Augustin-Louis+Cauchy

=Augustin-Louis Cauchy =

= = =Biography =
 * He was born in Paris, France on August 21, 1789.
 * He was educated at home until entering public school at the age of 13.
 * He was enrolled in the Polytechnique (a French College of Research) by age 16.
 * He graduated with a degree in civil engineering by the time he was 21 years old.
 * After graduating college, Cauchy worked on building naval bases for Napoleon. ("Cauchy, Augustin")
 * He returned home to begin pursuing mathematics.
 * He held professorships at multiple colleges including the Faculte de Sciences and the College de France.
 * He wrote a total of 789 papers explaining his mathematical discoveries in his lifetime. They are still referenced today.
 * He began suffering from lung problems when he was 67 and died on May 23, 1857. His last words to his students were, "I will explain it all in my next memoir." Unfortunately, Cauchy died before he could write this memoir, taking whatever discovery he had made to the grave. (Science Division - Bellevue College)

=Mathematical Achievements: = = =

Algebra:
Cauchy began working with the "inverse of the matrix, by formulating theorems on determinants formed by sub determinants, and proved that if a polynomial assumes more than two values under permutations of its n variables, then it assumes at least p values, where p is the largest prime in n" ("Augustin-Louis Cauchy"). He is also well known for "Cauchy's theorem," which states, "for any prime p dividing the order there is an element of order p" ("Augustin-Louis Cauchy").

Calculus:
Some say that it was Cauchy who first laid the foundation for calculus.He is remembered for "formulating conditions and proving propositions suca and the Cauchy criterion for convergence, that a continuous function has a zero between the endpoints where its signs are different, and 'invented what is now called the Jacobian," which he restricted to two and three dimensions" ("Augustin-Louis Cauchy") Cauchy is perhaps most famous for his work with complex functions. "Cauchy justifies algebraic and limit operations on complex numbers, incorporates absolute values, and defines continuity for complex functions. Cauchy also used logarithmic residues as a means in defining the number of roots of a function in a domain, as well as the formula for the sums over roots of the function﻿" ("Augustin-Louis Cauchy").