 
Summary: Principles of Analysis I:
Math 446
Fall 2010, MWF 10:2011:10 in the ZACH 119D
Professor: Michael Anshelevich, 326 Milner, manshel@math.tamu.edu, 8456679 (please
use email).
Webpage: www.math.tamu.edu/manshel/m446/m446.html.
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 higherlevel 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.
Course outline:
· Background and review.
Week 1. Calculus on the real line.
Week 2. Cardinality.
