Moderne Algebra
{{Short description|Book by van der Waerden (1930, 1931)}}
{{Redirect|Modern Algebra|the area of mathematics|Modern algebra}}
{{infobox book
| name = Moderne Algebra
| language = German
| author = Bartel Leendert van der Waerden
| pub_date = 1930
| image = File:Moderne_Algebra.png
}}
Moderne Algebra is a two-volume German textbook on graduate abstract algebra by {{harvs|txt|authorlink=Bartel Leendert van der Waerden|first=Bartel Leendert |last=van der Waerden|year1=1930|year2=1931}}, originally based on lectures given by Emil Artin in 1926 and by {{harvs|txt|authorlink=Emmy Noether|first=Emmy|last=Noether|year=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."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.
In 1975 van der Waerden described the sources he drew upon to write the book.{{Citation | last1=van der Waerden | first1=Bartel Leendert | author1-link=Bartel Leendert van der Waerden | title=On the sources of my book Moderne Algebra | doi=10.1016/0315-0860(75)90034-8 | mr=0465721 | year=1975 | journal=Historia Mathematica | issn=0315-0860 | volume=2 | pages=31–40| doi-access=free }}
In 1997 Saunders Mac Lane recollected the book's influence:{{Citation | last1=Mac Lane | first1=Saunders | author1-link=Saunders Mac Lane | title=Van der Waerden's Modern algebra | year=1997 | journal=Notices of the American Mathematical Society | issn=0002-9920 | volume=44 | issue=3 | pages=321–322 | url=https://www.ams.org/notices/199703/maclane.pdf | access-date=2023-12-03 | archive-date=2023-03-25 | archive-url=https://web.archive.org/web/20230325171728/https://www.ams.org/notices/199703/maclane.pdf | url-status=live }}
- 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
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).{{Citation | last1=Zelinsky | first1=Daniel | authorlink=Daniel Zelinsky (mathematician) | title=Book Review: Moderne Algebra | doi=10.1090/S0002-9904-1951-09496-3 | year=1951 | journal=Bulletin of the American Mathematical Society | issn=0002-9904 | volume=57 | issue=3 | pages=206–207| doi-access=free }} 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),{{cite journal|title=Review of Algebra, Part 2 (4th ed. of Moderne Algebra) by B. L. van der Waerden|author=Zelinsky, Daniel|journal=Bull. Amer. Math. Soc.|volume=67|year=1961|pages=83–86|doi=10.1090/S0002-9904-1961-10504-1|doi-access=free}} 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.
- {{cite book | title=Moderne Algebra. Teil I |first=Bartel Leendert |last=van der Waerden| publisher=Springer-Verlag | location=Berlin, New York | series= Die Grundlehren der mathematischen Wissenschaften | isbn=978-3-540-56799-8 | year=1930 | volume=33| mr=0009016 | lang=de }}
- {{cite book | title=Moderne Algebra. Teil II |first=Bartel Leendert |last=van der Waerden| publisher= Springer-Verlag | series=Die Grundlehren der mathematischen Wissenschaften | isbn=978-3-540-56801-8 | year=1931 | volume=34| mr= 0002841 |lang =de}}
- {{cite book | title=Modern Algebra. Vol I |first=Bartel Leendert |last=van der Waerden | translator-first=Fred|translator-last=Blum | publisher=Frederick Ungar Publishing Co. | location=New York, N. Y. | year=1949|mr=0029363}}
- {{cite book | title=Modern Algebra. Vol II |first=Bartel Leendert |last=van der Waerden | translator-first=Fred|translator-last=Blum | publisher=Frederick Ungar Publishing Co. | location=New York, N. Y. | year=1950}}
- {{cite book | title=Algebra. Vol 1 |first=Bartel Leendert |last=van der Waerden | url=https://books.google.com/books?id=Xw8lAQAAIAAJ | publisher=Frederick Ungar Publishing Co. | location=New York, N. Y. | translator-first=Fred|translator-last=Blum|translator2-first=John R.|translator2-last=Schulenberger| isbn=978-0-387-40624-4 | id= Reprinted by Springer | year=1970 | mr=0263582 }}
- {{cite book | title=Algebra. Vol. 2 |first=Bartel Leendert |last=van der Waerden| url=https://books.google.com/books?id=oWzoOWp_tWgC | publisher=Frederick Ungar Publishing Co. | location=New York, N. Y. | edition=3rd| translator-first=John R.|translator-last=Schulenberger| id= Reprinted by Springer | year=1970| mr=0263583 | isbn=9780387406251 }}
There were also Russian editions published in 1976 and 1979, and Japanese editions published in 1959 and 1967–1971.
