Math 6320, Introduction to Real Analysis 2
Semester 2, 2018-19
Dr. Judith Packer, Dept. of Mathematics
Tel: (303) 492-6979
Office: Math 227
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.
Math 6310, or instructor consent.
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
Lecture Hours and Venue:
- 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.
MWF 2 p.m.-2:50 p.m. ECCR 139
Mon. 4 p.m.=5 p.m., Wed., Fri. 3 p.m. - 4 p.m., and by appointment.
Some Important Names associated with Real Analysis :
- 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.
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Last modified January 12, 2019.