"Modern Algebra" redirects here. For the area of mathematics, see Modern algebra.
Moderne Algebra
Author
Bartel Leendert van der Waerden
Language
German
Publication date
1930
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]
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.
^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.
^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
ModerneAlgebra is a two-volume German textbook on graduate abstract algebra by Bartel Leendert van der Waerden (1930, 1931), originally based on lectures...
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations...
textbook, ModerneAlgebra. By the time of her plenary address at the 1932 International Congress of Mathematicians in Zürich, her algebraic acumen was...
27th year, Van der Waerden published his ModerneAlgebra, an influential two-volume treatise on abstract algebra, still cited, and perhaps the first treatise...
(1930) of Bartel van der Waerden's ModerneAlgebra. After that, elimination theory was ignored by most algebraic geometers for almost thirty years, until...
also contained some important algebraic developments, including the list of Pythagorean triples discovered algebraically, geometric solutions of linear...
later, B.L. van der Waerden published his influential ModerneAlgebra, the first abstract algebra textbook that took the groups-rings-fields approach to...
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...
Bartel Leendert (1931). ModerneAlgebra (in German). Berlin: Springer.. English translation (of 2nd revised edition): Modern algebra. New York: Frederick...
Bartel Leendert (1931). ModerneAlgebra (in German). Berlin: Springer.. English translation (of 2nd revised edition): Modern Algebra. New York: Frederick...
2023-09-25. van der Waerden, B. L. (1975). "On the sources of my book Modernealgebra". Historia Mathematica. 2 (1): 31–40. doi:10.1016/0315-0860(75)90034-8...
characterizes his planar graph theorem. Bartel van der Waerden publishes ModerneAlgebra. March 5 – Danish painter Einar Wegener begins to undergo sexual reassignment...
logic. Modern algebra Occasionally used for abstract algebra. The term was coined by van der Waerden as the title of his book ModerneAlgebra, which was...
Leçons d'algèbre moderne. Dunod. 1961. Lectures on Modern Algebra. Edinburgh: Oliver and Boyd. 1967. (English translation) Lecciones de álgebra moderna. Reverté...
need to spend a long time learning to express algebraic properties without symbols before learning algebraic notation. When learning symbols, many students...
German, for example the lectures on the theory of algebraic numbers by Erich Hecke, the book ModerneAlgebra by Bartel Leendert van der Waerden, the Problems...
tablets date from 1800 to 1600 BC, and cover topics that include fractions, algebra, quadratic and cubic equations and the Pythagorean theorem. The Babylonian...
theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. When Euclidean space...
August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory...
except the Tarrasch (which he awarded an exclamation mark) in his book Die moderne Schachpartie. (See chess punctuation.) The Tarrasch Defense is considered...
Topology and topological algebra Chapter XIII Integration Chapter XIV Integration in locally compact groups Chapter XV Normed algebras and spectral theory...
Global Information