Mathematics Department

MATH 424 - INTRODUCTION TO REAL ANALYSIS II
(Graduate Level, SPRING 2008)

GENERAL INFORMATION

• Course #: 86116
• Class meets: MW 12:30-1:45 in Yost 321B
  
• Instructor: Stanislaw J. Szarek (pronounced 'Shareck')
• Office: Yost 320
• Office hours: Currently M 10:30-11:30, T 2-3, by appointment or by luck
• Phone: 368-2913
• E-mail: szarek at cwru.edu (the preferred mode of communication)
• WWW Home Page: http://www.cwru.edu/artsci/math/szarek/
• Class WWW Page (this page): http://www.cwru.edu/artsci/math/szarek/MATH424/
• Catalog Course Description: Measures on locally compact spaces. Riesz representation theorem. Elements of functional analysis. Normed linear space.Hahn-Banach, Banach-Steinhaus, open mapping, closed graph theorems. Weak topologies. Banach-Alaoglu theorem. Function spaces. Stone-Weierstrass and Ascoli theorems. Basic Hilbert space theory. Application to Fourier series. Additional topics: Haar measure on locally compact groups. Prereq: MATH 423.
• Text: "Real Analysis" by Folland, second edition.
  Notes: (1) If you want to use an earlier edition, you may try AT YOUR OWN risk. (2) This is the same text as that used in MATH 423 last semester.

COURSE STRUCTURE & GRADES

The course: This is the second course of the MATH 423-424 sequence. MATH 423 covers general theory of measure and integration. The second course, MATH 424, covers elements of functional analysis and some its applications, as well as applications of topics covered in MATH 423. The sequence is required of most mathematics graduate students. It can also be useful to graduate students in other mathematical sciences such as statistics, operation research and systems engineering. Finally, the sequence can be taken by advanced undergraduates.

Exams & Grades: Your Final Grade in the course will be based on Attendance/Assignments/Various Forms of Class Participation (50%), Midterm Exam (20%; first week of March) and Final Exam (30%; 5/07/08, 8:30-11:30).
Students with special needs should contact Educational Services for Students ESS.

SYLLABUS & HOMEWORK

• We will cover approximately Chapters 5-7 from the textbook plus sections 4.6 and 4.7. Other sections of Chapter 4 provide a background in topology; they may be reviewed in class if and when needed, or assigned as a reading. We may venture into Chapter 8, time permitting.
• More detailed syllabus, including regularly updated assignments