Examples of using Invariant theory in English and their translations into Korean
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This work was a major contribution to invariant theory.
Invariant theory of finite groups.
He examined S-functions and applied these to invariant theory.
He also worked on invariant theory helping to develop a symbolic notation.
The journal specialised in complex analysis,algebraic geometry and invariant theory.
Hilbert's first work was on invariant theory and, in 1888, he proved his famous Basis Theorem.
Moritz Pasch was a geometer while Paul Gordan was famed for his work in invariant theory.
Interest in invariant theory had flagged somewhat, one reason for this being the introduction of tensors.
With his understanding of quadratic forms and invariant theory he created a theory of transformations in 1855.
Invariant theory was at its height in the 19th century with the work of Cayley, Sylvester, Clebsch, Gordan and others.
The topic for which Gordan is most famous is invariant theory and Clebsch introduced him to this topic in 1868.
In addition he taught some advanced courses such as elliptical functions,hyperelliptic functions, and invariant theory.
He worked on invariant theory, the geometry of curves and surfaces, algebraic curves and twisted curves.
Atiyah in divides Todd's mathematical interests into invariant theory, group theory and canonical systems.
He produced results in invariant theory, linear groups, Lie groups and generalised some of Emmy Noether 's results on rings.
Certain linear partial differential equations which he came across in his work are characteristic of invariant theory and are named after him.
In particular he wrote articles on invariant theory, third order surfaces, and surfaces of order higher than three.
He published results in the areas of analytic geometry, linear geometry and continued the directions of his teachers in his publications on invariant theory.
He also saw clearly how invariant theory fitted into the theory of groups but wrote that he had never followed through his ideas because of.
During this period, developments of his first papers led to further work in which he laid the foundations of invariant theory of forms in non-commutative algebra.
In particular Hilbert 's results on invariant theory were so powerful that they ended a chapter in the development of the subject and so Meyer's many contributions in this area are little remembered today.
Another reason was certainly the work of Hilbert, but Littlewood tried to remedy the"tensor reason" in a series of papers on tensors and invariant theory.
Clebsch helped build a school of algebraic geometry and invariant theory at Giessen which included Gordan, Brill, Max Noether, Lindemann and Lueroth.
He worked in a wide variety of mathematicalareas including general topology, topological vector spaces, algebraic geometry, invariant theory and the classical groups.
However Gordan had undertaken research on abelian functions before becoming fascinated by invariant theory, and Wiltheiss went on to undertake research on that topic, making a major contribution to the theory of abelian functions.
For the rest of his career, although Gordan did not work exclusively on this topic, it would be fair to say that invariant theory dominated his mathematical research.
Gordan was recognised as the leading world expert on invariant theory and he was also a close friend of Klein 's. However Klein recognised the importance of Hilbert 's work and assured him that it would appear in the Annalen without any changes whatsoever, as indeed it did.
Hilbert submitted his results to Mathematische Annalen and, since Gordan was the leading world expert on invariant theory, he was asked his opinion of the work.
He owed some of his greatest successes to his development of Riemann 's ideas and to the intimate alliance he forged between the later and the conception of invariant theory, of number theory and algebra, of group theory, and of multidimensional geometry and the theory of differential equations, especially in his own fields, elliptic modular functions and automorphic functions.
His mathematical work was extremely broad and his 67 papers range across many topics such as linear algebra, invariant theory, integral calculus, potential theory, functional analysis, and geometry.