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Massachusetts Institute of Technology (MIT), United States, Harvard University, Stanford University, University of Cambridge, United Kingdom, University of Oxford, University of California, Berkeley (UCB), Princeton University, ETH Zurich (Swiss Federal Institute of Technology), Switzerland, University of California, Los Angeles (UCLA), New York University (NYU)
Real Analysis: Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets, completeness of R. Power series (of real variable), Taylor's series, radius and interval of convergence, term-wise differentiation and integration of power series.
Sequences and Series of Real Numbers: Sequence of real numbers, convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers, Cauchy sequences, subsequences, Bolzano-Weierstrass theorem. Series of real numbers, absolute convergence, tests of convergence for series of positive terms — comparison test, ratio test, root test; Leibniz test for convergence of alternating series.