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Real Analysis is a math course. It's mentioned as one of the prerequisites to Stock Market Options as a Realization of Stochastic Processes

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  • Real Analysis
  • Real analysis
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  • 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: Some important results in real analysis include:
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  • 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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