Mathematics Department

MATH 423 - INTRODUCTION TO REAL ANALYSIS I
(Graduate Level, FALL 2011)

GENERAL INFORMATION

• Class Number: 1398
• Class meets: MWF 11:30-12:20 in Yost 321B
  
• Instructor: Stanislaw J. Szarek (pronounced 'Shareck')
• Office: Yost 320
• Office hours: Currently M 3-4, W 10-11, by appointment or by luck
• Phone: 216-368-2913
• 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/MATH423/
• Catalog Course Description: General theory of measure and integration. Measures and outer measures. Lebesgue measure on-N-space. Integration. Convergence theorems. Product measures and Fubini's theorem. Signed measures. Hahn-Jordan decomposition, Radon-Nikodym theorem, and Lebesgue decomposition. Lp spaces. Lebesgue differentiation theorem in N-space. Prereq: MATH 322.
• Text: "Real Analysis" by Folland, second edition (1999, 978-0471317166).
  Note: If you want to use an earlier edition, you may try AT YOUR OWN risk.

COURSE STRUCTURE & GRADES

The course: This is the first 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 course (or the sequence) can be taken by advanced undergraduates.

Grades: Your Final Grade in the course will be based on Attendance/Assignments/Various Forms of Class Participation (30%), Midterm Exam (20%) and Final Exam (50%). (Students with special needs should contact Educational Services for Students.)

Integrity: It is OK (and indeed encouraged) to discuss homework assignments with fellow students. However, any submitted work must be your own. See CWRU academic integrity policy.

SYLLABUS & HOMEWORK

• We will cover approximately Chapters 1-3 from the textbook. It is assumed that the students will familiarize themselves (at least roughly) with the "Prologue" on their own; but the more "sophisticated" points from there may be redone in class if and when needed.
• More detailed syllabus, including regularly updated assignments