Instructor: Rodolfo H. Torres
Office: 546 Snow
Telephone: 864-7310
e-mail: torres"AT"math.ku.edu
URL: http:// www.math.ku.edu/~torres
Office hours: TBA

Grader: Wei-Da Chen
Office: 557 Snow
Telephone: 864-7106
e-mail: w116c57"AT"ku.edu

Course description

This is a course on the fundamentals of real analysis from a modern perspective. The subjects to be covered include measure and integration, basic elements of functional analysis, L^p spaces, and, if time permits, rudiments of Fourier analysis.

Text: Real Analysis, Modern Techniques and Their Applications, Second Edition, by G. Folland, Wiley-Interscience. The text will be used as guide and additional material may be added.

Prerequisites: MATH 766

Tentative topics to be covered:

The material to be covered as well as its length and depth will depend, in part, on the students' background.

• The students should be familiar with basic facts about set theory, cardinality, the real numbers, differentiation, Riemann integration, sequences and series of functions, modes of convergence, metric spaces, compact sets, and continuous maps. Some of this material is summarized in Chapter 0 and Chapter 4 of the text and the students should review it on their own. For additional material review the Math 766 book.

• The students should also review basic results about compact spaces and the Stone-Weierstrass and Ascoli-Arzelà theorems. (Chapter 4 of the text.). This material is sometimes covered in 766.

• Measure theory, integration, and Lebesgue integral. (Chapter 1, 2, 3.)

• Elements of functional analysis. Linear functionals. (Chapter 5.)

• L^p theory. Duality and basic inequalities. (Chapter 6.)

• Elements of Fourier analysis. (Chapter 8.) (if time permits)

Grading: The grade will be computed based on the Homework and Final assignments. As usual in this graduate courses, 90% correct completion of all assigned work will guarantee and A, 80% a B, 70% a C, 60% a D. If further curving is needed the percentages to reach each grade may be lowered but they will never be increased.

Pursuant to the University of Kansas' Policy on Commercial Note-Taking Ventures, commercial note-taking is not permitted in Math 810. Lecture notes and course materials may be taken for personal use, for the purpose of mastering the course material, and may not be sold to any person or entity in any form. Any student engaged in or contributing to the commercial exchange of notes or course materials will be subject to discipline, including academic misconduct charges, in accordance with University policy. Please note: note-taking provided by a student volunteer for a student with a disability, as a reasonable accommodation under the ADA, is not the same as commercial note-taking and is not covered under this policy.