Carl Friedrich Gauss

Carl Friedrich Gauss

by: Vincent BissonnetteCarl Friedrich Gauss

OutlineBiographyHistorical & geographical contextLinear algebra worksGaussian Elimination

BiographyGerman nationality, lived in Basse-saxeLived between end of 18th century and the beginning of the 19th (1777-1855)Studied at Brunswick University of Technology (1972-1795)Elected as a member of the Royal Society in 1804Won the Lalande prize of the Acadmie des Sciences in 1810Won the Copley Medal in 1838 of the Royal Society of LondonDied in 1855 in Gttingen

Historical & Geographical ContextGermany at the beginning of the 19th century

World leader at that time for the development of science

Establishment of some of the oldest university of the worldMore centered on philosophy, theology and law than on science

Germany and its scientific literature from the early 19th century through the beginning of WW II were very important for the development of science throughout the world4Linear Algebra WorksFound a complete solution to the cyclotomic equationX^m-1=0

Found that every polynomial in one variable that has real coefficients is a product of quadratic and linear factors.Created the theorem and the proof

Cyclotomic EquationGauss showed that the cyclotomic equation can be reduced to solving a series ofQuadratic Equations wheneverpis aFermat Prime in the equation x^p=1.Fermat Prime: Fn=2^(2^n)+1The only Fermat primes know are: 3, 5, 17, 257, 65537

Gaussian EliminationGauss and Adrien-Marie Legendre invented a method to draw statistical inferences for the unknowns in overdetermined, simultaneous linear equations by minimizing the sum of the squares of the discrepancies.After this method of least square, many mathematicians modified the method depending on the societal need for computation which led to the method we know today.

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