## Math 6320, Introduction to Real Analysis 2

## Semester 2, 2018-19

**Course Lecturer: **
#### Dr. Judith Packer, Dept. of Mathematics

*Tel: (303) 492-6979*

Office: Math 227

Email: packer@euclid.colorado.edu

URL: http://math.colorado.edu/~packer

**Course Information:**

This course is meant to continue the study of analysis of real-valued functions of one or several variables,
with an emphasis on Lebesgue measure
and Lebesgue integration on the real line and **R^n**.
Topics to be covered include:

Functions of bounded variation on closed and bounded intervals in **R**, absolutely continuous functions, and
the Fundamental Theorem of Calculus expressed using the Lebesgue integral.
Locally compact Hausdorff spaces, the Stone-Weirstrass Theorem, the Arzela-Ascoli Theorem;
Elements of functional analysis, including normed
vector spaces, linear functionals, the Baire Category Theorem, Hilbert spaces;
**L^p** - spaces, definitions and examples; Minkowski's inequality, Holder's inequality, interpolation of $L^p$-spaces;
Radon measures: positive linear functionals on **C_C(X)** and the Riesz representation theorems,
regularity of measures, the dual of $C_0(X),$ products of Radon measures; Elements of Fourier analysis:
convolutions, the Fourier transform, summation of Fourier integrals and series
and appplications of Hilbert space theory, pointwise convergence of Fourier series, Fourier analysis of measures.

**Prerequisite:**

Math 6310, or instructor consent.

**Course Text:**

We will use as a primary text the book
"Real Analysis: Modern Techniques and their Applications", by G.B. Folland, covering most of Chapters 4 - 7, and part
of Chapter 8.

Folland has an errata page for this textbook at
http://www.math.washington.edu/~folland/Homepage/reals.pdf

**Assessment:**
- Homework Assignments (every two weeks or so): 30 %
- Midterm test 1 in class - Friday, Feb. 15, 2 p.m - 2:55 p.m. : 20 %
- Midterm test 2 take-home: given out Monday, April `1, 2:50 p.m., due Monday April 8, 2 p.m. : 20 %
- Final exam, Saturday, May 4 in class , 4:30 p.m. - 7 p.m. : 30 % .
- Click HERE for a detailed syllabus of the course, including all university
policies and procedures.

**Lecture Hours and Venue: **

MWF 2 p.m.-2:50 p.m. ECCR 139

**Office Hours: **

Mon. 4 p.m.=5 p.m., Wed., Fri. 3 p.m. - 4 p.m., and by appointment.

** Homework: **

- Assignment 1 , due Monday Jan. 28, 2019.
- Assignment 2 , due Monday Feb. 11, 2019.
- Assignment 3 , due Wednesday March 6,2019.
- Assignment 4 , due Friday March 22, 2019.
- Assignment 5 , due Wednesday, April 24, 2019.

**Some Important Names associated with Real Analysis :**

Back to the home page of Judith A. Packer

Last modified January 12, 2019.