Winter 2008: Math 245B
Real Analysis

Instructor: Inwon C.Kim, Office: MS 7620E

 Lecture: MWF 9-9:50 am,

 Quiz section: T 9-9:50 am,

 Office hours: M-Th-F 1-2pm, MS 7620E

 TA: Nobert Pozar 

 TA Office hours: W 1-2pm, Th 11-12am.

 Textbook: 1. Folland,  Real Analysis: Modern Techniques and Their Applications,   Wiley-Interscience Publication,
                   ISBN 0-471-31716-0
                     2. Stein and Shakarchi,  Real Analysis: Measure Theory, Integration, and Hilbert spaces,  Princeton University Press,
                   ISBN 0-691-11386-6.

 Materials to be covered: General measure theory (Chapter 6, Stein), basic functional analysis and L^p spaces (Folland), Fourier transform.




 Prerequisite: Math 121, 131A, 131B, 245A (or equivalent).


 Grading : (Homework 70%, Final 30%) or (Homework 50%, final 50%).
 You must present at least one homework problem at the blackboard in quiz section.

 Homework : There will be weekly homework assignments assigned, each set consisting of 5-6 problems.

Homework 1 (Due Jan.18th) Stein-Shakarchi p193: 21,22,23,25,28,30 

Homework 2 (Due Jan.25th) Stein-Shakarchi p193: 29,33,35. p 202: Problems 7,9. p 312: Exercise 3.

Homework 3 (Due Feb.4th) Stein-Shakarchi p312: 4,9,13,14,15. 

Homework 4 (Due Feb.15th) Stein-Shakarchi p312: 8,10,11,16.  Additional problem

Folland p 118: 4,5,6. p 123: 15,28.

Homework 5 (Due Feb.22nd) Folland p 123: 22,23,24 p 127 30,32,34,36

Homework 6 (Due Feb. 29th) Folland p 130: 38, 43. p 134: 47, 52, 54. p 138:58, 60. 

Homework 7 (Due Mar. 7th) Folland p 138:64. p 142: 67,69. p 156; 9,12. p 160 19,25.
Additional Problem: Show that a bounded sequence in a separable, reflexive Banach space contains a weakly convergent subsequence.

Homework 8 (Due Mar. 14th) Folland p164: 34,38,42. p170: 46,48,49. 
Additional Problem: Show that Hilbert spaces are reflexive.