## MATH 423 - INTRODUCTION TO REAL ANALYSIS I (Graduate Level, FALL 2022)

Last updated on 9/14/2022

### GENERAL INFORMATION

• Class Number: 1444
• Class meets: MW 12:45-2:00, Sears 325
• Instructor: Stanislaw J. Szarek (pronounced 'Shareck')
• Office: Yost 332
• Office hours: Starting the 3rd week of classes, Mondays 9:30-11:59 am (generally in-person in Yost 332, with remote option, see Canvas for the Zoom link), or by appointment, or by luck
• Phone: 216-368-2913
• E-mail: szarek at cwru.edu (the preferred mode of communication)

• Class Canvas site
• 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.
• Textbook: "Real Analysis" by G. B. Folland, second edition (1999, 978-0471317166).
Notes: (1) Here is a link to errata (list of misprints, mostly). (2) If you want to use an earlier edition, you may try AT YOUR OWN risk.
• Supplementary text: "Measure, Integration & Real Analysis" by S. Axler (legal free PDF from the author's website).

The course: This is the first course of the MATH 423-424 sequence. MATH 423 covers general theory of measure and integration. When you hear someone invoking integrals or probabilities, this class will help you understand what they are really talking about. The second course, MATH 424, covers elements of functional analysis and some of its applications. The sequence is required of most mathematics graduate students. It can also be useful to graduate students in other mathematical sciences (such as statistics and operation research) or in engineering. Finally, the course (or the sequence) can be taken by advanced undergraduates.

Prerequisites: This course assumes that you took an undergraduate analysis course or achieved an equivalent expertise by other means. See announcements in Canvas for details.

Grades: Your Final Grade in the course will be based on Attendance/Assignments/Various Forms of Class Participation (40%), Midterm Exam (20%) and Final Exam (40%). (Students with special needs should contact Division of Student Affairs. Please keep in mind that accommodations are not retroactive.)

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. Any violation of the policy will be reported to the Dean of Undergraduate Studies and the Office of Student Conduct & Community Standards.

### SYLLABUS & ASSIGNMENTS

• 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
• Solutions (and handouts etc.) will be posted on Canvas (under construction), as will announcements and such.