Van der Waerden AlgebraThe Waerden algebra
At first you should go through Dummit and Foote or Gallian once, then reading van der Warden will be cheaper.
Volume I | B.L. van der Waerden
This fine and enthusiastic text was intended to change the doctrine of algebra not only in Germany but also elsewhere in Europe and the United States. It was with the sophistication and the grasp with which Artin had referenced.... His modest but strict stylistic patterns for mathematic text in other disciplines, from Banach rooms to tabletopological group theories.... It is in my opinion the most authoritative text in algebra of the twentieth century. However, this was not the case.
It must have been thrilling to have heard Emil Artin and Emmy Noether talk about algebra in the 1920s, when the axial approximation to the topic was astonishing and new! He was there and took down his memos and published the classical text book of the industry. In the past, every would-be algebraicist had to read this text.
To this day, all those who work in algebra still owes them an enormous guilt; they have learnt from it second or third party, if not directly. The first edition of Van der Waerden's Modern Algebra, which appeared in 1930, sets the standards for a uniform way of approaching 20th cent. algraic structure.
Contemporary Algebra is a two-volume book on abstracted algebra by Bartel Leendert van der Waerden (1930, 1931), initially written on the basis of talks by Emil Artin in 1926 and Emmy Noether (1929) from 1924 to 1928. Although the 1949-1950 British version was called Moderne Algebra, a later, comprehensively reworked version was called Algebra in 1970.
After its release, it soon became clear that this was the way in which algebra should be presented. He had a straightforward but strict approach that patterned mathematics in other disciplines, from Banach algbras to topology group theories. Van der Waerden's] two volume on contemporary algebra.... drastically changes the way algebra is now learned by giving a crucial example of a clear and ingenious representation.
In my opinion, it is the most powerful text of algebra of the 20th cent. Modern algebra has a rather puzzling publishing story because it has gone through many different issues, some of which have been comprehensively transcribed, with sections and main themes added, removed or reordered. Moreover, the new versions of the first and second volume were published almost independent and at different dates, and the numbers of the British issues do not match the numbers of the issues in Ed.
At Brandt's instigation, the book's titles were altered from "Modern Algebra" to "Algebra" in 1955, so that the two vol. in the third issue of the book do not even have the same name. The first English issue was released in 1930 for Vol. 1, the second in 1937 (with the axiome of the election removed), the third in 1951 (with the axiome of the election reintroduced, and with more on ratings) The forth issue was released in 1955 (with the heading modified to algebra), the fifth in 1960, the seventh in 1964, the seventh in 1966, the eighth in 1971, the einth in 1993.
The first issue was released for Vol. 2 in 1931, the second in 1940, the third in 1955 (with the heading modified to algebra), the forth in 1959 (comprehensively transcribed, the removal theories being superseded by algraic features of 1 variable), the fifth in 1967 and the 6th in 1993. All of the English issues have been released by Springer.
First English issue was released 1949-1950 and was a version of the second English one. A second issue was issued in 1953, and a third issue under the new heading Algebra in 1970 was compiled from the seventh English issue of Vol. 1 and the fifth English issue of Vol. 2.
Initially the three issues were edited by Hungarian, the third issue in England was later printed by Springer. Expenditure was also made in Russia in 1976 and 1979 and in Japan in 1959 and 1967-1971.