Question: Which German mathematicianwho contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, mechanics, electrostatics, magnetic fields, astronomy, matrix theory, and optics is the namesake of the Gauss-Seidel method in linear algebra?

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Bryan Shader: Bryan L. Shader is a professor of mathematics at the University of Wyoming.  He received his Ph.D. from University of Wisconsin-Madison in 1990, his advisor was Professor Richard Brualdi.  Shader is the Editor-in-chief of the "Electronic Journal of Linear Algebra".  He is also Associate Editor of other two journals, "Linear Algebra and its Applications" (since 2003) and "Linear & Multilinear Algebra" (since 2009).  He is one of the most active mathematicians working on Combinatorial Matrix Theory.  He is also noted for his monograph on matrices of sign-solvable linear systems.  Besides organizing many workshops he is a Co-PI of Math Teacher Leadership Program, an NSF project (2009–2014).  Shader is Special Assistant to the Vice-President of Research of University of Wyoming.

Carl Friedrich Gauss: Johann Carl Friedrich Gauss ( ; German: "Gauß" , ] ; Latin: "Carolus Fridericus Gauss" ) (30 April 177723 February 1855) was a German mathematician who contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, mechanics, electrostatics, magnetic fields, astronomy, matrix theory, and optics.

Linear Algebra and its Applications: Linear Algebra and its Applications is a biweekly peer-reviewed mathematics journal published by Elsevier and covering matrix theory and finite-dimensional linear algebra.

Gabriel Kron: Gabriel Kron (1901 – 1968) was a Hungarian American electrical engineer who promoted the use of methods of linear algebra, multilinear algebra, and differential geometry in the field.  His method of system decomposition and solution called Diakoptics is still influential today.  Though he published widely, his methods were slow to be assimilated.  At Union College a symposium was organized by Schaffer Library on "Gabriel Kron, the Man and His Work", held October 14, 1969.  H.H. Happ edited the contributed papers, which were published by Union College Press as "Gabriel Kron and Systems Theory".

GRE Mathematics Test: The GRE subject test in mathematics is a standardized test in the United States created by the Educational Testing Service (ETS), and is designed to assess a candidate's potential for graduate or post-graduate study in the field of mathematics.  It contains questions from many fields of mathematics.  About 50% of the questions come from calculus (including pre-calculus topics, multivariate calculus, and differential equations), 25% from algebra (including linear algebra, abstract algebra, and number theory), and 25% from a broad variety of other topics typically encountered in undergraduate mathematics courses, such as point-set topology, probability and statistics, geometry, and real analysis.

Quantum differential calculus: In quantum geometry or noncommutative geometry a quantum differential calculus or noncommutative differential structure on an algebra formula_1 over a field formula_2 means the specification of a space of differential forms over the algebra.  The algebra formula_1 here is regarded as a coordinate ring but it is important that it may be noncommutative and hence not an actual algebra of coordinate functions on any actual space, so this represents a point of view replacing the specification of a differentiable structure for an actual space.  In ordinary differential geometry one can multiply differential 1-forms by functions from the left and from the right, and there exists an exterior derivative.  Correspondingly, a first order quantum differential calculus means at least the following:

Numerical linear algebra: Numerical linear algebra is the study of algorithms for performing linear algebra computations, most notably matrix operations, on computers.  It is often a fundamental part of engineering and computational science problems, such as image and signal processing, telecommunication, computational finance, materials science simulations, structural biology, data mining, bioinformatics, fluid dynamics, and many other areas.  Such software relies heavily on the development, analysis, and implementation of state-of-the-art algorithms for solving various numerical linear algebra problems, in large part because of the role of matrices in finite difference and finite element methods.

Gauss–Seidel method: In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a linear system of equations.  It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel, and is similar to the Jacobi method.  Though it can be applied to any matrix with non-zero elements on the diagonals, convergence is only guaranteed if the matrix is either diagonally dominant, or symmetric and positive definite.  It was only mentioned in a private letter from Gauss to his student Gerling in 1823.  A publication was not delivered before 1874 by Seidel.

Nicolae Popescu: Nicolae Popescu, Ph.D., D.Phil.  (] ; 22 September 1937 – 29 July 2010) was a Romanian mathematician and Emeritus Professor.  Popescu was elected a Member of the Romanian Academy in 1992.  He is best known for his contributions to Algebra and the theory of Abelian categories.  Since 1964 and until 2007 he collaborated on the characterization of abelian categories with the well-known French mathematician Pierre Gabriel.  His areas of expertise were: Category theory, Abelian categories with Applications to Rings and Modules, adjoint functors, limits/colimits, Theory of Sheaves, Theory of Rings, Fields and Polynomials, and Valuation Theory; he also had interests and published in the following areas: Algebraic Topology, Algebraic Geometry, Commutative Algebra, K-Theory, Class-Field theory, and Algebraic Function Theory.  He published between 1962 and 2008 more than 102 papers in peer-reviewed, mathematics journals, several monographs on the theory of sheaves, and also six books on abelian category theory and abstract algebra.  In a Grothendieck-like, energetic style, he initiated and provided scientific leadership to several seminars on category theory, sheaves and abstract algebra which resulted in a continuous stream of high-quality mathematical publications in international, peer-reviewed mathematics journals by several members participating in his Seminar series.  His book "Abelian Categories with Applications to Rings and Modules" continues to provide valuable information to mathematicians around the world.  His latest contributions have also branched into valuation and number theory.  He has published over 110 original, peer-reviewed articles in mathematics, mostly in category theory, algebraic geometry, and Galois and number theory.

Differential geometry: Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.  The theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century.

Supporting paragraphs: Gauss–Seidel method Carl Friedrich Gauss
Answer: Carl Friedrich Gauss