SUNY Stony Brook

Office: 4-112 Mathematics Building

Phone: (631)-632-8274

Dept. Phone: (631)-632-8290

FAX: (631)-632-7631

Time and place: TuTh 9:50-11:10, Math 4-130

We will use the text `Real Analysis: modern techniques and their applications' by Gerald Foland, second edition.

This course is a continuation of MAT 544 in Fall 2011. I expect to cover Chapter 3, selected sections of Chapters 4 and 5 and most of Chapters 6,7,8 and 9. In time permits, I will try to cover some sections from chapters 10 and 11 and perhaps add some supplementary material on PDEs.

My office hours will be Tu-Th 11:10-12:00 in my office, 4-112 in the Math Building.

Homework problems will be asssigned from the text each week and will be handed in at class each Thursday.

Although it is not required, you may wish to consider writing up your solution in TeX, since eventually you will probably use this to write your thesis and papers. Here are a sample LaTex file and what the resulting output looks like . You can use the first file as a template to create your own TeX files. Numerous guides exist online that give the basic rules and commands.

The first lecture is Tuesday, Jan 24. The last class meeting is Thursday May 3. There is no class during spring recess: April 2-8. There will be a midterm exam on Thursday March 29 (date tentative; location in Math 4-130) and a final at 11:15am-1:45pm on Thursday, May 10 (regular room, Math 4-130). Homework, midterm and final will each count for one third of your grade. Lecture Schedule (this is tentative and only approximate; it will almost certainly change as we proceed).Link to Sample MIDTERM

Lecture 1, Tuesday, Jan 24

Overview of course

Lecture 2, Thursday, Jan 26

3.1 Signed Measures

Homework: 3,4,5,7 Due Thursday Feb 2

Lecture 3, Tuesday, Jan 31

3.2 Radon-Nikodym

Homework: 10,11,14,17 Due Thursday Feb 9

Lecture 4, Thursday, Feb 2

3.3 Complex measures

Lecture 5, Tuesday, Feb 7

3.4 Lebesgue Differentiation

Homework: 22,23,24,25 Due Thursday Feb 16

Lecture 6, Thursday Feb 9

3.5 Bounded variation

Homework: 30, 31, 37, 39, 40

Lecture 7, Tuesday, Feb 14

3.5 continued

Lecture 8, Thursday, Feb 16

Review of 4.7, 5.1, 5.2: Stone-Weierstrass,
normed vector spaces, Hahn-Banach

Homework:

Lecture 9, Tuesday, Feb 21

5.3 Baire Category; open mapping, closed graph, uniform
boundedness

Homework: 27,33,40,41,42, due March 8

Lecture 10, Thursday, Feb 23

6.1 L^p spaces

Homework: 5,7, 10,
12, 18, 19, Due March 8

Lecture 11, Tuesday, Feb 28

6.2 Dual Spaces 6.4 Weak L^p

Homework: 27,30,36,38,40

Lecture 12, Thursday, Mar 1

6.3 Some inequalities

Lecture 13, Tuesday, Mar 6

Class Cancelled

Lecture 14, Thursday, Mar 8

6.3 continued, 6.4 Weak L^p

Lecture 15, Tuesday, Mar 13

6.4 Interpolation

Homework: 37, 40, 42, 43, 45

Lecture 16, Thursday, Mar 15

6.4 continued
Introduction to Fourier Analysis

Homework:

Lecture 17, Tuesday, Mar 20

6.4 continued (short class today)

Homework:

Lecture 18, Thursday, Mar 22

8.1 Introduction to Fourier analysis

Homework:

Lecture 19, Tuesday, Mar 27

REVIEW

Homework:

Lecture 20, Thursday, Mar 29

MIDTERM

Homework:

April 2-9: SPRING BREAK

Lecture 21, Tuesday, Apr 10

8.2 Convolutions ,

Lecture 22, Thursday, Apr 12

8.2 continued

Lecture 23, Tuesday, Apr 17

8.3 Fourier series

Lecture 24, Thursday, Apr 19

8.3 Fourier transform

Last Homework: 8,9,10, 14,18, 25

Lecture 25, Tuesday, Apr 17

8.4

Homework:

Lecture 26, Thursday, Apr 19

8.5

Homework:

Lecture 27, Tuesday, Apr 24

9.1

Homework:

Lecture 28, Thursday, Apr 26

9.2

Homework:

Lecture 29, Tuesday, May 1

9.3

Homework:

Lecture 30, Thursday, May 3

Thursday, May 10, FINAL, 11:15-1:45, Room TBA

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