# Folland Homework Solutions

__Math 240A Homework (Fall 01)__

Click on the highlighted link to retrieve the homework assignment. You should look try all of the problems assigned but **only** hand in those problems with a "*" on them.

- Homework #1 is due Friday September 28. Do Exercises 2.1 -- 2.13 from Chapter 2 of the lecture notes, but
**only**hand in problems 2.5*, 2.6*, 2.7*, 2.12* and 2.13*. - Homework #2 is due Friday October 5. Do the following exercises from Chapter 2 and Chapter 3 (Old Version) of the lecture notes.

Chapter 2: 2.14, 2.15, 2.16*, 2.17*

Chapter 3: 3.2*, 3.3, 3.4*, 3.5, 3.6, 3.7*, 3.9,~~3.10*, 3.11*, 3.12*,~~3.18*, 3.21*, 3.22* (Revised 10/1/01) - Homework #3 is due Friday October 12. Do the following exercises from Chapter 3 (Old Version) of the lecture notes.

Chapter 3: , 3.10*, 3.11*, 3.12*, 3.13, 3.14*, 3.15*, 3.16, 3.19, 3.20, 3.24*, 3.25*, 3.27*, 3.28*, 3.29 - Homework #4 is due Friday October 19. Do the following exercises from Chapter 3 (Revised version) and Chapter 4 of the lecture notes.

Chapter 3: 3.27*, 3.29, 3.35*, 3.36*, 3.37

Chapter 4: 4.1*, 4.2*, 4.3 ,4.4,~~4.5, 4.6*, 4.8, 4.9*~~(Note reduction in problems.) - Homework #5 is due Friday November 2. Do the following exercises from Chapter 4 (Revised version) and Chapter 5 of the lecture notes.

Chapter 4: 4.3, 4.4, 4.5*, 4.7*, 4.10* , 4.11, 4.15*

Chapter 5: 5.1, 5.2*, 5.3, 5.8* - Homework #6 is due Friday November 9. Do the following exercises from Chapter 5 of the lecture notes.

Chapter 5: 5.5*, 5.6*, 5.7*, 5.9*, 5.10, 5.13*, 5.16, 5.17*, 5.19, 5.20*, 5.21* (The formula in Folland is off by a minus sign. Please also notice that Exercise 5.7 had some errors, the hopefully correct version is here.) - Homework #7 is due
~~Monday November 19~~., Wednesday November 21. Do the following exercises from Chapter 6 of the lecture notes.

Chapter 6: 6.6, 6.7, 6.8*, 6.9*, 6.10*, 6.11*, 6.12*, 6.13, 6.16*,~~6.18, 6.19*~~

(6.18, 6.19* are now postponed to Homework #8.) - Homework #8 is due Friday November 30. Do the following exercises from Chapter 6 and Chapter 7.

Chapter 6: 6.18, 6.19*

Chapter 7: 7.3*, 7.4, 7.9*, 7.12*

Solutions to homework 8: hm8solutions

### Remarks on Homework

The homework is an **important** part of this class. The homework is your best chance to learn the material in this course. You **may** consult others on the problems, but in the end you are responsible for understanding the material. I suggest that you try all the problems on your own before consulting others. Even false starts on problems will help you learn.

Dan Curtis is the grader for this course. Here is what he will be looking for in your solutions.

- The solutions must be written clearly. This includes
**good handwriting**and**good English**. If I have to struggle to read what you have written, I will not grade the problem! - The solutions should be complete and clear. A good rule of thumb is: if you have some doubt about your solution it is probably
**wrong**or at best**incomplete**. - Results that you use in your proof from undergraduate analysis or from the text book or the notes should be stated clearly. Here is an example of what I am looking for:

… So we have shown that *f _{n}* converges to

*f*uniformly. Since each

*f*is continuous

_{n}*and the uniform limit of continuous functions is continuous,*we know that

*f*is continuous.

The reference to a theorem from undergraduate analysis is in Italics.

## MAT 550 (Real Analysis II), Spring 2015

### Instructor

### Contact

- malik.younsi@stonybrook.edu

### Lecture

- TuTh 10:00am-11:20am, Math Tower 4-130.

### Office hours

- Tuesdays 8:30 - 10:00, Thursdays 8:30 - 10:00, and by appointment. Math Tower 4-118.

### Special Announcements

- There will be a make up class on Friday April 17, 11:00-12:20 in 4-130.

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