Real Analysis II : Math 624

Meeting : TuTh 11:15   

Instructor : Luc Rey-Bellet

 Office :  1423 J LGRT
 Phone :  545-6020
 E-Mail :  luc@math.umass.edu
 Office Hours :   TuTh 2:45--3:45,   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.
  
  
• 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
  
  

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) Basics of Fourier Analysis: Fourier Series and Fourier Transform.

• 2) Abstract measure theory. Integration, Fubini theorem, Absolute continuity and the Radon-Nykodym theorem.

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

• 4) Examples of measures: Hausdorff measures and fractals.

• 5) Examples of measures: Spaces of continuous functions and their duals.
  

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

Exams:

• Midterm:         Room:        
  
  
• Final:         Room:        
  

Homework :

Homework #1 (due on 2/13 ):   HWK #1 PDF file      

Homework #2 (due on 2/27 ):   HWK #2 PDF file      

Homework #3 (due on 3/13):   HWK #3 PDF file      

Homework #4 (due on 3/27 ):   HWK #4 PDF file      

Homework #5 (due on 4/19):   HWK #5 PDF file      

Homework #6 (due on 5/3 ):   HWK #6 PDF file      

Homework #7 (due on 5/15):   HWK #7 PDF file