by: Vincent Bissonnette Carl Friedrich Gauss by: Vincent Bissonnette

Outline Biography Historical & geographical context Linear algebra works Gaussian Elimination

Biography German nationality, lived in Basse-saxe Lived 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 1804 Won the Lalande prize of the Académie des Sciences in 1810 Won the Copley Medal in 1838 of the Royal Society of London Died in 1855 in Göttingen

Historical & Geographical Context Germany 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 world More 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 world

Linear Algebra Works Found a complete solution to the “cyclotomic equation”  X^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 Equation Gauss showed that the cyclotomic equation can be reduced to solving a series of Quadratic Equations whenever p is a Fermat Prime in the equation x^p=1. Fermat Prime: Fn=2^(2^n)+1 The only Fermat primes know are: 3, 5, 17, 257, 65537

Gaussian Elimination Gauss 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.

END Thank you