21-455 Intermediate Real Analysis I

12 units, Carnegie Mellon University

This course provides a rigorous and proofbased treatment of the general theory of functions on metric spaces. The course serves as a more advanced version of 21355 Principles of Real Analysis and is primarily intended for students who have taken 21269. Topics include Metric spaces Completeness, density, separability, compactness, connectedness. Baire theorem and applications. Contraction maps fixed points, applications, inverse, and implicit function theorems. Spaces of functions uniform and pointwise convergence, StoneWeierstrass theorem, ArzelaAscoli theorem. Three 50 minute lectures, one 50 minute recitation

Prerequisites: 21-268 or 21-269

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