Real Analysis II : Math 624

Meeting : TuTh 9:30--10:45 LGRT 1234   

Instructor : Luc Rey-Bellet

 Office :  1423 J LGRT
 Phone :  545-6020
 E-Mail :  luc@math.umass.edu
 Office Hours :   Th 11:00--12:00, Fr 1:00-2:00,   or by appointment.

Text: The text book for the class is the two-volume set

• Real Analysis. Measure Theory, Integration & Hilbert Spaces, by E. M. Stein & R. Shakarchi. Princeton Lecture Notes in Analysis III, Princeton University Press 2005.
  
  
• Functional Analysis. Introduction to Further Topics in Analysis, by E. M. Stein & R. Shakarchi. Princeton Lecture Notes in Analysis IV, Princeton University Press 2011.
  
  

• 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.
  
  
• Real and Abstract Analysis, by E. Hewitt and K. Stromberg. Graduate Text in Mathematics. Springer.
  
  

• Analysis by its History, by E. Hairer and G. Wanner. Undergraduate Texts in Mathematics. Springer 2008.
  
  
• The Way of Analysis, by R.S. Strichartz, Jones & Bartlett Learning 2000.
  
  

Syllabus: This is the second part of a 2-semester introduction to real analysis (Math 623-624). The prerequisites for this class is Math 623 or equivalent. Among the topics covered in this class are

• 1) Fourier Analysis: Fourier Series and Fourier Transform.

• 2) Differentiation and functions of bounded variation

• 3) Banach spaces and L^p space theory.

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

Exams:

• Midterm:          
  
  
• Final:         Room:        
  

Homework :

Homework #1 (due on Tuesday February 4):   HWK #1 PDF file      

Homework #2 (due on Tuesday February 11):   HWK #2      

Homework #3 (due on Tuesday March 4 ): HWK #3        

Homework #4 (due on Tuesday March 25): HWK #4        

Homework #5 (due on Wednesday April 30 ): HWK #5  

Homework #6 (due on Wednesday April 30 ): HWK #6