Ernst Schröder

Ernst Schröder ( born November 25, 1841 in Mannheim, † June 16, 1902 in Karlsruhe, full name Ernst Friedrich Wilhelm Karl Schroeder ) was a German mathematician and logician.

Life and work

After studying mathematics and physics at the Ruprecht -Karls- University of Heidelberg and Albertus University of Königsberg Schröder habilitated at the University of Zurich, 1865. According to a school service in 1874 he became professor of mathematics at the Technical University of Darmstadt, then in 1876 at the Technical University of Karlsruhe, where he 1890/91 also served as director.

His main areas of work were the foundations of mathematics, theory of functions and combinatorial analysis. In his work About iterirte functions from the year 1871, he examined the named after him today Dersche Schröder functional equation, which plays an important role in the complex dynamics. That the logic of self- discipline, is due to his work on theoretical algebra and symbolic logic. With his work on the algebra of logic, he won international recognition. He optimized the logic of George Boole and developed in 1877 the first complete system of axioms of Boolean algebra. In his three-volume algebra of logic of 1890-95 he went in contrast to Boole, who built his calculus on the identity of classes, based on the inclusion of classes. Schröder also developed the relational algebra (see relation theory ), introduced the term normal form and discovered the principle of duality in the class logic (see Boolean algebra). He also solved special cases of the decision problem by elimination of quantifiers.

Giuseppe Peano was based on Schroeder's logic; also tied Norbert Wiener in his dissertation A comparision Between The treatment of the algebra of relatives by Schröder and did by Whitehead and Russell with the work of Schroeder. For Alfred Tarski 's work was the basis for a modern theory of algebra and the history of logic.

He is one of the namesake for the set of Schröder- Bernstein. The Schröder numbers are named after him. Ernst Schröder has created with his three-volume magnum opus on the algebra of logic, one of the bases for Conceptual Knowledge Processing. Hence the ErnstSchröderZentrum for Conceptual Knowledge Processing bears his name. It promotes education, research and development in the field of conceptual knowledge processing and their application.

Writings

• Textbook of arithmetic and algebra, 1873
• About the formal elements of absolute algebra, 31 S., Stuttgart, 1874
• The operation of the circuit Logikkalkuls, 1877
• Lectures on the algebra of logic ( Exact logic), 3 volumes, Leipzig 1890-1905

Algebra and logic of the Relative, the lectures on the algebra of logic 3 Volume 3, Division 1, Leipzig, BG Teubner, 1890-1905

• About the characters, Karlsruhe, 1890
• About two definitions of finiteness and G. Cantor sets - Treatise in the series Leopoldino Imperial German - Carolinian Academy of Sciences Vol 71, pp. 301-362, Halle, 1898
• Summary of the algebra of logic, 2 parts, Leipzig, 1909/1910