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The development of algebraic methods has been stimulated by medical tomography.
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To be sure, Wallace emphasizes, his critique is not directed against the use of algebraic methods, e.g. when studying inequivalent representations.
In this magisterial work Hilbert provides a unified account of the development of algebraic number theory up to the end of the nineteenth century.
Noether is credited with the fundamental ideas that led to the development of algebraic topology from the earlier combinatorial topology, specifically, the idea of homology groups.
But he avoided the use of infinitesimals in the determination of tangents to curves, instead developing purely algebraic methods for the purpose.
His decision to eschew analysis constituted a striking rejection of the algebraic methods that had been important in his own early researches on the calculus.
A rich repertoire of geometrical and algebraic methods have been developed to solve Apollonius' problem, which has been called "the most famous of all" geometry problems.
Until the advent of more sophisticated algebraic methods in the early 1950s (Serre) the Pontrjagin isomorphism was the main tool for computing the homotopy groups of spheres.
This interaction might occur through the study of combinatorial structures using algebraic methods, or the application of combinatorial methods to algebraic problems.
This paper presents the development of an algebraic dynamic multilevel method (ADM) for fully implicit simulations of multiphase flow in homogeneous and heterogeneous porous media.
The details of implementation and effectiveness of the algebraic method can be found in [ 27].
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