abstract
| - Real Analysis is a math course. It's mentioned as one of the prerequisites to Stock Market Options as a Realization of Stochastic Processes
- As an academic subject, real analysis is typically taken in college after a two- or three-semester course in calculus, and usually after a course in rigorous mathematical proof. As such, it can be seen as a generalization of calculus to higher dimensions and to more general types of functions. Some major concepts in real analysis include: File:Wikipedia logo.pngSee also the Wikipedia article: List of real analysis topics
* fundamental calculus notions such as limits, continuity, derivatives, integrals, and the convergence and divergence of infinite series
* sequences of sets and unions and intersections of arbitrary numbers of sets
* least upper bound and greatest lower bound of a set
* elementary notions of topology, including open, closed, countable, connected, and compact sets
* liminf and limsup, respectively the "limit inferior" and "limit superior" of a sequence
* Cauchy sequences and their relation to convergent sequences
* metrics and metric spaces, which generalize the notions of distance and Euclidean spaces
* pointwise convergence and uniform convergence of sequences of functions
* rates of convergence and "Big O notation"
* sigma algebras, measures and measure spaces Some important results in real analysis include:
* basic calculus results such as the fundamental theorem of calculus, intermediate value theorem, mean value theorem, and monotone convergence theorem
* Bolzano-Weierstrass theorem
* Heine-Borel theorem
* inverse function theorem and implicit function theorem
* Fubini's theorem
* Banach fixed point theorem
* and various inequalities:
* Triangle inequality
* Cauchy-Schwarz inequality
* Hölder's inequality
* Minkowski inequality
* Jensen's inequality
* Chebyshev's inequality
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