Summary: Principles of Analysis I:
Fall 2010, MWF 10:2011:10 in the ZACH 119D
Professor: Michael Anshelevich, 326 Milner, firstname.lastname@example.org, 8456679 (please
Office hours: MW 11:3012:30, T 2:003:00, or by appointment.
Textbook: Carothers, REAL ANALYSIS, Cambridge University Press, ISBN 0521497566.
Prerequisites: Math 409; junior or senior classification.
Learning Objectives: By the end of the course, students (1) should be comfortable writing proofs
(2) will learn fundamental theorems and counterexamples from Analysis on metric spaces, and (3)
will master and learn to apply fundamental approximation theorems for sequences of functions. For
future teachers, this knowledge will provide a valuable higher-level perspective for the more famil-
iar calculus and geometry results. For the students interested in learning more advanced mathe-
matics, this course provides essential background for Real Analysis, Topology, Harmonic Analysis,
Probability, and numerous other courses.
· Background and review.
Week 1. Calculus on the real line.
Week 2. Cardinality.