Math 6710                    Real Analysis II                    Spring 2012

Instructor:  Dr. Jim Zhu
Office: 5516 EV, Tel: 387-4535, e-mail: zhu@wmich.edu
Web: http://homepages.wmich.edu/~zhu/
Office Hours: T.R.1:00-2:00pm, others by appointment
Class Hours:  T.R. 2:00-3:15 Sangren Hall 03209
Text:  Real Analysis by H. L. Royden and P. M. Fitzpatrick, 4th edition 

General:  This is the second part of an one year real analysis sequence. We will concentrate on general measure and integration theory and Baire category theory.

We will also discuss some elementary results in functional analysis and their applications. Students are responsible for all material in the text and all material presented in class. This includes any material not in the text and all material in the text that was not presented in class.

Study hint: The only way to learn mathematics is by doing it. This is particularly true in this course. The course will be problem solving oriented. I will highlight the main concepts, theorems and techniques and ask you to read the details and do exercises. Part of the exercises will be assigned as homeworks. You are encouraged to work in groups. I expect you to ask many questions and will spend a large portion of the class meeting time to discuss them with you. I expect your active participation in the discussion.

Homework and board work:   You can find the homework and board work assignment below along with a tentative schedule.

You will be assigned to groups, for the purpose of preparing homework and board works. Groups are encouraged to turn in just one version of the homework, provided they actually work together. Names of group members on the top sheet will get the same credit. Homework is due at the beginning of class on the due date. Group members should take turns to work on board work problems. Students who are responsible for the board work should come to the class a little early to put the board work on the board and then explain the board work to the class.

Exams:   Two exams will be given on February16 and March 22.  No make up exams will be given.

Final:  The final exam will be 12:30--2:30pm on Thursday, April 26.

Grading:  The final is 25%,  the exams count for 10% each, the board work counts for 5% and the remainder 50% is from homework. This gives a total of 100%. No partial credit will be given to incorrect answer and arguments. Grading scale is approximately as follows: 
                                      A (83-100%) BA(78-82.99%) B (71-77.99%) CB(63-70.99%)
                                    C(55-62.99%) DC(50-54.99%) D(43-49.99%) E(0-42.99%) 

Math 6710 Homework Assignments 
Section Date  Homework  Due Date   Boardwork
Review 1/10 Setting up groups 1/12    
7.3-7.4 1/12 23,25,32,33,36,39 1/17      
9.1-9.2 1/17 4,10,13,18 1/24 Chap 7-24,26,29,38,42[A-E]
9.3 1/19 28,32 1/24  Chap 9- 1,2,6,14,19[E-A]
9.4 1/24 38,41,46 1/31 Chap 9-25,29,36[A-C]
      9.5   1/26 52,59,62 1/31 Chap 9-37,39[D-E]
      9.6
1/31
 77,782/7 Chap 9-54[B],56[C]
10.1
2/2
 3,6,12 2/7Chap 9-74[A],75[D],76[E]
     10.2

   2/7

 20,21,22 2/14 Chap 10-1[A],4[B],7[C]
10.3 2/9 33,36, 39 2/14Chap 10-16[A],17[D],19[E]
Review 2/14       Chap 10-29[B],31[C],32[A]
Exam12/16            
17.1-17.2 2/21 3,5,6,15  2/28
17.3 2/23        Chap 17 1[A],11-14[B-E]
17.4-17.5 2/2818,19,23,28,343/13    
18.1-18.2 3/1 12,14,18,24 3/13 Chap 17 20[A],22[B], 26[C]
Spring Break 3/4-9            
18.3
3/13
33,41 3/20 Chap 18 1[A], 3[B],19[C],22[D]
18.4
3/15 
49,51,55 3/20

Chap 18 28[A], 39[B], 42[C]

R eview 3/20         Chap 18 50,52,53[A-E]
Exam 2
3/22
            
19.1
3/27
3,5        
19.2 3/29 6,7         Chap 19 1[A], 2[B]
19.3 4/3 12          
19.4 4/5 16(i)        
20.1
4/10
2,3,9      Chap 19 13[C] 

20.2
4/12
32,33     Chap 20 1[D],10[E]
20.3 4/17 35,38,44      Chap 20 15[A],
Review 4/19           Chap 20 36[B]
  
             
             
                      
Final Exam
4/26
Thursday       12:30-2:30pm