MATH 440 - Introductory Real Analysis

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Proof-oriented introduction to topics in mathematical analysis. Topics include: field axioms of real numbers, completeness axiom, set theory, relations and functions, infinite sets, countable sets, open and closed sets, closure, limit points, Bolzano-Weierstrass theorem, limits and partial limits of sequences, monotone sequences, Cauchy sequences, limits of functions, continuity, extreme value theorem, intermediate value theorem, uniform continuity, differentiation, chain rule, mean value theorem, L’Hopital’s rule, convergent series, tests for convergence of series, rearrangement of series, Riemann sums, Riemann integrability, Fundamental Theorem of Calculus, change of variables, sequences of functions, uniform convergence, and power series. Prereq: MATH 280.