MATH 4331/6312 - Fall 2017
Introduction to Real Analysis
Course Info. View syllabus.
Office hours: PGH 604, Tu 11:30am-12:30pm, We 1-2pm.
Week 1. The topology of
Rn. Cauchy sequences and completeness. Open and closed
Homework Set 1 (Solutions), due
date deferred to September 7.
Week 2. Closure of a set. Compactness.
Homework Set 2 (Solutions), due
Week 3. Heine Borel property and other
properties of compact sets. Limits and continuity of functions.
Homework Set 3 (Solutions), due
Week 4. Discontinuous
functions. Uniform continuity.
Homework Set 4 (Solutions), due
Week 5. Connectedness and the
Intermediate Value Theorem in higher dimensions.
Summary of the material in a handout.
Exam 1, October 5, in class. When you feel prepared,
try a practice
Week 6. Differentiablity and the
Mean Value Theorem.
Homework Set 5 (Solutions), due October
Week 7. The Riemann integral and its
Homework Set 6 (Solutions), due October
Week 8. The Fundamental Theorem of Calculus,
see handout. Normed vector spaces.
Homework Set 7 (Solutions), due November
Week 9. Inner product spaces. Cauchy-Schwarz
inequality. Relation between inner product and norm.
Exam 2, November 9, in class. Covers material
from the Intermediate Value Theorem (and its
higher-dimensional generalization) to normed vector spaces.
When you feel prepared,
try a practice
Week 10. Hölder and Minkowski
inequalities for functions and sequences.
Homework Set 8, due Tuesday, November
Week 11. Limits of sequences of
functions. Uniform convergence. Completeness of C(K).
Homework Set 9, due November