Real Analysis I : Math 623

Meeting : MWF 9:05   

Instructor : Luc Rey-Bellet

 Office :  1423 J LGRT
 Phone :  545-6020
 E-Mail :  luc@math.umass.edu
 Office Hours :   MW 2:00--3:30,   or by appointment.

Text: The text book for the class is

• Real Analysis. Measure Theory, Integration & Hilbert Spaces, by E. M. Stein & R. Shakarchi. Princeton Lecture Notes in Analysis III, Princeton University Press 2005.
  
  

• Real Analysis: Modern Techniques and their applications, by G.B. Folland. 2nd ed. Wiley 1999.
  
  
• Real Analysis, by H.L. Royden. 3rd ed. Collier Macmillan 1988
  
  
• Measure and Integral: An Introduction to Real Analysis, by R.L. Wheeden and A. Zygmund. M Dekker 1977.
  
  

• Analysis by its History, by E. Hairer and G. Wanner. Undergraduate Texts in Mathematics. Springer
  
  

Syllabus: This is the first part of a 2-semester introduction to real analysis (Math 623-624). The prerequisites for this class is a working knowledge of the basics of analysis taught in a class like M523, see for example Chapter 3 and 4 of Analysis by its History.

• 1) Measure theory: Lebesgue measure and Integrable functions

• 2) Integration theory: Lebesgue integral, convergence theorems and Fubini theorem

• 3) Differentiation and Integration. Functions of bounded variation.

• 4) Hilbert spaces. Examples and Applications

• 5) Abstract measure theory.

Grade: There will be a midterm and a final. Homework will be assigned regularly.

Exams:

• Midterm:         Room:        
  
  
• Final:         Room:        
  

Homework :

Homework #1 (due on 9/22):   HW#1 PDF file and a few things you should know about limsup and liminf SUP#1 PDF file      

Homework #2 (due on 10/4 ):   HW#2 PDF file      

Homework #3 (due on 10/18):   HW#3 PDF file      

Homework #4 (due on 10/31 ):   HW#4 PDF file      

Homework #5 (due on 11/17):   HW#5 PDF file      

Homework #6 (due on 12/4):   HW#6 PDF file      

Homework #7 (due on 12/13):   HW#7 PDF file