 3rd ed New York N Y Frederick Ungar Publishing Co ISBN 9780387406251 MR 0263583 Reprinted by Springer There were also Russian editions published in 1976 and 1979 and Japanese editions published in 1959 and 1967 1971 References edit Bernard Behan amp Karl Sigmund 2008 A Short Tale of Two Cities Otto Schrier and the Hamburg Vienna Connection p 33 Mathematical Intelligencer 30 3 27 35 van der Waerden Bartel Leendert 1975 On the sources of my book Moderne Algebra Historia Mathematica 2 31 40 doi 10 1016 0315 0860 75 90034 8 ISSN 0315 0860 MR 0465721 Mac Lane Saunders 1997 Van der Waerden s Modern algebra PDF Notices of the American Mathematical Society 44 3 321 322 ISSN 0002 9920 archived PDF from the original on 2023 03 25 retrieved 2023 12 03 Zelinsky Daniel 1951 Book Review Moderne Algebra Bulletin of the American Mathematical Society 57 3 206 207 doi 10 1090 S0002 9904 1951 09496 3 ISSN 0002 9904 Zelinsky Daniel 1961 Review of Algebra Part 2 4th ed of Moderne Algebra by B L van der Waerden Bull Amer Math Soc 67 83 86 doi 10 1090 S0002 9904 1961 10504 1 Hahn H Taussky Olga 1932 Literaturberichte Moderne Algebra Monatshefte fur Mathematik und Physik 39 1 A11 A12 doi 10 1007 BF01699101 ISSN 0026 9255 S2CID 197662655 Hofreiter 1936 Literaturberichte Moderne Algebra Monatshefte fur Mathematik und Physik 45 1 A25 A26 doi 10 1007 BF01708057 ISSN 0026 9255 S2CID 124462638 Hofreiter 1941 Literaturberichte Moderne Algebra Monatshefte fur Mathematik und Physik 49 1 A21 doi 10 1007 BF01707351 ISSN 0026 9255 Ore Oystein 1931 Recent Publications Reviews Moderne Algebra The American Mathematical Monthly 38 4 226 doi 10 2307 2301771 ISSN 0002 9890 JSTOR 2301771 Ore Oystein 1932 Book Review Moderne Algebra Bulletin of the American Mathematical Society 38 5 327 329 doi 10 1090 S0002 9904 1932 05385 X ISSN 0002 9904 Ore Oystein 1938 Book Review Moderne Algebra Bulletin of the American Mathematical Society 44 5 320 321 doi 10 1090 S0002 9904 1938 06737 7 ISSN 0002 9904 Noether Emmy 1929 Hyperkomplexe Grossen und Darstellungstheorie Mathematische Zeitschrift 30 641 692 doi 10 1007 BF01187794 ISSN 0025 5874 S2CID 120464373 Schlote K H 2005 Chapter 70 B L van der Waerden Moderne Algebra in Grattan Guinness Ivor ed Landmark writings in western mathematics 1640 1940 Elsevier B V Amsterdam pp 901 916 ISBN 978 0 444 50871 3 MR 2169816 Taussky Olga 1933 Literaturberichte Moderne Algebra Monatshefte fur Mathematik und Physik 40 1 A3 A4 doi 10 1007 BF01708891 ISSN 0026 9255 S2CID 124038027 Retrieved from https en wikipedia org w index php title Moderne Algebra amp oldid 1188126401, wikipedia, wiki, book, books, library,
