Augustin-Louis Cauchy was a pioneer in analysis and group theory. He wrote an influential 1821 textbook, Cours d'Analyse.
Cauchy described the basic concepts of differential and integral calculus in terms of limits. His conception of limits was based on infinitesimal variables, which do not appear as such in modern mathematics, although they have been variously identified with sequences (that converge to zero), ultrafilters (that converge to zero), hyperpoints (in the infinitesimal neighbourhood of zero) in the sense of nonstandard analysis, etc. (His infinitesimals were not nilpotent.)
Cauchy's student Karl Weierstrass defined limits in terms of Richard Dedekind's static conceptions of real numbers and functions, thereby creating modern analysis.
Cauchy is associated with:
Cauchy sequences (and thus Cauchy nets, Cauchy filters, and Cauchy spaces, although Cauchy himself knew none of these)
Cauchy integral?
Cours d'Analyse, a textbook on infinitesimal analysis/epsilontic analysis
Cauchy integral theorem and Cauchy integral formula (for contour integrals in complex analysis)
Cauchy sum theorem (“Cauchy's mistake”) from his 1821 textbook Cours d'Analyse
Last revised on May 31, 2022 at 05:46:06. See the history of this page for a list of all contributions to it.