References
{{Reflist}}
- {{Citation | last1=Hahn | first1=H. | author1-link=Hans Hahn (mathematician) | last2=Taussky | first2=Olga | author2-link=Olga Taussky-Todd | title=Literaturberichte: Moderne Algebra | doi=10.1007/BF01699101 | year=1932 | journal=Monatshefte für Mathematik und Physik | issn=0026-9255 | volume=39 | issue=1 | pages=A11–A12| s2cid=197662655 }}
- {{Citation | last1=Hofreiter | title=Literaturberichte: Moderne Algebra | doi=10.1007/BF01708057 | year=1936 | journal=Monatshefte für Mathematik und Physik | issn=0026-9255 | volume=45 | issue=1 | pages=A25–A26| s2cid=124462638 }}
- {{Citation | last1=Hofreiter | title=Literaturberichte: Moderne Algebra | doi=10.1007/BF01707351 | year=1941 | journal=Monatshefte für Mathematik und Physik | issn=0026-9255 | volume=49 | issue=1 | pages=A21| doi-access=free }}
- {{Citation | last1=Ore | first1=Oystein | title=Recent Publications: Reviews: Moderne Algebra | doi=10.2307/2301771 | year=1931 | journal=The American Mathematical Monthly | issn=0002-9890 | volume=38 | issue=4 | pages=226| jstor=2301771 }}
- {{Citation | last1=Ore | first1=Oystein | title=Book Review: Moderne Algebra | doi=10.1090/S0002-9904-1932-05385-X | year=1932 | journal=Bulletin of the American Mathematical Society | issn=0002-9904 | volume=38 | issue=5 | pages=327–329| doi-access=free }}
- {{Citation | last1=Ore | first1=Oystein | title=Book Review: Moderne Algebra | doi=10.1090/S0002-9904-1938-06737-7 | year=1938 | journal=Bulletin of the American Mathematical Society | issn=0002-9904 | volume=44 | issue=5 | pages=320–321| doi-access=free }}
- {{Citation | last1=Noether | first1=Emmy | author1-link=Emmy Noether | title=Hyperkomplexe Größen und Darstellungstheorie | doi=10.1007/BF01187794 | year=1929 | journal=Mathematische Zeitschrift | issn=0025-5874 | volume=30 | pages=641–692| s2cid=120464373 }}
- {{Citation | last1=Schlote | first1=K.-H. | editor1-last=Grattan-Guinness | editor1-first=Ivor | title=Landmark writings in western mathematics 1640--1940 | chapter-url=https://books.google.com/books?id=UdGBy8iLpocC&pg=PA901 | publisher=Elsevier B. V., Amsterdam | isbn=978-0-444-50871-3 | mr=2169816 | year=2005 | chapter=Chapter 70 B. L. van der Waerden, Moderne Algebra|pages=901–916}}
- {{Citation | last1=Taussky | first1=Olga | author1-link=Olga Taussky-Todd | title=Literaturberichte: Moderne Algebra | doi=10.1007/BF01708891 | year=1933 | journal=Monatshefte für Mathematik und Physik | issn=0026-9255 | volume=40 | issue=1 | pages=A3–A4| s2cid=124038027 }}
Category:History of mathematics
Category:Mathematics textbooks