Bartel Leendert van der Waerden (February 2, 1903, Amsterdam, Netherlands – January 12, 1996, Zürich, Switzerland) was a Dutch mathematician.

Van der Waerden learned advanced mathematics at the University of Amsterdam and the University of Göttingen, from 1919 until 1926. He was much influenced by Emmy Noether at Göttingen. Amsterdam awarded him a Ph.D. for a thesis on algebraic geometry, supervised by Hendrick de Vries. Göttingen awarded him the habilitation in 1928.

In his 27th year, Van der Waerden published his Algebra, an influential two-volume treatise on abstract algebra, still cited, and perhaps the first treatise to treat the subject as a comprehensive whole. This work systematized an ample body of research by Emmy Noether, David Hilbert, Richard Dedekind, and Emil Artin. In the following year, 1931, he was appointed professor at the University of Leipzig.

The Third Reich made life difficult for Van der Waerden as a foreigner teaching in Germany, but he refused to give up his Dutch nationality. He filled the chair in mathematics at the University of Amsterdam, 1948–1951, then moved to the University of Zurich, where he spent the rest of his career, supervising more than 40 Ph.D. students.

Van der Waerden is mainly remembered for his work on abstract algebra. He also wrote on algebraic geometry, topology, number theory, geometry, combinatorics, analysis, probability and statistics, and quantum mechanics (he and Heisenberg had been colleagues at Leipzig). In his later years, he turned to the history of mathematics and science. His historical writings include Ontwakende wetenschap (1950), which was translated into English as Science Awakening (1954), Geometry and Algebra in Ancient Civilizations (1983), and A History of Algebra (1985).

Review

From the reviews:

"The book … is a reprinted version of the original English translation of the first volume of B. L. van der Waerden’s ‘Algebra’, without any alterations. However, it is the first softcover printing, worth the price and particularly handy. It is very gratifying to have such an edition … so that further generations of students can both afford it and use it as still one of the best sources … . is one of the most influential textbooks in mathematics of the 20th century." (Werner Kleinert, Zentralblatt MATH, Vol. 1032 (7), 2004)

"In the glad to have you back department, I’m delighted that Springer has decided to reprint the two volumes of B.L.van der Waerden’s Algebra. Based in part on lectures by Emmy Noether and Emil Artin, this is the book that brought ‘abstract algebra’ to the mathematical world. … the book reflects the excitement that accompanied the birth of axiomatic algebra. … a book to treasure. I am glad it’s back." (MAA-Online, March, 2004)

Product Description

This widely known textbook, formally titled Modern Algebra, by the noted Dutch mathematician van der Waerden is now back in print. Algebra originated from notes taken by the author from Emil Artin's lectures. The author extended the scope of these notes to include research of Emmy Noether and her students. The first German edition appeared in 1930-1931, with subsequent editions having been brought up to date. "The basic notions of algebra, groups, rings, modules, fields, and the main theories pertaining to these notions are treated in the classical two volume textbook of van der Waerden. Although more than half a century has elapsed since the appearance of this remarkable book, it is in no way dated, and for the majority of the questions it treats, no better source can be found even today." (I.R. Shafarevich: Encyclopaedia of Mathematical Sciences, Volume 11.1990)

Language Notes

Text: English (translation)

Original Language: German --This text refers to an out of print or unavailable edition of this title.

From the Back Cover

...This beautiful and eloquent text served to transform the graduate teaching of algebra, not only in Germany, but elsewhere in Europe and the United States. It formulated clearly and succinctly the conceptual and structural insights which Noether had expressed so forcefully. This was combined with the elegance and understanding with which Artin had lectured...Its simple but austere style set the pattern for mathematical texts in other subjects, from Banach spaces to topological group theory...It is, in my view, the most influential text in algebra of the twentieth century.

- Saunders MacLane, Notices of the AMS

How exciting it must have been to hear Emil Artin and Emmy Noether lecture on algebra in the 1920's, when the axiomatic approach to the subject was amazing and new! Van der Waerden was there, and produced from his notes the classic textbook of the field. To Artin's clarity and Noether's originality he added his extraordinary gift for synthesis. At one time every would-be algebraist had to study this text. Even today, all who work in Algebra owe a tremendous debt to it; they learned from it by second or third hand, if not directly. It is still a first-rate (some would say, the best) source for the great range of material it contains.

- David Eisenbud, Mathematical Sciences Research Institute

Van der Waerden's book Moderne Algebra, first published in 1930, set the standard for the unified approach to algebraic structures in the twentieth century. It is a classic, still worth reading today.

- Robin Hartshorne, University of California, Berkeley

--This text refers to an alternate Paperback edition.